This vignette was made for version 2.1.0-18 of CHNOSZ, a package for the R software environment. For more information on R, see “An Introduction to R” and the contributed documentation for R.
CHNOSZ has been developed since 2006 as a tool for thermodynamic calculations in geochemistry and geochemical biology. The package provides functions and a thermodynamic database that can be used to calculate the stoichiometric and energetic properties of reactions involving minerals and inorganic and/or organic aqueous species. These functions also enable calculations of chemical affinities and metastable equilibrium distributions of proteins. A major feature of the package is the production of diagrams to visualize the effects of changing temperature, pressure, and activities of basis species on the potential for reactions among various species.
After starting R, install CHNOSZ by selecting the “Install packages from CRAN” or similar menu item in the R GUI or by using the following command:
Then load the CHNOSZ package to make its data and functions available in your R session:
CHNOSZ is now ready to go with the default thermodynamic database and
an empty system definition. After running some calculations, you may
want to “start over” with the default values. To clear the system
settings and restore the default thermodynamic database, use reset()
.
## reset: resetting "thermo" object
## OBIGT: loading default database with 2018 aqueous, 3570 total species
Note: Throughout this document, syntax highlighting is applied to the
input of the code chunks. Double hash marks (##
)
precede the output, where black text denotes results
and blue text is used for messages.
After CHNOSZ is installed, type help.start()
to browse the R help
documents, then choose “Packages” followed by “CHNOSZ”. That shows an
index of the manual (help pages) for each function; many of the
help pages include examples. There are also links to the demos
(longer examples) and vignettes (more in-depth documentation;
this document is a vignette).
Suggestions for accessing the documentation are indicated here with
blue text. For example, read ?`CHNOSZ-package`
to get an
overview of the package and a list of features. Placeholder (you should
not see this)
CHNOSZ is made up of a set of functions and supporting datasets. The major components of the package are shown in the figure below, which is an updated version of the diagram in Dick (2008). Rectangles and ellipses represent functions and datasets; bold text indicates primary functions.
Many functions in CHNOSZ have no side effects. That is, the function
only returns a result; to use the result elsewhere, it can be assigned
to a variable with <-
. In this document, the names of
these functions are shown in green text
(not applicable to the code chunks). Placeholder (you should not see
this) Major functions without side effects in CHNOSZ are:
info()
: search for
species in the thermodynamic database;subcrt()
: calculate
the thermodynamic properties of species and reactions;affinity()
: calculate
the affinities of formation reactions using given chemical
activities;equilibrate()
:
calculate the equilibrium chemical activities of the species of
interest;diagram()
: plot the
results.Some functions in CHNOSZ do have side effects: they modify the
thermo
data object in the current R session. In this
document, the names of these functions are shown in red text (but not in the code chunks). Major
functions with side effects are:
basis()
: set the basis
species and their chemical activities;species()
: set the
species of interest and their (non-equilibrium) chemical
activities;reset()
: reset the
database, restoring all settings to their default values.The following pseudocode shows a common sequence of commands. In
actual usage, the ...
are replaced by arguments that define
the chemical species and variables:
info()
functioninfo()
provides an
interface to the OBIGT thermodynamic database that is packaged with
CHNOSZ. Suppose you are interested in the thermodynamic properties of
aqueous methane. Because the database is assembled with aqueous species
first, they take precedence over other states. Searching by chemical
formula alone gives the first matching species, in this case aqueous
methane:
## info.character: found CH4(aq); also available in gas, liq
## [1] 917
The number that is returned is the species index in the database. A second argument can be used to specify a physical state with lower precedence:
## [1] 2772
While some species are identified only by chemical formula, others have distinct names (in English) listed in the database. For CH4 and inorganic substances that are represented by both gaseous and aqueous forms, the name is applied only to the gas. However, the names of organic substances other than methane are applied to aqueous species, which have precedence, and those in other states. The following commands get the species indices for some common gases:
## info.character: found methane(gas); also available in liq
## [1] 2772
## [1] 2762
## [1] 2754
A special case is sulfur; the name refers to both the native mineral, which has precedence, and the gas. These two phases can be identifed with the formulas S2 and S, respectively.
## info.character: found S(cr) [sulfur] with 2 polymorphic transitions
## [1] 2199
## [1] 2764
Taking the species number of aqueous methane returned by info()
, use the function again
to retrieve the set of standard molal thermodynamic properties and
equations of state parameters:
## name abbrv formula state ref1 ref2 date model E_units G H S
## 917 CH4 <NA> CH4 aq PS01 <NA> 2000-10-04 HKF cal -8140 -20930 21
## Cp V a1 a2 a3 a4 c1 c2 omega Z
## 917 60.23 36 1.769 -1530 -67.88 114700 40.87 64500 -40000 0
Liquid water is species number 1; it has NA entries in the database because dedicated functions are used to compute its properties:
## name abbrv formula state ref1 ref2 date model E_units G H S Cp V
## 1 water <NA> H2O liq HGK84 JOH92 2006-10-25 H2O cal NA NA NA NA NA
## a b c d e f lambda T
## 1 NA NA NA NA NA NA NA NA
Calling info()
with a
string that does not exactly match the name of any species invokes a
fuzzy search of the database:
## info.approx: 'acid' is ambiguous; has approximate matches to 87 species:
## [1] "a-aminobutyric acid" "acetamide" "formic acid" "acetic acid" "propanoic acid" ## [6] "n-butanoic acid" "n-pentanoic acid" "n-hexanoic acid" "n-heptanoic acid" "n-octanoic acid" ## [11] "n-nonanoic acid" "n-decanoic acid" "n-undecanoic acid" "n-dodecanoic acid" "n-benzoic acid" ## [16] "o-toluic acid" "m-toluic acid" "p-toluic acid" "oxalic acid" "malonic acid" ## [21] "succinic acid" "glutaric acid" "adipic acid" "pimelic acid" "suberic acid" ## [26] "azelaic acid" "sebacic acid" "glycolic acid" "lactic acid" "2-hydroxybutanoic acid" ## [31] "2-hydroxypentanoic acid" "2-hydroxyhexanoic acid" "2-hydroxyheptanoic acid" "2-hydroxyoctanoic acid" "2-hydroxynonanoic acid" ## [36] "2-hydroxydecanoic acid" "uracil" "citric acid" "aspartic acid" "glutamic acid" ## [41] "cis-aconitic acid" "isocitric acid" "a-ketoglutaric acid" "fumaric acid" "malic acid" ## [46] "oxaloacetic acid" "pyruvic acid" "cyclohexane carboxylic acid" "N-acetylmuramic acid" "diaminopimelic acid" ## [51] "glutamic-acid+1" "metacinnabar" "acide fulvique" "acide humique" "aspartic acid" ## [56] "glutamic acid" "2-iodobenzoic acid" "3-iodobenzoic acid" "4-iodobenzoic acid" "uracil" ## [61] "phosphoric acid" "citric acid" "acetamide" "nicotinamide,red" "nicotinamide,ox" ## [66] "2-iodobenzoic acid" "3-iodobenzoic acid" "4-iodobenzoic acid" "acetic acid" "propanoic acid" ## [71] "n-butanoic acid" "n-pentanoic acid" "n-hexanoic acid" "n-heptanoic acid" "n-octanoic acid" ## [76] "n-nonanoic acid" "n-decanoic acid" "n-undecanoic acid" "n-dodecanoic acid" "n-tridecanoic acid" ## [81] "n-tetradecanoic acid" "n-pentadecanoic acid" "n-hexadecanoic acid" "n-heptadecanoic acid" "n-octadecanoic acid" ## [86] "n-nonadecanoic acid" "n-eicosanoic acid"
## [1] NA
The message includes e.g. “uracil” and “metacinnabar” because their names have some similarity to the search term. Since “ribose” is the name of a species in the database, to find species with similar names, add an extra character to the search:
## info.approx: ' ribose' is ambiguous; has approximate matches to 8 species:
## [1] "ribose" "deoxyribose" "ribose-5-phosphate" ## [4] "ribose-5-phosphate-1" "ribose-5-phosphate-2" "ribose" ## [7] "deoxyribose" "ribose-5-phosphate"
## [1] NA
The messages may be useful for browsing the database, but owing to
their ambiguous results, these fuzzy searches return an NA
value for the species index.
ZC()
Continuing with the example of aqueous methane, let’s look at its chemical formula:
## [1] "CH4"
We can use makeup()
to
count the elements in the formula, followed by as.chemical.formula()
to rewrite
the formula on one line:
## C H
## 1 4
## [1] "CH4"
For organic species, a calculation of the average oxidation state of carbon (ZC) is possible given the species index, chemical formula, or elemental count:
## [1] -4
## [1] -4
## [1] -4
To calculate the standard molal properties of species and reactions,
use subcrt()
. The name of
this function is derived from the SUPCRT package (Johnson et al., 1992),
which is also the source of the Fortran subroutine used to calculate the
thermodynamic properties of H2O.
