Source code for ase.phasediagram

import fractions
import functools
import re
from collections import OrderedDict
from typing import Dict, List, Tuple

import numpy as np
from scipy.spatial import ConvexHull

import ase.units as units
from ase.formula import Formula

_solvated: List[Tuple[str, Dict[str, int], float, bool, float]] = []

def parse_formula(formula):
    aq = formula.endswith('(aq)')
    if aq:
        formula = formula[:-4]
    charge = formula.count('+') - formula.count('-')
    if charge:
        formula = formula.rstrip('+-')
    count = Formula(formula).count()
    return count, charge, aq

def float2str(x):
    f = fractions.Fraction(x).limit_denominator(100)
    n = f.numerator
    d = f.denominator
    if abs(n / d - f) > 1e-6:
        return f'{f:.3f}'
    if d == 0:
        return '0'
    if f.denominator == 1:
        return str(n)
    return f'{f.numerator}/{f.denominator}'

[docs]def solvated(symbols): """Extract solvation energies from database. symbols: str Extract only those molecules that contain the chemical elements given by the symbols string (plus water and H+). Data from: Johnson JW, Oelkers EH, Helgeson HC (1992) Comput Geosci 18(7):899. doi:10.1016/0098-3004(92)90029-Q and: Pourbaix M (1966) Atlas of electrochemical equilibria in aqueous solutions. No. v. 1 in Atlas of Electrochemical Equilibria in Aqueous Solutions. Pergamon Press, New York. Returns list of (name, energy) tuples. """ if isinstance(symbols, str): symbols = Formula(symbols).count().keys() if len(_solvated) == 0: for line in _aqueous.splitlines(): energy, formula = line.split(',') name = formula + '(aq)' count, charge, aq = parse_formula(name) energy = float(energy) * 0.001 * units.kcal / units.mol _solvated.append((name, count, charge, aq, energy)) references = [] for name, count, charge, aq, energy in _solvated: for symbol in count: if symbol not in 'HO' and symbol not in symbols: break else: references.append((name, energy)) return references
def bisect(A, X, Y, f): a = [] for i in [0, -1]: for j in [0, -1]: if A[i, j] == -1: A[i, j] = f(X[i], Y[j]) a.append(A[i, j]) if np.ptp(a) == 0: A[:] = a[0] return if a[0] == a[1]: A[0] = a[0] if a[1] == a[3]: A[:, -1] = a[1] if a[3] == a[2]: A[-1] = a[3] if a[2] == a[0]: A[:, 0] = a[2] if not (A == -1).any(): return i = len(X) // 2 j = len(Y) // 2 bisect(A[:i + 1, :j + 1], X[:i + 1], Y[:j + 1], f) bisect(A[:i + 1, j:], X[:i + 1], Y[j:], f) bisect(A[i:, :j + 1], X[i:], Y[:j + 1], f) bisect(A[i:, j:], X[i:], Y[j:], f) def print_results(results): total_energy = 0.0 print('reference coefficient energy') print('------------------------------------') for name, coef, energy in results: total_energy += coef * energy if abs(coef) < 1e-7: continue print(f'{name:14}{float2str(coef):>10}{energy:12.3f}') print('------------------------------------') print(f'Total energy: {total_energy:22.3f}') print('------------------------------------')
[docs]class Pourbaix: def __init__(self, references, formula=None, T=300.0, **kwargs): """Pourbaix object. references: list of (name, energy) tuples Examples of names: ZnO2, H+(aq), H2O(aq), Zn++(aq), ... formula: str Stoichiometry. Example: ``'ZnO'``. Can also be given as keyword arguments: ``Pourbaix(refs, Zn=1, O=1)``. T: float Temperature in Kelvin. """ if formula: assert not kwargs kwargs = parse_formula(formula)[0] if 'O' not in kwargs: kwargs['O'] = 0 if 'H' not in kwargs: kwargs['H'] = 0 self.kT = units.kB * T self.references = [] for name, energy in references: if name == 'O': continue count, charge, aq = parse_formula(name) if all(symbol in kwargs for symbol in count): self.references.append((count, charge, aq, energy, name)) self.references.append(({}, -1, False, 0.0, 'e-')) # an electron self.count = kwargs self.N = {'e-': 0} for symbol in kwargs: if symbol not in self.N: self.N[symbol] = len(self.N)