If no reaction coefficients are given, subcrt()
calculates the standard
molal properties of individual species:
## subcrt: 1 species at 15 values of T (ºC) and P (bar) (wet) [energy units: J]
## $species
## name formula state ispecies model
## 1 water H2O liq 1 water.SUPCRT92
##
## $out
## $out$water
## T P rho logK G H S V Cp
## 1 0.01 1.00000 0.999829 45.0352 -235515 -287724 63.3139 18.0183 76.1722
## 2 25.00 1.00000 0.997061 41.5524 -237181 -285837 69.9242 18.0683 75.3605
## 3 50.00 1.00000 0.988030 38.6327 -239006 -283954 75.9912 18.2335 75.3314
## 4 75.00 1.00000 0.974864 36.1543 -240977 -282069 81.6083 18.4797 75.4862
## 5 100.00 1.01322 0.958393 34.0269 -243084 -280176 86.8580 18.7973 75.9728
## 6 125.00 2.32014 0.939073 32.1831 -245315 -278267 91.8050 19.1840 76.7067
## 7 150.00 4.75717 0.917058 30.5717 -247665 -276335 96.4997 19.6446 77.6819
## 8 175.00 8.91805 0.892343 29.1531 -250125 -274373 100.9851 20.1887 79.0063
## 9 200.00 15.53650 0.864743 27.8959 -252691 -272370 105.3036 20.8330 80.8718
## 10 225.00 25.47860 0.833873 26.7753 -255355 -270311 109.5002 21.6042 83.5561
## 11 250.00 39.73649 0.799072 25.7711 -258112 -268173 113.6247 22.5452 87.4971
## 12 275.00 59.43125 0.759236 24.8670 -260959 -265925 117.7377 23.7281 93.5177
## 13 300.00 85.83784 0.712408 24.0494 -263890 -263512 121.9248 25.2878 103.5098
## 14 325.00 120.45757 0.654577 23.3072 -266901 -260836 126.3367 27.5219 123.2082
## 15 350.00 165.21129 0.574688 22.6310 -269989 -257632 131.3656 31.3478 182.4162
That uses the default temperature and pressure settings, i.e. equally spaced temperature intervals from 0 to 350 °C at Psat, i.e. 1 bar below 100 °C, or the pressure of liquid-vapor saturation (i.e. boiling) at higher temperatures. The columns in the output are temperature, pressure, density of water, logarithm of the equilibrium constant (only meaningful for reactions; see below), standard molal Gibbs energy and enthalpy of formation from the elements, standard molal entropy, volume, and heat capacity. Placeholder (you should not see this)
A custom temperature-pressure grid can be specified. Here, we calculate the properties of H2O on a T, P grid in the supercritical region, with conditions grouped by pressure:
## subcrt: 1 species at 9 values of T (ºC) and P (bar) (wet) [energy units: J]
## T P rho logK G H S V Cp
## 1 400 200 0.1005447 21.5271 -277426 -236979 163.338 179.1760 114.7691
## 2 500 200 0.0677109 19.8868 -294360 -229366 173.961 266.0607 58.8996
## 3 600 200 0.0550386 18.6703 -312097 -224011 180.484 327.3197 50.0435
## 4 400 400 0.5236661 21.4118 -275941 -252941 137.419 34.4021 157.0325
## 5 500 400 0.1779739 19.6639 -291060 -235360 161.939 101.2238 104.4640
## 6 600 400 0.1238075 18.4123 -307785 -227449 171.608 145.5098 64.8105
## 7 400 600 0.6124511 21.3631 -275313 -254523 134.136 29.4149 108.2861
## 8 500 600 0.3384430 19.5659 -289610 -241392 152.263 53.2296 135.7227
## 9 600 600 0.2071976 18.2784 -305546 -230936 165.050 86.9469 81.0704
The additional operations ($out$water
) are used to
extract a specific part of the results; this can be used with e.g. R’s
write.table()
or plot()
for further
processing:
sres <- subcrt("water", T=seq(0,1000,100), P=c(NA, seq(1,500,1)), grid="T")
water <- sres$out$water
plot(water$P, water$rho, type = "l")
The default units of temperature, pressure, and energy in the input
and output of subcrt()
are
°C, bar, and Joules. The functions T.units()
, P.units()
, and E.units()
can be used to change
the units used by subcrt()
and some other functions in CHNOSZ. What is the Gibbs energy in J/mol
(the default) and cal/mol of aqueous methane at 298.15 K and 0.1
MPa?
## changed temperature units to K
## changed pressure units to MPa
## info.character: found CH4(aq); also available in gas, liq
## subcrt: 1 species at 298.15 K and 0.1 MPa (wet) [energy units: J]
## [1] -34057.8
## changed energy units to cal
## info.character: found CH4(aq); also available in gas, liq
## subcrt: 1 species at 298.15 K and 0.1 MPa (wet) [energy units: cal]
## [1] -8140
The parameters for each species in the OBIGT database have the units
indicated by the E_units
column there, which is independent
of the setting of E.units()
.
Unlike subcrt()
, info()
always displays the
database values in the units given in the database. A separate function,
convert()
, can be used to
convert values to selected units. The following code shows that the
database parameters for CH4(aq) are in calories, then
converts the standard Gibbs energy from cal/mol to J/mol.
## name abbrv formula state ref1 ref2 date model E_units G H S
## 917 CH4 <NA> CH4 aq PS01 <NA> 2000-10-04 HKF cal -8140 -20930 21
## Cp V a1 a2 a3 a4 c1 c2 omega Z
## 917 60.23 36 1.769 -1530 -67.88 114700 40.87 64500 -40000 0
## [1] -34057.8
Note that converting the database value to J/mol gives the same
result as running subcrt("CH4", T = 25)
with the default
E.units()
setting of J.
Use reset()
to restore
the units and all other settings for CHNOSZ to their defaults:
## reset: resetting "thermo" object
## OBIGT: loading default database with 2018 aqueous, 3570 total species
To calculate the thermodynamic properties of reactions, give the
names of species, the physical states (optional), and reaction
coefficients as the arguments to subcrt()
. Here we calculate
properties for the dissolution of CO2. This doesn’t
correspond to the solubility of CO2; see the solubility section in this
vignette and demo(solubility)
for examples
of solubility calculations.
## subcrt: 2 species at 6 values of T (ºC) and P (bar) (wet) [energy units: J]
## $reaction
## coeff name formula state ispecies model
## 2754 -1 carbon dioxide CO2 gas 2754 CGL
## 692 1 CO2 CO2 aq 692 HKF
##
## $out
## T P rho logK G H S V
## 1 0.01 1.00000 0.999829 -1.10873 5798.19 -24718.86 -111.7182 23.6978
## 2 50.00 1.00000 0.988030 -1.71865 10632.66 -16517.28 -84.0162 36.9843
## 3 100.00 1.01322 0.958393 -2.00354 14313.00 -9506.03 -63.8321 41.5584
## 4 150.00 4.75717 0.917058 -2.10770 17074.67 -2494.13 -46.2453 44.5642
## 5 200.00 15.53650 0.864743 -2.09919 19015.19 5141.36 -29.3221 47.9553
## 6 250.00 39.73649 0.799072 -2.01184 20149.75 14698.81 -10.4193 54.3882
## Cp
## 1 205.626
## 2 144.875
## 3 138.259
## 4 143.687
## 5 164.790
## 6 233.124
In order to make a plot like Figure 18 of Manning et al. (2013), let’s run more calculations and store the results. In addition to the reaction definition, we specify a greater number of temperature points than the default:
T <- seq(0, 350, 10)
CO2 <- subcrt(c("CO2", "CO2"), c("gas", "aq"), c(-1, 1), T = T)$out$logK
CO <- subcrt(c("CO", "CO"), c("gas", "aq"), c(-1, 1), T = T)$out$logK
CH4 <- subcrt(c("CH4", "CH4"), c("gas", "aq"), c(-1, 1), T = T)$out$logK
logK <- data.frame(T, CO2, CO, CH4)
Now we can make the plot, using R’s matplot()
. Here,
axis.label()
and expr.species()
are used to
create formatted axis labels and chemical formulas:
A balanced chemical reaction conserves mass. subcrt()
won’t stop you from
running an unbalanced reaction, but it will give you a warning:
## info.character: found CO2(aq); also available in gas
## info.character: found CH4(aq); also available in gas, liq
## subcrt: 2 species at 15 values of T (ºC) and P (bar) (wet) [energy units: J]
## subcrt: reaction is not balanced; it is missing this composition:
## H O ## -4 2
## Warning in subcrt(c("CO2", "CH4"), c(-1, 1)): reaction among CO2,CH4 was ## unbalanced, missing H-4O2
In other words, to balance the reaction, we should add 4 H to the left and 2 O to the right. That could be done manually be redefining the reaction with the appropriate species. There is another option: balancing the reaction automatically using basis species.
Basis species are a minimal number of chemical species that linearly combine to give the composition of any species in the system. The basis species are similar to thermodynamic components, but can include charged species. Basis species are used in CHNOSZ to automatically balance reactions; they are also required for making chemical activity diagrams.
Let’s start with an example that doesn’t work:
## Error in put.basis(ispecies, logact): singular stoichiometric matrix
That set of species has a singular (non-invertible) stoichiometric matrix. An error would also result from either an underdetermined or overdetermined system. A valid set of basis species has an invertible stoichiometric matrix and the same number of species as elements:
## C H O ispecies logact state
## CO2 1 0 2 692 0 aq
## H2 0 2 0 62 0 aq
## H2O 0 2 1 1 0 liq
The composition of any species made up of C, H, and O can be represented by a single linear combination of these basis species.
Methanogenic metabolism in reducing environments may proceed by acetoclastic or hydrogenotrophic processes. To consider reactions involving a charged species (acetate), let’s define a basis with H+:
## C H O Z ispecies logact state
## CO2 1 0 2 0 692 0 aq
## H2 0 2 0 0 62 0 aq
## H2O 0 2 1 0 1 0 liq
## H+ 0 1 0 1 3 0 aq
By identifying species other than the basis species, the reactions will be automatically balanced. This produces the balanced reaction for acetoclastic methanogenesis:
## coeff name formula state ispecies model
## 1107 -1 acetate C2H3O2- aq 1107 HKF
## 917 1 CH4 CH4 aq 917 HKF
## 692 1 CO2 CO2 aq 692 HKF
## 3 -1 H+ H+ aq 3 HKF
We can similarly consider reactions for hydrogenotrophic methanogenesis as well as acetate oxidation (without production of methane):
acetate_oxidation <- subcrt("acetate", -1)
hydrogenotrophic <- subcrt("CH4", 1)
acetoclastic <- subcrt(c("acetate", "CH4"), c(-1, 1))
Use describe.reaction()
to write the reactions on a plot:
plot(0, 0, type = "n", axes = FALSE, ann=FALSE, xlim=c(0, 5), ylim=c(5.2, -0.2))
text(0, 0, "acetoclastic methanogenesis", adj = 0)
text(5, 1, describe.reaction(acetoclastic$reaction), adj = 1)
text(0, 2, "acetate oxidation", adj = 0)
text(5, 3, describe.reaction(acetate_oxidation$reaction), adj = 1)
text(0, 4, "hydrogenotrophic methanogenesis", adj = 0)
text(5, 5, describe.reaction(hydrogenotrophic$reaction), adj = 1)
Usually, subcrt()
returns only standard state thermodynamic properties. Placeholder (you
should not see this) Thermodynamic models often consider a non-standard
state (i.e. non-unit activity). The activities of basis species can be
modified with basis()
, and
those of the other species using the logact
argument in
subcrt()
.
Let us calculate the chemical affinity of acetoclastic
methanogenesis. Placeholder (you should not see this) We change the
states of CO2 and H2 in the basis from
aq
(aqueous) to gas
, and set the logarithm of
fugacity of gaseous H2 and the pH, using values from Mayumi et al. (2013).
The activity of acetate and fugacity of methane, as well as temperature
and pressure, are set in the call to subcrt()
:
## T P rho logK G H S V Cp logQ
## 1 55 50 0.987821 13.5983 -85429.6 18706.9 317.685 -40.1339 39.2144 10.52
## A
## 1 19339.3
The new A
column shows the affinity; the other columns
are unaffected and still show the standard-state properties. Let’s
repeat the calculation for hydrogenotrophic methanogenesis.
## T P rho logK G H S V Cp logQ A
## 1 55 50 0.987821 18.828 -118284 -251807 -407.195 36.4746 33.4702 15.5 20907.6
Under the specified conditions, the affinities of hydrogenotrophic and acetoclastic methanogenesis are somewhat greater than and less than 20 kJ, respectively. This result matches Figure 4b in Mayumi et al. (2013) at unit fugacity of CO2.
We can go even further and reproduce their plot. Placeholder (you should not see this) To make the code neater, we write a function that can run any of the reactions:
rxnfun <- function(coeffs) {
subcrt(c("acetate", "CH4"), coeffs,
c("aq", "gas"), logact = c(-3.4, -0.18), T = 55, P = 50)$out
}
Now we’re ready to calculate and plot the affinities. Here, we use
R’s lapply()
to list the results at two values of logarithm
of fugacity of CO2. We insert an empty reaction to get a line
at zero affinity. R’s do.call()
and rbind()
are used to turn the list into a data frame that can be plotted with R’s
matplot()
. There, we plot the negative affinities, equal to
Gibbs energy, as shown in the plot of Mayumi et al. (2013).
Adat <- lapply(c(-3, 3), function(logfCO2) {
basis("CO2", logfCO2)
data.frame(logfCO2,
rxnfun(c(0, 0))$A,
rxnfun(c(-1, 0))$A,
rxnfun(c(-1, 1))$A,
rxnfun(c(0, 1))$A
)
})
Adat <- do.call(rbind, Adat)
matplot(Adat[, 1], -Adat[, -1]/1000, type = "l", lty = 1, lwd = 2,
xlab = axis.label("CO2"), ylab = axis.label("DG", prefix = "k"))
legend("topleft", c("acetate oxidation", "acetoclastic methanogenesis",
"hydrogenotrophic methanogenesis"), lty = 1, col = 2:4)
Let’s not forget to clear the system settings, which were modified by
basis()
, before running
other calculations:
affinity()
affinity()
offers
calculations of chemical affinity of formation reactions over a
configurable range of T, P, and activities of basis
species.
By formation reaction is meant the stoichiometric
requirements for formation of one mole of any species from the basis
species. The species()
function is used to set these formed species. Let’s consider
the stoichiometry of some aqueous sulfur-bearing species. Here we use
basis()
with a keyword to
load a preset basis definition. To use Eh as a variable, the electron
(e-) should be in the basis, so we use the keyword
(basis("CHNOSe")
).
Placeholder (you should not see this) Placeholder (you should not see
this)
## CO2 H2O NH3 H2S e- H+ ispecies logact state name
## 1 0 0 0 1 0 0 65 -3 aq H2S
## 2 0 0 0 1 0 -1 22 -3 aq HS-
## 3 0 4 0 1 -8 -9 25 -3 aq HSO4-
## 4 0 4 0 1 -8 -10 24 -3 aq SO4-2
Aqueous species are assigned default activities of 10-3
(logact
is -3). Now, we can use affinity()
to calculate the
affinities of the formation reactions of each of the species. R’s
unlist()
is used here to turn the list of values of
affinity into a numeric object that can be printed in a couple of lines
(note that the names correspond to ispecies
above):
## affinity: temperature is 25 ºC
## affinity: pressure is Psat
## subcrt: 10 species at 25 ºC and 1 bar (wet) [energy units: J]
## 65 22 25 24
## -4.00000 -3.98774 76.30184 81.32273
The values returned by affinity()
are dimensionless,
i.e. A/(2.303RT). Although subcrt()
can also calculate
affinities (in units of cal/mol or J/mol), the main advantage of affinity()
is that it can
perform calculations on an arbitrary grid of T, P, or
activities of basis species. This is the foundation for making many
types of diagrams that are useful in geochemistry.
Given the values of affinity, the diagram()
function identifies
the species that has the maximum affinity at each grid point. The result
is equivalent to a “predominance diagram” (Dick, 2019), where the fields represent the
predominant aqueous species and the boundaries are equal-activity lines.
If both aqueous species and minerals are present, it is common practice
to assign a constant activity to all aqueous species and unit activity
(i.e. log activity = 0) for minerals. More sophisticated diagrams can be
made by showing the solubility contours of a metal on the diagram; see
demo(contour)
for an
example.
Let’s use diagram()
to
make a simple Eh-pH diagram for aqueous species in the system S-O-H.
After running the basis()
and species()
commands
above, we can calculate the affinities on an Eh-pH grid. With the
default settings in diagram()
, areas beyond the
stability limits of water are colored gray. This can be changed by
setting the limit.water
argument to FALSE (to not show the
stability region of water) or TRUE (to plot the main diagram only in the
stable region of water). The names of species that can be parsed as
chemical formulas are formatted with subscripts and superscripts; if
this is not desired, set format.names = FALSE
.
Other arguments in diagram()
can be used to control
the line type (lty
), width (lwd
), and color
(col
), field colors (fill
), and species labels
(name
). Additional arguments are passed to R’s plotting
functions; here, we use las
to change the orientation of
axes labels. Another function, water.lines()
, can be used to
draw lines at the water stability limits:
diagram(a, fill = "terrain", lwd = 2, lty = 3,
names = c("hydrogen sulfide", "bisulfide", "bisulfate", "sulfate"),
las = 0)
water.lines(a, col = 6, lwd = 2)
See the demos in the package for other examples of Eh-pH diagrams. In
particular, demo(Pourbaix)
shows how to
plot the concentrations of metals as equisolubility (or isosolubility)
lines on Eh-pH diagrams (Pourbaix, 1974).
Mineral stability diagrams often depict activity ratios, e.g. log
(aCa+2/aH+2),
on one or both axes. The variables used for potential calculations in
CHNOSZ include only a single chemical activity, e.g. log
aCa+2. However, you can set pH = 0 to
generate diagrams that are geometrically equivalent to those calculated
using activity ratios, and use ratlab()
to make the axes labels
for the ratios. Moreover, diagram()
has a “saturation”
option that can be used to draw saturation limits for minerals that do
not contain the conserved basis species. See demo(saturation)
for an
example that uses activity ratios on the axes and plots saturation
limits for calcite, magnesite, dolomite, and brucite on a diagram for
the H2O–CO2–CaO–MgO–SiO2 system. That
demo can be used as a template to produce a wide range of diagrams
similar to those in Bowers et al. (1984).
Most of the diagrams in this vignette are made by giving the names of
all the species. However, it can be tedious to find all the species by
manually searching the OBIGT database. The retrieve()
function can be used
to identify the available species that contain particular chemical
elements. For example, to get Mn-bearing aqueous species and minerals
including the single element, oxides and oxyhydroxides, use this:
## MnO4- Mn+2 Mn+3 MnO4-2 MnOH+ MnO HMnO2- MnO2-2
## 423 432 509 510 602 603 604 605
## MnO MnO2 Mn2O3 Mn3O4 Mn Mn(OH)2
## 2250 2251 2252 2253 2254 2255
Below, these commands are used to identify the species in an Eh-pH diagram for the Mn-O-H system at 100 °C. This diagram includes Mn oxides (pyrolusite, bixbyite, hausmannite), Mn(OH)2, and aqueous Mn species.
# Set decimal logarithm of activity of aqueous species,
# temperature and plot resolution
logact <- -4
T <- 100
res <- 400
# Start with the aqueous species
basis(c("Mn+2", "H2O", "H+", "e-"))
iaq <- retrieve("Mn", c("O", "H"), "aq")
species(iaq, logact)
aaq <- affinity(pH = c(4, 16, res), Eh = c(-1.5, 1.5, res), T = T)
# Show names for only the metastable species here
names <- names(iaq)
names[!names(iaq) %in% c("MnOH+", "MnO", "HMnO2-")] <- ""
diagram(aaq, lty = 2, col = "#4169E188", names = names, col.names = 4)
# Overlay mineral stability fields
icr <- retrieve("Mn", c("O", "H"), "cr")
species(icr, add = TRUE)
# Supply the previous result from affinity() to use
# argument recall (for plotted variables and T)
acr <- affinity(aaq)
diagram(acr, add = TRUE, bold = acr$species$state=="cr", limit.water = FALSE)
# Add legend
legend <- c(
bquote(log * italic(a)["Mn(aq)"] == .(logact)),
bquote(italic(T) == .(T) ~ degree*C)
)
legend("topright", legend = as.expression(legend), bty = "n")
This introductory vignette shows examples for diagrams with a single metal. Other functions are available to make diagrams for multiple metals; see the vignette Diagrams with multiple metals for more information.