[docs] def decompose(self, U, pH, verbose=True, concentration=1e-6): """Decompose material. U: float Potential in V. pH: float pH value. verbose: bool Default is True. concentration: float Concentration of solvated references. Returns optimal coefficients and energy: >>> from ase.phasediagram import Pourbaix, solvated >>> refs = solvated('CoO') + [ ... ('Co', 0.0), ... ('CoO', -2.509), ... ('Co3O4', -9.402)] >>> pb = Pourbaix(refs, Co=3, O=4) >>> coefs, energy = pb.decompose(U=1.5, pH=0, ... concentration=1e-6, ... verbose=True) 0 HCoO2-(aq) -3.974 1 CoO2--(aq) -3.098 2 H2O(aq) -2.458 3 CoOH+(aq) -2.787 4 CoO(aq) -2.265 5 CoOH++(aq) -1.355 6 Co++(aq) -0.921 7 H+(aq) 0.000 8 Co+++(aq) 1.030 9 Co 0.000 10 CoO -2.509 11 Co3O4 -9.402 12 e- -1.500 reference coefficient energy ------------------------------------ H2O(aq) 4 -2.458 Co++(aq) 3 -0.921 H+(aq) -8 0.000 e- -2 -1.500 ------------------------------------ Total energy: -9.596 ------------------------------------ """ alpha = np.log(10) * self.kT entropy = -np.log(concentration) * self.kT # We want to minimize, x) under the constraints: # #, eq2) == eq1 # # with bounds[i,0] <= x[i] <= bounds[i, 1]. # # First two equations are charge and number of hydrogens, and # the rest are the remaining species. eq1 = [0] + list(self.count.values()) eq2 = [] energies = [] bounds = [] names = [] for count, charge, aq, energy, name in self.references: eq = np.zeros(len(self.N)) eq[0] = charge for symbol, n in count.items(): eq[self.N[symbol]] = n eq2.append(eq) if name in ['H2O(aq)', 'H+(aq)', 'e-']: bounds.append((-np.inf, np.inf)) if name == 'e-': energy = -U elif name == 'H+(aq)': energy = -pH * alpha else: bounds.append((0, np.inf)) if aq: energy -= entropy if verbose: print('{:<5}{:10}{:10.3f}'.format(len(energies), name, energy)) energies.append(energy) names.append(name) from scipy.optimize import linprog result = linprog(c=energies, A_eq=np.transpose(eq2), b_eq=eq1, bounds=bounds) if verbose: print_results(zip(names, result.x, energies)) return result.x,
[docs] def diagram(self, U, pH, plot=True, show=False, ax=None): """Calculate Pourbaix diagram. U: list of float Potentials in V. pH: list of float pH values. plot: bool Create plot. show: bool Open graphical window and show plot. ax: matplotlib axes object When creating plot, plot onto the given axes object. If none given, plot onto the current one. """ a = np.empty((len(U), len(pH)), int) a[:] = -1 colors = {} f = functools.partial(self.colorfunction, colors=colors) bisect(a, U, pH, f) compositions = [None] * len(colors) names = [ref[-1] for ref in self.references] for indices, color in colors.items(): compositions[color] = ' + '.join(names[i] for i in indices if names[i] not in ['H2O(aq)', 'H+(aq)', 'e-']) text = [] for i, name in enumerate(compositions): b = (a == i) x =, U) / b.sum() y =, pH) / b.sum() name = re.sub(r'(\S)([+-]+)', r'\1$^{\2}$', name) name = re.sub(r'(\d+)', r'$_{\1}$', name) text.append((x, y, name)) if plot: import as cm import matplotlib.pyplot as plt if ax is None: ax = plt.gca() # rasterized pcolormesh has a bug which leaves a tiny # white border. Unrasterized pcolormesh produces # unreasonably large files. Avoid this by using the more # general imshow. ax.imshow(a, cmap=cm.Accent, extent=[min(pH), max(pH), min(U), max(U)], origin='lower', aspect='auto') for x, y, name in text: ax.text(y, x, name, horizontalalignment='center') ax.set_xlabel('pH') ax.set_ylabel('potential [V]') ax.set_xlim(min(pH), max(pH)) ax.set_ylim(min(U), max(U)) if show: return a, compositions, text