If sulfur is an element in the basis species, then we should consider that its speciation is sensitive to Eh and pH, as shown in a previous diagram. Mosaic diagrams account for speciation of the basis species and are useful for visualizing the stabilities of many types of minerals including oxides, sulfides, and carbonates. These diagrams are made by constructing individual diagrams for the possible basis species. The individual diagrams are then combined, each one contributing to the final diagram only in the range of stability of the corresponding basis species.
Let’s use mosaic()
to
make a diagram for aqueous species and minerals in the
Cu-S-Cl-H2O system. To know what aqueous copper chloride
complexes are available in the database, we can use a fuzzy search:
## info.approx: ' CuCl' is ambiguous; has approximate matches to 7 species:
## [1] "CuCl3-2" "CuCl+" "CuCl2" "CuCl3-" "CuCl4-2" "CuCl" "CuCl2-"
Next we define the basis, and set the activities of the
H2S and Cl- basis species. These represent the
total activity of S and Cl in the system, which are distributed among
the minerals and aqueous species. Aqueous copper chloride complexes and
four minerals are added. Be sure to include add = TRUE
in
the second call to species()
; otherwise, the minerals
would simply replace the previously added aqueous species.
basis(c("Cu", "H2S", "Cl-", "H2O", "H+", "e-"))
basis("H2S", -6)
basis("Cl-", -0.7)
species(c("CuCl", "CuCl2-", "CuCl3-2", "CuCl+", "CuCl2", "CuCl3-", "CuCl4-2"))
species(c("chalcocite", "tenorite", "cuprite", "copper"), add = TRUE)
Note that chalcocite (Cu2S) undergoes polymorphic
transitions. To get the temperatures of the polymorphic transitions from
thermo()$OBIGT
(in Kelvin, regardless of the T.units()
), we can use info()
. We see that at 200 °C
(473.15 K) the second phase is stable; this one is automatially used by
CHNOSZ for this diagram.
## [1] 376 717 1403
We use mosaic()
to
generate and combine diagrams for each candidate basis species
(H2S, HS-, HSO4-, or
SO4-2) as a function of Eh and pH. The key
argument is bases
, which identifies the candidate basis
species, starting with the one in the current basis. The other
arguments, like those of affinity()
, specify the ranges
of the variables; res
indicates the grid resolution to use
for each variable (the default is 256). The first call to diagram()
plots the species of
interest; the second adds the predominance fields of the basis species.
We also use water.lines()
to draw dashed blue lines at the water stability limits:
T <- 200
res <- 200
bases <- c("H2S", "HS-", "HSO4-", "SO4-2")
m1 <- mosaic(bases, pH = c(0, 12, res), Eh=c(-1.2, 0.75, res), T=T)
diagram(m1$A.species, lwd = 2)
diagram(m1$A.bases, add = TRUE, col = 4, col.names = 4, lty = 3,
italic = TRUE)
water.lines(m1$A.species, col = "blue1")
The diagrams are combined according to the relative abundances of the
different possible basis species listed in bases
along with
a term for the Gibbs energy of mixing (see ?mosaic
). The smooth transitions
between basis species can result in curved field boundaries, in this
case around the chalcocite field. If we added the argument
blend = FALSE
, the diagrams would instead be assembled
using the single predominant basis species at any point on the Eh-pH
grid, and all of the line segments would be straight.
The reactions used to make this diagram are balanced on Cu, so that
no Cu appears in reactions between any two other species (minerals or
aqueous species). If diagram()
is run with
balance = 1
, then the reactions are balanced on formula
units. That is, one mole of the mineral formulas appears on each side of
the reaction, with the possibility of Cu appearing as an additional
species to conserve the elements. This may be problematic, as Cu would
be be present in some reactions in Eh-pH space where it is not a stable
phase. However, it is common in low-temperature aqueous geochemical
calculations to “turn off” particular redox reactions that are not
thought to attain equilibrium, so decoupling a species from equilibrium
may be justified in some circumstances. Changing the balance to 1
results in the loss of the tenorite stability field and extension of
chalcocite stability to lower pH, as shown in Figure 5a of Caporuscio et al. (2017).
Above, we used evenly-spaced grids of chemical activities of basis
species; the ranges of variables were given by two or three values
(minimum, maximum, and optionally resolution). affinity()
can also perform
calculations along a transect, i.e. a particular path along one or more
variables. A transect is calculated when there are four or more values
assigned to the variable(s). Let’s use this feature to calculate
affinities (negative Gibbs energies) of methanogenesis and biosynthetic
reactions in a hydrothermal system.
Some results of mixing calculations for seawater and vent fluid from
the Rainbow hydrothermal field, calculated using EQ3/6 by Shock and Canovas (2010), are included in a data file in
CHNOSZ. Reading the file with R’s read.csv()
, we set
check.names = FALSE
to preserve the NH4+
column name (which is not a syntactically valid variable name):
file <- system.file("extdata/cpetc/SC10_Rainbow.csv", package = "CHNOSZ")
rb <- read.csv(file, check.names = FALSE)
We take a selection of the species from Shock and Canovas (2010) with activities equal to 10-6; aqueous CH4 is assigned an activity of 10-3. We will write the synthesis reactions of organic species in terms of these basis species: Placeholder (you should not see this)
basis(c("CO2", "H2", "NH4+", "H2O", "H2S", "H+"))
species("CH4", -3)
species(c("adenine", "cytosine", "aspartic acid", "deoxyribose",
"CH4", "leucine", "tryptophan", "n-nonanoic acid"), -6)
Now we can calculate affinities along the transect of changing
temperature and activities of five basis species. Each variable is given
as a named argument; NH4+
must be quoted. Placeholder (you
should not see this) Placeholder (you should not see this) Using R’s
lapply()
to run convert()
for each species, we
first convert the affinity from dimensionless values
(A/(2.303RT)) to J/mol. A second call to convert()
is used to obtain
energies in cal/mol, and these are finally converted to kcal/mol.
a <- affinity(T = rb$T, CO2 = rb$CO2, H2 = rb$H2,
`NH4+` = rb$`NH4+`, H2S = rb$H2S, pH = rb$pH)
T <- convert(a$vals[[1]], "K")
a$values <- lapply(a$values, convert, "G", T)
a$values <- lapply(a$values, convert, "cal")
a$values <- lapply(a$values, `*`, -0.001)
Finally, we use diagram()
to plot the results.
Although only temperature is shown on the x axis, pH and the
activities of CO2, H2, NH4+,
and H2S are also varied according to the data in
rb
. By default, diagram()
attempts to scale the
affinities by dividing by the reaction coefficients of a shared basis
species (in this case, CO2). To override that behavior, we
set balance = 1
to plot the affinities of the formation
reactions as written (per mole of the product species).
diagram(a, balance = 1, ylim = c(-100, 100), ylab = quote(italic(A)*", kcal/mol"),
col = rainbow(8), lwd = 2, bg = "slategray3")
abline(h = 0, lty = 2, lwd = 2)
When making line plots, diagram()
automatically places
the labels near the lines. The additional arguments adj
and
dy
can be used to fine-tune the positions of the labels
(they are used in a couple of examples below). If labeling of the lines
is not desired, add e.g. legend.x = "topright"
to make a
legend instead, or names = FALSE
to prevent any plotting of
the names.
There is one other feature of affinity()
that can be mentioned
here. Can we go the other direction: calculate the activities of basis
species from the activities of the species of interest? This question
relates to the concept of chemical activity buffers. In CHNOSZ there are
two ways to perform buffer calculations:
thermo()$buffer
)
to the basis species:mod.buffer()
to
change or add buffers in thermo()$buffer
;demo(buffer)
uses it for
mineral buffers (solid lines).type
argument of diagram()
to solve for the
activity of the indicated basis species:demo(buffer)
uses it for
aqueous organic species as buffers (dotted and dashed lines).As an example of method 1, let’s look at the pyrite-pyrrhotite-magnetite (PPM) buffer at 300 °C. Placeholder (you should not see this) Without the buffer, the basis species have default activities of zero. Under these conditions, the minerals are not in equilibrium, as shown by their different affinities of formation:
basis(c("FeS2", "H2S", "O2", "H2O"))
species(c("pyrite", "magnetite"))
species("pyrrhotite", "cr2", add = TRUE)
Placeholder (you should not see this)
## 2160 2058 2162
## 0.0000 -50.6944 -20.6134
We use mod.buffer()
to
choose the cr2
phase of pyrrhotite, which is stable at this
temperature (see above for how to get
this information for minerals with polymorphic transitions). Then, we
set up H2S and O2 to be buffered by PPM, and
inspect their buffered activities (logarithmic values):
## mod.buffer: changed state and/or logact of pyrrhotite in PPM buffer
## H2S O2 FeS2
## -2.3669 -36.4930 0.0000
We have found logaH2S and logfO2 that are compatible with the coexistence of the three minerals. Under these conditions, the affinities of formation reactions of the minerals in the buffer are all equal to zero:
## 2160 2058 2162
## 0 0 0
Another example, based on Figure 6 of Schulte
and Shock (1995), is given in demo(buffer)
. Here, values of
logfH2 buffered by minerals or set by
equilibrium with given activities of aqueous species are calculated
using the two methods:
Above we considered this question: for equal activities of species, what are the affinities of their formation reactions from basis species? Turning the question around, we would like to know: for equal affinities of formation reactions, what are the activities of species? The first question is about non-equilibrium conditions; the second is about equilibrium.
Before presenting some examples, it is helpful to know about the limitations of the functions. CHNOSZ does not take account of all possible reactions in the speciation of a system. Instead, it assumes that the total activity of species in the system is set by the activity of one basis species. Placeholder (you should not see this) This balanced, or conserved, basis species must be present (with a positive or negative coefficient) in the formation reactions of all species considered.
For a given total activity of the balanced basis species, activities of the species can be found such that the affinities of the formation reactions are all equal. This is an example of metastable equilibrium. With additional constraints, the affinities of the formation reactions are not only equal to each other, but equal to zero. This is total equilibrium. An example of total equilibrium was given above for the PPM buffer. In contrast, models for systems of organic and biomolecules often involve metastable equilibrium constraints.
The equilibrate()
function in CHNOSZ automatically chooses between two methods for
calculating equilibrium. The method based on the Boltzmann equation is
fast, but is applicable only to systems where the coefficient on the
balanced basis species in each of the formation reactions is one. The
reaction-matrix method is slower, but can be applied to systems were the
balanced basis species has reaction coefficients other than one.
The distribution of aqueous carbonate species as a function of pH (a
type of Bjerrum plot) is a classic example of an equilibrium
calculation. We can begin by plotting the affinities of formation, for
equal activities of the species, calculated at 25 °C and 150 °C. Here,
CO2 is in the basis, so it has zero affinity, which is
greater than the affinities of HCO3- and
CO3-2 at low pH. To avoid overplotting the lines,
we offset the species labels in the y direction using the
dy
argument:
par(mfrow = c(3, 1))
basis("CHNOS+")
species(c("CO2", "HCO3-", "CO3-2"))
a25 <- affinity(pH = c(4, 13))
a150 <- affinity(pH = c(4, 13), T = 150)
diagram(a25, dy = 0.4)
diagram(a150, add = TRUE, names = FALSE, col = "red")
Now we use equilibrate()
to calculate the
activities of species. Our balancing constraint is that the total
activity of C is 10-3. This shows a hypothetical metastable
equilibrium; we know that for true equilibrium the total activity of C
is affected by pH.
e25 <- equilibrate(a25, loga.balance = -3)
e150 <- equilibrate(a150, loga.balance = -3)
diagram(e25, ylim = c(-6, 0), dy = 0.15)
diagram(e150, add = TRUE, names = FALSE, col = "red")
To display the species distribution, or degree of formation, add
alpha = TRUE
to the argument list:
It is important to remember that equilibrate()
calculates an
equilibrium distribution of species for a given total activity of the
conserved basis species. For instance, the previous diagram shows the
relative abundances of CO2, HCO3-, and
CO3-2 as a function of pH assuming that the
possible reactions between species are all balanced on 1 C and the total
activity of C is constant. Although this assumption of metastable
equilibrium is useful for making many types of diagrams for aqueous
species, the aqueous solutions would not be in equilibrium with other
phases, including gases or solids such as carbon dioxide or calcite.
Moving away from metastable equilibrium to complete equilibrium actually involves a simplification of the computations. Instead of finding the activities of aqueous species where the affinities of formation reactions are equal to each other, equilibrium occurs when the affinities of all formation reactions are equal to zero. However, the solubility calculation comes with a different constraint: all reactions between the pure substance that is being dissolved and any of the possible formed aqueous species must be able to be balanced on the same element (usually the main metal in the system). This balancing constraint can be expressed as a conserved basis species, i.e. one that is present in non-zero quantity in the formation reactions of all species considered.
The solubility()
function provides a way to compute activities of aqueous species in
equilibrium with one or more minerals or gases. The following example
for corundum (Al2O3) is based on Figure 15 of
Manning (2013).
To more closely reproduce the diagram, we use superseded thermodynamic
data that are kept in the SLOP98
optional data file.
The basis species are defined with the main element (Al) first. The
mineral we want to dissolve, corundum, is loaded as a formed species.
The aqueous species that can form by dissolution of corundum are listed
in the iaq
argument of solubility()
. The next arguments
describe the variables for the affinity()
calculations. Note
that setting IS
to 0 has no effect on the calculations, but
signals diagram()
to label
the y axis with logarithm of molality instead of logarithm of
activity. An additional argument, in.terms.of
, is used to
compute the total molality of Al in solution, that is, twice the number
of moles of Al2O3 that are dissolved.
diagram()
is used
twice, first to plot the total molality of Al, then the concentrations
of the individual species, using adj
and dy
to
adjust the positions of labels in the x- and
y-directions. At the end of the calculation, we use reset()
to restore the default
thermodynamic database.
add.OBIGT("SLOP98")
basis(c("Al+3", "H2O", "H+", "O2"))
species("corundum")
iaq <- c("Al+3", "AlO2-", "AlOH+2", "AlO+", "HAlO2")
s <- solubility(iaq, pH = c(0, 10), IS = 0, in.terms.of = "Al+3")
diagram(s, type = "loga.balance", ylim = c(-10, 0), lwd = 4, col = "green3")
diagram(s, add = TRUE, adj = c(0, 1, 2.1, -0.2, -1.5), dy = c(0, 0, 4, -0.3, 0.1))
legend("topright", c("25 °C", "1 bar"), text.font = 2, bty = "n")
Other examples of using solubility()
are available in
CHNOSZ. See demo(solubility)
for
calculations of the solubility of CO2(gas) and calcite
as a function of pH and temperature. The calculation considers the
stoichiometric dissolution of calcite, in which CaCO3
dissociates to form equal quantities of Ca+2 and
CO3-2 ions. Adding in activity coefficients, an
example in ?solubility
uses
the find.IS
option to find the final ionic strength for
dissolving calcite into pure water. demo(gold)
shows calculations
of the solubility of gold as a function of pH and T as well as
oxygen fugacity set by diferent mineral buffers, and considers ionic
strength effects on activity coefficients, so that activities are
transformed to molalities (see
below).
For calculating activity coefficients of charged species, nonideal()
uses the extended
Debye–Hückel equation as parameterized by Helgeson et al. (1981)
for NaCl-dominated solutions to high pressure and temperature, or
optionally using parameters described in Chapter 3 of Alberty (2003), which
are applicable to relatively low-temperature biochemical reactions. The
activity coefficients are calculated as a function of ionic strength
(I), temperature, and charge of each species, without any other
species-specific parameters. Using the default Helgeson
method, the extended term parameter (“B-dot”) is derived from data of
Helgeson (1969)
and Helgeson et al. (1981), and extrapolations of Manning et al. (2013).
Following the main workflow of CHNOSZ, nonideal()
normally does not
need to be used directly. Intead, invoke the calculations by setting the
IS
argument in subcrt()
or affinity()
. There are a few
things to remember when using activity coefficients:
H+ is assumed to behave ideally, so its activity
coefficient is 1 for any ionic strength. You can calculate activity
coefficients of H+ by running
thermo("opt$ideal.H" = FALSE)
.
Using subcrt()
with
IS
not equal to zero, calculated values of G
are the adjusted Gibbs energy at specified ionic
strength [denoted by ΔG°(I); Alberty (1996)].
Using subcrt()
with
IS
not equal to zero, values in the logact
argument stand for log molality of aqueous species in
affinity calculations.
Using affinity()
with IS
not equal to zero, the following values stand for
log molality of aqueous species:
logact
set by basis()
;logact
set by species()
.Using equilibrate()
on the output of affinity calculated with IS
not equal to
zero, the following values stand for log molality of
aqueous species:
loga.balance
used by equilibrate()
(i.e., logarithm
of total molality of the balancing basis species);loga.equil
returned by equilibrate()
.In other words, the activation of activity coefficients effects a
transformation from activity to molality in the main workflow. A simple
but comprehensive series of calculations demonstrating these
tranformations is in inst/tinytest/test-logmolality.R
.
Because it is not possible to dynamically change the names of
arguments in the functions, the user should be aware of the
transformations mentioned above. However, the labels on diagrams
can be automatically adjusted; accordingly, activities of
aqueous species are relabeled as molalities by diagram()
when IS
is used in the calculation of affinity()
.
For the following calculations, we change the nonideality method to
Alberty
; this is a simpler formulation with parameters that
are suitable for biochemical species at relatively low temperatures:
## nonideal: setting nonideal option to use Alberty equation
Let’s take a look at calculated activity coefficients at two temperatures and their effect on the standard Gibbs energies of formation (ΔG°f) of species with different charge:
## subcrt: 3 species at 2 values of T (ºC) and P (bar) (wet) [energy units: J]
## nonideal: calculations for MgC10H12N5O13P3-2, MgC10H13N5O13P3- (Alberty equation)
## nonideal: calculations for MgC10H14N5O13P3 (Setchenow equation)
## $`MgATP-2`
## T P G loggam IS
## 1 25 1.00000 -3236780 0.000000 0.00
## 2 100 1.01322 -3265305 -0.662587 0.25
##
## $`MgHATP-`
## T P G loggam IS
## 1 25 1.00000 -3267679 0.000000 0.00
## 2 100 1.01322 -3303769 -0.165647 0.25
##
## $MgH2ATP
## T P G loggam IS
## 1 25 1.00000 -3289461 0.00000000 0.00
## 2 100 1.01322 -3326343 -0.00195159 0.25
The logarithms of the activity coefficients (loggam
) are
more negative for the higher-charged species, as well as at higher
temperature, and have a stabilizing effect. That is, the adjusted Gibbs
energies at I > 0 are less than the standard Gibbs energies
at I = 0.
We can use these calculations to make some speciation plots, similar to Figures 1.2–1.5 in Alberty (2003). These figures show the distribution of differently charged species of adenosine triphosphate (ATP) as a function of pH, and the average number of H+ and Mg+2 bound to ATP in solution as a function of pH or pMg (-logaMg+2).
Use info()
to see what
ATP species are available. The sources of high-temperature thermodynamic
data for these species are two papers by LaRowe and Helgeson (2006 a; 2006 b).