def colorfunction(self, U, pH, colors): coefs, energy = self.decompose(U, pH, verbose=False) indices = tuple(sorted(np.where(abs(coefs) > 1e-3)[0])) color = colors.get(indices) if color is None: color = len(colors) colors[indices] = color return color
[docs]class PhaseDiagram: def __init__(self, references, filter='', verbose=True): """Phase-diagram. references: list of (name, energy) tuples List of references. The energy must be the total energy and not energy per atom. The names can also be dicts like ``{'Zn': 1, 'O': 2}`` which would be equivalent to ``'ZnO2'``. filter: str or list of str Use only those references that match the given filter. Example: ``filter='ZnO'`` will select those that contain zinc or oxygen. verbose: bool Write information. """ if not references: raise ValueError("You must provide a non-empty list of references" " for the phase diagram! " "You have provided '{}'".format(references)) filter = parse_formula(filter)[0] self.verbose = verbose self.species = OrderedDict() self.references = [] for name, energy in references: if isinstance(name, str): count = parse_formula(name)[0] else: count = name if filter and any(symbol not in filter for symbol in count): continue if not isinstance(name, str): name = Formula.from_dict(count).format('metal') natoms = 0 for symbol, n in count.items(): natoms += n if symbol not in self.species: self.species[symbol] = len(self.species) self.references.append((count, energy, name, natoms)) ns = len(self.species) self.symbols = [None] * ns for symbol, id in self.species.items(): self.symbols[id] = symbol if verbose: print('Species:', ', '.join(self.symbols)) print('References:', len(self.references)) for i, (count, energy, name, natoms) in enumerate(self.references): print(f'{i:<5}{name:10}{energy:10.3f}') self.points = np.zeros((len(self.references), ns + 1)) for s, (count, energy, name, natoms) in enumerate(self.references): for symbol, n in count.items(): self.points[s, self.species[symbol]] = n / natoms self.points[s, -1] = energy / natoms if len(self.points) == ns: # Simple case that qhull would choke on: self.simplices = np.arange(ns).reshape((1, ns)) self.hull = np.ones(ns, bool) elif ns == 1: # qhull also doesn't like ns=1: i = self.points[:, 1].argmin() self.simplices = np.array([[i]]) self.hull = np.zeros(len(self.points), bool) self.hull[i] = True else: hull = ConvexHull(self.points[:, 1:]) # Find relevant simplices: ok = hull.equations[:, -2] < 0 self.simplices = hull.simplices[ok] # Create a mask for those points that are on the convex hull: self.hull = np.zeros(len(self.points), bool) for simplex in self.simplices: self.hull[simplex] = True if verbose: print('Simplices:', len(self.simplices))
[docs] def decompose(self, formula=None, **kwargs): """Find the combination of the references with the lowest energy. formula: str Stoichiometry. Example: ``'ZnO'``. Can also be given as keyword arguments: ``decompose(Zn=1, O=1)``. Example:: pd = PhaseDiagram(...) pd.decompose(Zn=1, O=3) Returns energy, indices of references and coefficients.""" if formula: assert not kwargs kwargs = parse_formula(formula)[0] point = np.zeros(len(self.species)) N = 0 for symbol, n in kwargs.items(): point[self.species[symbol]] = n N += n # Find coordinates within each simplex: X = self.points[self.simplices, 1:-1] - point[1:] / N # Find the simplex with positive coordinates that sum to # less than one: eps = 1e-14 for i, Y in enumerate(X): try: x = np.linalg.solve((Y[1:] - Y[:1]).T, -Y[0]) except np.linalg.linalg.LinAlgError: continue if (x > -eps).all() and x.sum() < 1 + eps: break else: assert False, X indices = self.simplices[i] points = self.points[indices] scaledcoefs = [1 - x.sum()] scaledcoefs.extend(x) energy = N *, points[:, -1]) coefs = [] results = [] for coef, s in zip(scaledcoefs, indices): count, e, name, natoms = self.references[s] coef *= N / natoms coefs.append(coef) results.append((name, coef, e)) if self.verbose: print_results(results) return energy, indices, np.array(coefs)
[docs] def plot(self, ax=None, dims=None, show=False, **plotkwargs): """Make 2-d or 3-d plot of datapoints and convex hull. Default is 2-d for 2- and 3-component diagrams and 3-d for a 4-component diagram. """ import matplotlib.pyplot as plt N = len(self.species) if dims is None: if N <= 3: dims = 2 else: dims = 3 if ax is None: projection = None if dims == 3: projection = '3d' from mpl_toolkits.mplot3d import Axes3D Axes3D # silence pyflakes fig = plt.figure() ax = fig.add_subplot(projection=projection) else: if dims == 3 and not hasattr(ax, 'set_zlim'): raise ValueError('Cannot make 3d plot unless axes projection ' 'is 3d') if dims == 2: if N == 2: self.plot2d2(ax, **plotkwargs) elif N == 3: self.plot2d3(ax) else: raise ValueError('Can only make 2-d plots for 2 and 3 ' 'component systems!') else: if N == 3: self.plot3d3(ax) elif N == 4: self.plot3d4(ax) else: raise ValueError('Can only make 3-d plots for 3 and 4 ' 'component systems!') if show: return ax
def plot2d2(self, ax=None, only_label_simplices=False, only_plot_simplices=False): x, e = self.points[:, 1:].T names = [re.sub(r'(\d+)', r'$_{\1}$', ref[2]) for ref in self.references] hull = self.hull simplices = self.simplices xlabel = self.symbols[1] ylabel = 'energy [eV/atom]' if ax: for i, j in simplices: ax.plot(x[[i, j]], e[[i, j]], '-b') ax.plot(x[hull], e[hull], 'sg') if not only_plot_simplices: ax.plot(x[~hull], e[~hull], 'or') if only_plot_simplices or only_label_simplices: x = x[self.hull] e = e[self.hull] names = [name for name, h in zip(names, self.hull) if h] for a, b, name in zip(x, e, names): ax.text(a, b, name, ha='center', va='top') ax.set_xlabel(xlabel) ax.set_ylabel(ylabel) return (x, e, names, hull, simplices, xlabel, ylabel) def plot2d3(self, ax=None): x, y = self.points[:, 1:-1].T.copy() x += y / 2 y *= 3**0.5 / 2 names = [re.sub(r'(\d+)', r'$_{\1}$', ref[2]) for ref in self.references] hull = self.hull simplices = self.simplices if ax: for i, j, k in simplices: ax.plot(x[[i, j, k, i]], y[[i, j, k, i]], '-b') ax.plot(x[hull], y[hull], 'og') ax.plot(x[~hull], y[~hull], 'sr') for a, b, name in zip(x, y, names): ax.text(a, b, name, ha='center', va='top') return (x, y, names, hull, simplices) def plot3d3(self, ax): x, y, e = self.points[:, 1:].T ax.scatter(x[self.hull], y[self.hull], e[self.hull], c='g', marker='o') ax.scatter(x[~self.hull], y[~self.hull], e[~self.hull], c='r', marker='s') for a, b, c, ref in zip(x, y, e, self.references): name = re.sub(r'(\d+)', r'$_{\1}$', ref[2]) ax.text(a, b, c, name, ha='center', va='bottom') for i, j, k in self.simplices: ax.plot(x[[i, j, k, i]], y[[i, j, k, i]], zs=e[[i, j, k, i]], c='b') ax.set_xlim3d(0, 1) ax.set_ylim3d(0, 1) ax.view_init(azim=115, elev=30) ax.set_xlabel(self.symbols[1]) ax.set_ylabel(self.symbols[2]) ax.set_zlabel('energy [eV/atom]') def plot3d4(self, ax): x, y, z = self.points[:, 1:-1].T a = x / 2 + y + z / 2 b = 3**0.5 * (x / 2 + y / 6) c = (2 / 3)**0.5 * z ax.scatter(a[self.hull], b[self.hull], c[self.hull], c='g', marker='o') ax.scatter(a[~self.hull], b[~self.hull], c[~self.hull], c='r', marker='s') for x, y, z, ref in zip(a, b, c, self.references): name = re.sub(r'(\d+)', r'$_{\1}$', ref[2]) ax.text(x, y, z, name, ha='center', va='bottom') for i, j, k, w in self.simplices: ax.plot(a[[i, j, k, i, w, k, j, w]], b[[i, j, k, i, w, k, j, w]], zs=c[[i, j, k, i, w, k, j, w]], c='b') ax.set_xlim3d(0, 1) ax.set_ylim3d(0, 1) ax.set_zlim3d(0, 1) ax.view_init(azim=115, elev=30)