## info.approx: ' ATP' is ambiguous; has approximate matches to 14 species:
## [1] "ATP-4" "HATP-3" "H2ATP-2" "H3ATP-" "H4ATP" "dATP-4" ## [7] "dHATP-3" "dH2ATP-2" "dH3ATP-" "dH4ATP" "MgATP-2" "MgHATP-" ## [13] "MgH2ATP" "Mg2ATP"
The plots for this system in Alberty’s book were made for I = 0.25 M and T = 25 °C. As a demonstration of CHNOSZ’s capabilities, we can assign a temperature of 100 °C.
Use the following commands to set the basis species, add the variously protonated ATP species, calculate the affinities of the formation reactions, equilibrate the system, and make a degree of formation (α) or mole fraction diagram. This is similar to Figure 1.3 of Alberty (2003), but is calculated for I = 0 M and T = 100 °C: Placeholder (you should not see this)
basis("MgCHNOPS+")
species(c("ATP-4", "HATP-3", "H2ATP-2", "H3ATP-", "H4ATP"))
a <- affinity(pH = c(3, 9), T = T)
e <- equilibrate(a)
d <- diagram(e, alpha = TRUE, tplot = FALSE)
Note that we have saved the numeric results of diagram()
, i.e. the degrees of
formation of the species (α). With that, we can calculate and plot the
average number of protons bound per ATP molecule. To do so, we use R’s
rbind()
and do.call()
to turn
alpha
into a matrix, then multiply by the number of protons
bound to each species, and sum the columns to get the total
(i.e. average proton number, NH+):
alphas <- do.call(rbind, d$plotvals)
nH <- alphas * 0:4
Hlab <- substitute(italic(N)[H^`+`])
plot(a$vals[[1]], colSums(nH), type = "l", xlab = "pH", ylab=Hlab, lty=2, col=2)
Adding the IS
argument to affinity()
, we can now plot
NH+ at the given ionic strength. Here we
set plot.it = FALSE
in diagram()
because we use the
computed α to make our own plot. This is similar to Figure 1.3 of
Alberty (2003), but at higher temperature:
a <- affinity(pH = c(3, 9), IS = 0.25, T = T)
e <- equilibrate(a)
d <- diagram(e, alpha = TRUE, plot.it = FALSE)
alphas <- do.call(rbind, d$plotvals)
nH <- alphas * 0:4
lines(a$vals[[1]], colSums(nH))
Next, we add the Mg+2-complexed ATP species:
Here is a function to calculate and plot NH+ for a given pMg:
Hplot <- function(pMg, IS = 0.25) {
basis("Mg+2", -pMg)
a <- affinity(pH = c(3, 9), IS = IS, T = T)
e <- equilibrate(a)
d <- diagram(e, alpha = TRUE, plot.it = FALSE)
alphas <- do.call(rbind, d$plotvals)
NH <- alphas * c(0:4, 0, 1, 2, 0)
lines(a$vals[[1]], colSums(NH), lty = 7 - pMg, col = 7 - pMg)
}
With that function in hand, we plot the lines corresponding to pMg = 2 to 6. This is similar to Figure 1.4 of Alberty (2003):
The next function calculates and plots the average number of
Mg+2 bound to ATP (NMg+2) for
a given pH. Here we multiply alpha
by the number of
Mg+2 in each species, and negate
logaMg+2 (the variable used in affinity()
) to get pMg:
Mgplot <- function(pH, IS = 0.25) {
basis("pH", pH)
a <- affinity(`Mg+2` = c(-2, -7), IS = IS, T = T)
e <- equilibrate(a)
d <- diagram(e, alpha = TRUE, plot.it = FALSE)
alphas <- do.call(rbind, d$plotvals)
NMg <- alphas * species()$`Mg+`
lines(-a$vals[[1]], colSums(NMg), lty = 10 - pH, col = 10 - pH)
}
Using that function, we plot the lines corresponding to pH = 3 to 9. This is similar to Figure 1.5 of Alberty (2003):
Mglab <- substitute(italic(N)[Mg^`+2`])
plot(c(2, 7), c(0, 1.2), type = "n", xlab = "pMg", ylab = Mglab)
lapply(3:9, Mgplot)
We have calculated the distribution of ATP species and average
binding number of H+ and Mg+2 for given pH, pMg,
ionic strength, and temperature. Accounting for the distribution of
chemical species lends itself to thermodynamic models for reactions
between reactants that have multiple ionized and complexed states. In
contrast, Alberty (2003) and others propose models for biochemical
reactions where the ionized and complexed species are combined into a
single representation. Those models invoke Legendre-transformed
thermodynamic properties, such as transformed Gibbs energies that are
tabulated for specified pH, pMg, and ionic strength. Although the
conceptual pathways are different, the two approaches lead to equivalent
results concerning the energetics of the overall reactions and the
conditions for equilibrium (Sabatini et al., 2012). The example here
shows how the required calculations can be performed at the species
level using conventional standard Gibbs energies for species referenced
to infinite dilution (zero ionic strength). The effects of ionic
strength are modeled “on the fly” in CHNOSZ by setting the
IS
argument in subcrt()
or affinity()
to invoke the
nonideality model on top of the standard Gibbs energies of species.
Now that we’re finished, we can reset the nonideality method to the default. (This really isn’t needed here, because there aren’t any nonideality calculations below):
## nonideal: setting nonideal option to use Bdot equation
Proteins in CHNOSZ are handled a little bit differently from other species. Amino acid group additivity is used to obtain the thermodynamic properties of proteins. Therefore, CHNOSZ has a data file with amino acid compositions of selected proteins, as well as functions for reading and downloading amino acid sequence data.
When proteins in CHNOSZ are identified by name, they include an
underscore, such as in LYSC_CHICK
(chicken lysozyme C). Use
pinfo()
to search for one
or more proteins by name; multiple proteins from the same organism can
be specified using the organism
argument. The name search
returns the rownumbers of thermo()$protein
(i.e. iprotein
, the protein indices). Supply those protein
indices to pinfo()
to get
the amino acid compositions:
## protein organism ref abbrv chains Ala Cys Asp Glu Phe Gly His Ile
## 6 LYSC CHICK UniProt P00698 1 12 8 7 2 3 12 1 6
## 441 SHH HUMAN UniProt Q15465.N 1 14 3 10 14 5 16 6 7
## 442 OLIG2 HUMAN UniProt Q13516 1 51 5 10 10 5 35 18 7
## Lys Leu Met Asn Pro Gln Arg Ser Thr Val Trp Tyr
## 6 6 8 2 14 2 3 11 10 7 6 6 3
## 441 15 11 3 8 7 3 13 12 8 9 3 7
## 442 14 29 11 4 31 5 13 50 11 10 1 3
The length and chemical formula of one or more proteins are returned
by protein.length()
and
protein.formula()
. We can
calculate the formula of the protein, and the per-residue formula, and
show that both have the same average oxidation state of carbon:
Placeholder (you should not see this)
pl <- protein.length("LYSC_CHICK")
pf <- protein.formula("LYSC_CHICK")
list(length = pl, protein = pf, residue = pf / pl,
ZC_protein = ZC(pf), ZC_residue = ZC(pf / pl))
## $length
## [1] 129
##
## $protein
## C H N O S
## LYSC_CHICK 613 959 193 185 10
##
## $residue
## C H N O S
## LYSC_CHICK 4.75194 7.43411 1.49612 1.43411 0.0775194
##
## $ZC_protein
## [1] 0.0163132
##
## $ZC_residue
## [1] 0.0163132
The group additivity calculations for proteins are based on equations
and data from Amend and Helgeson (2000), Dick et al.
(2006), and LaRowe and Dick (2012).
There are two major options for the calculations: whether to calculate
properties for crystalline or aqueous groups, and, for the latter,
whether to model the ionization of the sidechain and terminal groups as
a function of pH (and T and P). By default, additivity
of aqueous groups is used, but the ionization calculations are not
available in subcrt()
:
## T P rho logK G H S V Cp
## 1 0.01 1.00000 0.999829 3465.97 -18125553 -44827095 16093.4 10049.2 18448.6
## 2 25.00 1.00000 0.997061 3250.22 -18552315 -44238615 18149.6 10421.0 26842.5
## 3 50.00 1.00000 0.988030 3076.73 -19034574 -43528036 20436.8 10600.2 29597.5
## 4 75.00 1.00000 0.974864 2936.70 -19573864 -42770559 22694.0 10708.1 30863.6
## 5 100.00 1.01322 0.958393 2823.19 -20168495 -41989264 24860.9 10782.9 31582.7
## 6 125.00 2.32014 0.939073 2730.69 -20814620 -41191982 26925.1 10840.9 32071.2
Let’s compare experimental values of heat capacity of four proteins, from Privalov and Makhatadze (1990), with those calculated using group additivity. We divide Privalov and Makhatadze’s experimental values by the lengths of the proteins to get per-residue values, then plot them.
PM90 <- read.csv(system.file("extdata/cpetc/PM90.csv", package = "CHNOSZ"))
plength <- protein.length(colnames(PM90)[2:5])
Cp_expt <- t(t(PM90[, 2:5]) / plength)
matplot(PM90[, 1], Cp_expt, type = "p", pch = 19,
xlab = axis.label("T"), ylab = axis.label("Cp0"), ylim = c(110, 280))
The loop calculates the properties of each protein using group additivity with aqueous or crystalline groups, then plots the per-residue values.
for(i in 1:4) {
pname <- colnames(Cp_expt)[i]
aq <- subcrt(pname, "aq", T = seq(0, 150))$out[[1]]
cr <- subcrt(pname, "cr", T = seq(0, 150))$out[[1]]
lines(aq$T, aq$Cp / plength[i], col = i)
lines(cr$T, cr$Cp / plength[i], col = i, lty = 2)
}
legend("right", legend = colnames(Cp_expt),
col = 1:4, pch = 19, lty = 1, bty = "n", cex = 0.9)
legend("bottomright", legend = c("experimental", "calculated (aq)",
"calculated (cr)"), lty = c(NA, 1, 2), pch = c(19, NA, NA), bty = "n")
Although subcrt()
has
no provision for protein ionization, the properties of ionization can be
calculated via affinity()
,
which calls ionize.aa()
if
a charged species is in the basis. Placeholder (you should not see this)
The following plot shows the calculated affinity of reaction between
nonionized proteins and their ionized forms as a function of pH. Charged
and uncharged sets of basis species are used to to activate and suppress
the ionization calculations. The calculation of affinity for the ionized
proteins returns multiple values (as a function of pH), but there is
only one value of affinity returned for the nonionized proteins, so we
need to use R’s as.numeric()
to avoid subtracting
nonconformable arrays:
ip <- pinfo(c("CYC_BOVIN", "LYSC_CHICK", "MYG_PHYCA", "RNAS1_BOVIN"))
basis("CHNOS+")
a_ion <- affinity(pH = c(0, 14), iprotein = ip)
basis("CHNOS")
a_nonion <- affinity(iprotein = ip)
plot(c(0, 14), c(50, 300), xlab = "pH", ylab = quote(italic(A/2.303*RT)), type="n")
for(i in 1:4) {
A_ion <- as.numeric(a_ion$values[[i]])
A_nonion <- as.numeric(a_nonion$values[[i]])
lines(a_ion$vals[[1]], A_ion - A_nonion, col=i)
}
legend("topright", legend = a_ion$species$name,
col = 1:4, lty = 1, bty = "n", cex = 0.9)
The affinity is always positive, showing the strong energetic drive for ionization of proteins in aqueous solution. The degrees of ionization of amino and carboxyl groups increase at low and high pH, respectively, giving rise to the U-shaped lines.
There, we used the indices returned by pinfo()
in the
iprotein
argument of affinity()
to specify the
proteins in the calculation. That approach utilizes some optimizations
that can be realized due to group additivity, and is useful for
calculations involving many proteins. An alternative, but slower,
approach is to identify the proteins to species()
; this produces results
that are equivalent to using the iprotein
argument:
## 3572 3571 3575 3577
## 55.6138 -470.0056 228.6681 -495.7897
Placeholder (you should not see this)
## -5 -6 -7 -9
## 52.6138 -473.0056 225.6681 -498.7897
Functions in CHNOSZ make it easy to get the chemical formulas of proteins from their amino acid compositions. Calculations based on the formulas, such as the average oxidation state of carbon (ZC), and the coefficients of basis species in formation reactions, are also available.
Let’s compare the ZC of Rubisco with optimal growth
temperature of organisms, as shown in Figure 6a of Dick (2014). First we
read a CSV file with the IDs of the proteins and the optimal growth
temperatures (Topt); the midpoint of the range of
Topt is used for plotting. Then we use
canprot::read_fasta()
to read a FASTA file holding the
amino acid sequences of the proteins; the function returns a data frame
with the amino acid counts. To put the proteins in the right order, the
IDs in the CSV file are matched to the names of the proteins in the
FASTA file. Then, we calculate ZC from the formulas of
the proteins. Next, point symbols are assigned according to domain
(Archaea, Bacteria, Eukaryota); numbers inside the symbols show the
ordering of Topt in three temperature ranges (0–35
°C, 37.5–60 °C, and 65–100 °C).
datfile <- system.file("extdata/cpetc/rubisco.csv", package = "CHNOSZ")
fastafile <- system.file("extdata/protein/rubisco.fasta", package = "CHNOSZ")
dat <- read.csv(datfile)
aa <- canprot::read_fasta(fastafile)
Topt <- (dat$T1 + dat$T2) / 2
idat <- match(dat$ID, substr(aa$protein, 4, 9))
aa <- aa[idat, ]
ZC <- ZC(protein.formula(aa))
pch <- match(dat$domain, c("E", "B", "A")) - 1
col <- match(dat$domain, c("A", "B", "E")) + 1
plot(Topt, ZC, pch = pch, cex = 2, col = col,
xlab = expression(list(italic(T)[opt], degree*C)),
ylab = expression(italic(Z)[C]))
text(Topt, ZC, rep(1:9, 3), cex = 0.8)
abline(v = c(36, 63), lty = 2, col = "grey")
legend("topright", legend = c("Archaea", "Bacteria", "Eukaryota"),
pch = c(2, 1, 0), col = 2:4, pt.cex = 2)
Let’s look at different ways of representing the chemical
compositions of the proteins. protein.basis()
returns the
stoichiometry for the formation reaction of each proteins. Dividing by
protein.length()
gives the
per-residue reaction coefficients. Using the set of basis species we
have seen before (CO2, NH3, H2S,
H2O, O2) there is a noticeable correlation between
nO2 and ZC, but even
more so between nH2O and
ZC (shown in the plots on the left). Placeholder (you
should not see this) The QEC
keyword to basis()
loads basis species
including three amino acids (glutamine, glutamic acid, cysteine,
H2O, O2). This basis strengthens the relationship
between ZC and nO2, but
weakens that between ZC and
nH2O (shown in the plots on the
right).
layout(matrix(1:4, nrow = 2))
par(mgp = c(1.8, 0.5, 0))
pl <- protein.length(aa)
ZClab <- axis.label("ZC")
nO2lab <- expression(italic(n)[O[2]])
nH2Olab <- expression(italic(n)[H[2]*O])
lapply(c("CHNOS", "QEC"), function(thisbasis) {
basis(thisbasis)
pb <- protein.basis(aa)
nO2 <- pb[, "O2"] / pl
plot(ZC, nO2, pch = pch, col = col, xlab = ZClab, ylab = nO2lab)
nH2O <- pb[, "H2O"] / pl
plot(ZC, nH2O, pch = pch, col = col, xlab = ZClab, ylab = nH2Olab)
mtext(thisbasis, font = 2)
})
By projecting the compositions of proteins into the QEC
set of basis species, nO2 emerges as a
strong indicator of oxidation state, while
nH2O is a relatively uncorrelated
(i.e. independent) variable. These independent variables make it easier
to distinguish the effects of oxidation and hydration state in proteomic
datasets (Dick et al.,
2020).
canprot::read_fasta()
).As with other systems, a balance must be chosen for calculations of the metastable equilibrium distribution for proteins. Balancing on the number of backbone units (the sequence length) seems a reasonable choice given the polymeric structure of proteins. Placeholder (you should not see this) However, there is an additional consideration: owing to the large size of proteins compared to the basis species, the distribution of proteins in metastable equilibrium has many orders of magnitude separation between the activities of the dominant and less-dominant proteins. The metastable coexistence of the residues (i.e. per-residue formulas, or residue equivalents) of the same proteins spans a much smaller range of chemical activities. In CHNOSZ, the calculation of metastable equilibrium activities of the residue equivalents is referred to as normalization.
Let’s look at the metastable equilibrium distribution of selected proteins in the ER-to-Golgi location of S. cerevisiae (yeast) (this example is taken from Dick (2009)) Here, we list the names and relative abundances of proteins taken from the YeastGFP study of Ghaemmaghami et al. (2003). There are six proteins identified in the ER-to-Golgi location; one has NA abundance, so it is excluded from the comparisons:
Placeholder (you should not see this)
protein <- c("YDL195W", "YHR098C", "YIL109C", "YLR208W", "YNL049C", "YPL085W")
abundance <- c(1840, 12200, NA, 21400, 1720, 358)
ina <- is.na(abundance)
Next, we find the rownumbers of the proteins in
thermo()$protein
:
The YeastGFP study reported absolute abundances of molecules, but the
thermodynamic calculations give relative chemical activities of the
proteins. In order to make a comparison between them, we use unitize()
to scale the
abundances or activities of proteins (in logarithmic units) such that
the total abundance or activity of residue equivalents is unity. To do
that, we must have the lengths of the proteins. Here, the first call to
unitize()
generates equal
logarithms of activities of proteins for unit total activity of
residues; this is used as the reference state for affinity()
. The second call to
unitize()
scales the
logarithms of experimental abundances for unit total activity of
residues; this is used for comparison with the theoretical results:
pl <- protein.length(ip)
logact <- unitize(numeric(5), pl)
logabundance <- unitize(log10(abundance[!ina]), pl)
Now we can load the proteins and calculate their activities in
metastable equilibrium as a function of
logfO2. The commented line uses add.OBIGT()
to load group
additivity parameters that were present in older versions of CHNOSZ
(Dick et al., 2006). The default database contains newer group
additivity parameters for the sidechain groups of methionine (LaRowe and
Dick, 2012) and glycine and the protein backbone (Kitadai, 2014).
par(mfrow = c(1, 3))
basis("CHNOS+")
a <- affinity(O2 = c(-80, -73), iprotein = ip, loga.protein = logact)
e <- equilibrate(a)
diagram(e, ylim = c(-5, -2), col = 1:5, lwd = 2)
Whoa! The proteins look very non-coexistent in metastable
equilibrium. We get a different view by considering per-residue rather
than per-protein reactions, through the normalize
argument
for equilibrate()
:
Placeholder (you should not see this)
e <- equilibrate(a, normalize = TRUE)
diagram(e, ylim = c(-5, -2.5), col = 1:5, lwd = 2)
abline(h = logabundance, lty = 1:5, col = 1:5)
The experimental relative abundances are plotted as thin horizontal lines with the same style and color as the thicker curved lines calculated for metastable equilibrium. With the exception of YNL049C, the correspondence between the calculations and experiments looks to be greatest near the middle-left part of the figure.
An attempt has been made to assemble a default database that has no major inconsistencies between species. As the database includes thermodynamic data from many sources, it can not be guaranteed to be fully internally consistent. For crucial problems, check not only the accuracy of entries in the database, but also the suitability of the data for your problem. If there are any doubts, consult the primary sources.
Most of the species in OBIGT have parameters for one of two models
for calculating thermodynamic properties. The coefficients in these
models are indicated by the column names with a dot, for example
a1.a
. Most aqueous species use the revised
Helgeson-Kirkham-Flowers (HKF) equations (text before the dot), and
crystalline, gas and liquid species other than H2O use a
polynomial equation for heat capacity. See ?hkf
and ?cgl
for information about the
equations used for thermodynamic properties.
Besides this vignette, here’s where to look for more information about the database:
?thermo
for information about the
format of the OBIGT data frame.thermo.refs()
The OBIGT database lists one or two sources for each entry, and
citation information for the sources is listed in
thermo()$refs
. You can locate and view the references with
thermo.refs()
. Running the
function without any arguments opens a browser window with the complete
table of references. Placeholder (you should not see this) Where
available, links to the web page for the articles and books are
displayed:
A numeric argument to thermo.refs()
gives one or more
species indices for which to get the references:
## key author year citation note
## 148 LH06a D. E. LaRowe and H. C. Helgeson 2006 Geochim. Cosmochim. Acta 70, 4680-4724 nucleic-acid bases, nucleosides, and nucleotides
## 150 LH06b D. E. LaRowe and H. C. Helgeson 2006 Thermochim. Acta 448, 82-106 Mg-complexed adenosine nucleotides (ATP), NAD, and NADP
## URL
## 148 https://doi.org/10.1016/j.gca.2006.04.010
## 150 https://doi.org/10.1016/j.tca.2006.06.008
A character argument gives the source key(s):
## key author year citation note URL
## 7 HDNB78 H. C. Helgeson, J. M. Delany et al. 1978 Am. J. Sci. 278A, 1-229 minerals https://www.worldcat.org/oclc/13594862
## 134 MGN03 J. Majzlan, K.-D. Grevel and A. Navrotsky 2003 Am. Mineral. 88, 855-859 goethite, lepidocrocite, and maghemite GHS https://doi.org/10.2138/am-2003-5-614
If the argument holds the result of subcrt()
, references for all
species in the reaction are returned: Placeholder (you should not see
this)
## key author year citation note
## 123 PS01 A. V. Plyasunov and E. L. Shock 2001 Geochim. Cosmochim. Acta 65, 3879-3900 aqueous nonelectrolytes (organic species)
## 30 SHS89 E. L. Shock, H. C. Helgeson and D. A. Sverjensky 1989 Geochim. Cosmochim. Acta 53, 2157-2183 inorganic neutral species
## 124 PS01.1 A. V. Plyasunov and E. L. Shock 2001 Geochim. Cosmochim. Acta 65, 3879-3900 aqueous nonelectrolytes (Ar, Xe, and CO<sub>2</sub>)
## 17 HGK84 L. Haar and J. S. Gallagher and G. S. Kell 1984 NBS/NRC Steam Tables H<sub>2</sub>O
## 43 JOH92 J. W. Johnson and E. H. Oelkers and H. C. Helgeson 1992 Comp. Geosci. 18, 899-947 H<sub>2</sub>O
## URL
## 123 https://doi.org/10.1016/S0016-7037(01)00678-0
## 30 https://doi.org/10.1016/0016-7037(89)90341-4
## 124 https://doi.org/10.1016/S0016-7037(01)00678-0
## 17 https://www.worldcat.org/oclc/858456124
## 43 https://doi.org/10.1016/0098-3004(92)90029-Q
The URLs of the references can be copied to a browser, or opened
using R’s browseURL()
:
Thermodynamic properties of minerals in the default database are
mostly taken from Berman (1988) (including silicates,
aluminosilicates, calcite, dolomite, hematite, and magnetite) and Helgeson et al. (1978)
(native elements, sulfides, halides, sulfates, and selected carbonates
and oxides that do not duplicate any in the Berman dataset). Minerals
are identified by the state cr
, and (for the Helgeson
dataset) cr2
, cr3
, etc. for higher-temperature
polymorphs.
Compared to SUPCRT92/SLOP98 (see below), the default database include
updates for aqueous Al species (Tagirov and Schott, 2001), Au species (Pokrovski et al.,
2014) (see demo(gold)
), and
arsenic-bearing aqueous species and minerals, as compiled in the
SUPCRTBL package (Zimmer et
al., 2016). This list of updates is incomplete; see the
vignette OBIGT
thermodynamic database for a detailed list of data
sources.
Some optional datasets can be activated by using add.OBIGT()
. The first couple of
these contain data that have been replaced by or are incompatible with
later updates; the superseded data are kept here to reproduce published
calculations and for comparison with the newer data:
add.OBIGT("SUPCRT92")
–
This file contains data for minerals from SUPCRT92 (mostly Helgeson et
al., 1978) that have been replaced by the Berman data set.
add.OBIGT("SLOP98")
–
This file contains data from slop98.dat
or later slop
files, from Everett Shock’s GEOPIG group at Arizona State University,
that were previously used in CHNOSZ but have been replaced by more
recent data updates. Some calculations using the older data are shown in
this vignette.
The updates for these data have been taken from various publications
(LaRowe and Dick,
2012; Kitadai,
2014; Azadi et
al., 2019) A comparison of logK of metal-glycinate
complexes using the updated data is in demo(glycinate)
.
The next three optional datasets are provided to support newer data or models:
add.OBIGT("DEW")
– These
are parameters for aqueous species that are intended for use with the
Deep Earth Water (DEW) model (Sverjensky et al., 2014). You should also
run water("DEW")
to activate
the equations in the model; then, they will be used by subcrt()
and affinity()
. Examples are in demo(DEW)
.
add.OBIGT("AD")
– These
data are used in the Akinfiev-Diamond model for aqeuous nonelectrolytes
(Akinfiev and Diamond,
2003).
add.OBIGT("GEMSFIT")
–
Thermodynamic data for aqueous species in the system
Ca-Mg-Na-K-Al-Si-O-H-C-Cl obtained from global optimization of Gibbs
energies with the GEMSFIT package (Miron et al., 2017).
add.OBIGT("AS04")
– This
file has data for aqueous SiO2 from Apps and Spycher (2004)
and modified HSiO3-. These data reflect a revised
(higher) solubility of quartz compared to previous compilations, but are
not included in the default database in order to maintain compatibility
with existing data for minerals that are linked to the older aqueous
SiO2 data. See demo(aluminum)
for an
example.
info()
automatically
performs some cross-checks of the thermodynamic data. Placeholder (you
should not see this) Given a numeric species index, it runs check.EOS()
, which compares the
given values of CP° and V° with
those calculated from the HKF or heat capacity parameters. info()
also runs check.GHS()
, which compares the
given value of ΔG°f with that calculated
from ΔH°f, S°, and the entropy of
the elements (Cox et al.,
1989) in the chemical formula of the species. If any of the
differences is above a certain tolerance (see ?check.GHS
for details), a
message to this effect is produced.
Some species in the default and optional databases are known to have inconsistent parameters. For instance, we can check the data for the trisulfur radical ion (S3-) from Pokrovski and Dubessy (2015):
## check.GHS: calculated ΔG°f of S3-(aq) differs by 661 cal mol-1 from database value
The calculated value of ΔG°f is 661 cal mol-1 higher than the given value. After checking for any typographical errors in the entries for ΔG°f, ΔH°f, S°, and the chemical formula, the literature may need to be revisited for further clarification.
All of the species with inconsistencies detected in this manner, in
both OBIGT and the optional data files, are listed in the file
OBIGT_check.csv
.
file <- system.file("extdata/adds/OBIGT_check.csv", package = "CHNOSZ")
dat <- read.csv(file, as.is = TRUE)
nrow(dat)
## [1] 400
Without additional information, there is often no clear strategy for “fixing” these inconsistent data, and they are provided as-is. Users are encouraged to send any corrections to the package maintainer.
For calculations of the thermodynamic and dielectric properties of
liquid and supercritical H2O, CHNOSZ uses a Fortran
subroutine (H2O92
) from SUPCRT92 (Johnson et al., 1992).
Alternatively, the IAPWS-95 formulation for thermodynamic properties
(Wagner and Pruß,
2002) can be utilized. In part because of intrinsic
thermodynamic differences between SUPCRT92 and IAPWS-95, as well as
different equations used in CHNOSZ for calculating the dielectric
constant when the IAPWS-95 option is active, this option could introduce
inconsistencies with the data for aqueous species in the database and is
not recommended for general use in CHNOSZ. However, the IAPWS-95
equations are useful for other applications, and may be extrapolated to
a greater range of T and P than SUPCRT. See ?water
for more information, as
well as the last example in ?subcrt
, where uncommenting the
line for the IAPWS95
option allows extrapolation to lower
temperatures for supercooled water.
An implementation of the Deep Earth Water (DEW) model is also available; see Optional data for more information.
Some functions in CHNOSZ lie outside the main workflow described above.
RH2OBIGT()
implements a group additivity calculation of standard molal
thermodynamic properties and equations of state parameters of
crystalline and liquid organic molecules from Richard and Helgeson (1998).
EOSregress()
and
related functions can be used to regress “equation of state” parameters
(e.g. coefficients in the HKF equations) from heat capacity and
volumetric data. See ?EOSregress
and the vignette Regressing
thermodynamic data.
Some functions are available (see ?taxonomy
) to read data from NCBI taxonomy files,
traverse taxonomic ranks, and get scientific names of taxonomic
nodes.
To cite CHNOSZ, use this reference:
Dick JM (2019). “CHNOSZ: Thermodynamic calculations and diagrams for geochemistry.” Frontiers in Earth Science, 7, 180. doi:10.3389/feart.2019.00180.
For the features described in the multi-metal vignette, use this reference:
Dick JM (2021). “Diagrams with multiple metals in CHNOSZ.” Applied Computing and Geosciences, 10, 100059. doi:10.1016/j.acags.2021.100059.
If you found a bug or have questions that aren’t answered in the documentation please contact the maintainer:
## [1] "Jeffrey Dick <[email protected]>"
Thank you for reading, and have fun!
“The real fun of life is this perpetual testing to realize how far out you can go with any potentialities.”
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