_aqueous = """\ -525700,SiF6-- -514100,Rh(SO4)3---- -504800,Ru(SO4)3---- -499900,Pd(SO4)3---- -495200,Ru(SO4)3--- -485700,H4P2O7 -483700,Rh(SO4)3--- -483600,H3P2O7- -480400,H2P2O7-- -480380,Pt(SO4)3---- -471400,HP2O7--- -458700,P2O7---- -447500,LaF4- -437600,LaH2PO4++ -377900,LaF3 -376299,Ca(HSiO3)+ -370691,BeF4-- -355400,BF4- -353025,Mg(HSiO3)+ -346900,LaSO4+ -334100,Rh(SO4)2-- -325400,Ru(SO4)2-- -319640,Pd(SO4)2-- -317900,Ru(SO4)2- -312970,Cr2O7-- -312930,CaSO4 -307890,NaHSiO3 -307800,LaF2+ -307000,LaHCO3++ -306100,Rh(SO4)2- -302532,BeF3- -300670,Pt(SO4)2-- -299900,LaCO3+ -289477,MgSO4 -288400,LaCl4- -281500,HZrO3- -279200,HHfO3- -276720,Sr(HCO3)+ -275700,Ba(HCO3)+ -273830,Ca(HCO3)+ -273100,H3PO4 -270140,H2PO4- -266500,S2O8-- -264860,Sr(CO3) -264860,SrCO3 -263830,Ba(CO3) -263830,BaCO3 -262850,Ca(CO3) -262850,CaCO3 -260310,HPO4-- -257600,LaCl3 -250200,Mg(HCO3)+ -249200,H3VO4 -248700,S4O6-- -246640,KSO4- -243990,H2VO4- -243500,PO4--- -243400,KHSO4 -242801,HSiO3- -241700,HYO2 -241476,NaSO4- -239700,HZrO2+ -239300,LaO2H -238760,Mg(CO3) -238760,MgCO3 -237800,HHfO2+ -236890,Ag(CO3)2--- -236800,HNbO3 -236600,LaF++ -235640,MnSO4 -233400,ZrO2 -233000,HVO4-- -231600,HScO2 -231540,B(OH)3 -231400,HfO2 -231386,BeF2 -231000,S2O6-- -229000,S3O6-- -229000,S5O6-- -228460,HTiO3- -227400,YO2- -227100,NbO3- -226700,LaCl2+ -223400,HWO4- -221700,LaO2- -218500,WO4-- -218100,ScO2- -214900,VO4--- -210000,YOH++ -208900,LaOH++ -207700,HAlO2 -206400,HMoO4- -204800,H3PO3 -202350,H2PO3- -202290,SrF+ -201807,BaF+ -201120,BaF+ -200400,MoO4-- -200390,CaF+ -199190,SiO2 -198693,AlO2- -198100,YO+ -195900,LaO+ -195800,LaCl++ -194000,CaCl2 -194000,HPO3-- -191300,LaNO3++ -190400,ZrOH+++ -189000,HfOH+++ -189000,S2O5-- -187600,ZrO++ -186000,HfO++ -183700,HCrO4- -183600,ScO+ -183100,H3AsO4 -180630,HSO4- -180010,H2AsO4- -177930,SO4-- -177690,MgF+ -174800,CrO4-- -173300,SrOH+ -172300,BaOH+ -172200,HBeO2- -171300,CaOH+ -170790,HAsO4-- -166000,ReO4- -165800,SrCl+ -165475,Al(OH)++ -165475,AlOH++ -164730,BaCl+ -164000,La+++ -163800,Y+++ -163100,CaCl+ -162240,BO2- -158493,BeF+ -158188,AlO+ -155700,VOOH+ -155164,CdF2 -154970,AsO4--- -153500,Rh(SO4) -152900,BeO2-- -152370,HSO5- -151540,RuCl6--- -149255,MgOH+ -147400,H2S2O4 -146900,HS2O4- -146081,CdCl4-- -145521,BeCl2 -145200,Ru(SO4) -145056,PbF2 -143500,S2O4-- -140330,H2AsO3- -140300,VO2+ -140282,HCO3- -140200,Sc+++ -139900,BeOH+ -139700,MgCl+ -139200,Ru(SO4)+ -139000,Pd(SO4) -138160,HF2- -138100,HCrO2 -138000,TiO++ -137300,HGaO2 -136450,RbF -134760,Sr++ -134030,Ba++ -133270,Zr++++ -133177,PbCl4-- -132600,Hf++++ -132120,Ca++ -129310,ZnCl3- -128700,GaO2- -128600,BeO -128570,NaF -128000,H2S2O3 -127500,Rh(SO4)+ -127200,HS2O3- -126191,CO3-- -126130,HSO3- -125300,CrO2- -125100,H3PO2 -124900,S2O3-- -123641,MnF+ -122400,H2PO2- -121000,HMnO2- -120700,RuCl5-- -120400,MnO4-- -120300,Pt(SO4) -119800,HInO2 -116300,SO3-- -115971,CdCl3- -115609,Al+++ -115316,BeCl+ -112280,AgCl4--- -111670,TiO2++ -111500,VOH++ -111430,Ag(CO3)- -110720,HZnO2- -108505,Mg++ -108100,HSeO4- -108000,LiOH -107600,MnO4- -106988,HgCl4-- -106700,InO2- -106700,VO++ -106100,VO+ -105500,SeO4-- -105100,RbOH -105000,CsOH -104500,KOH -104109,ZnF+ -103900,PdCl4-- -103579,CuCl4-- -102600,MnO2-- -102150,PbCl3- -101850,H2SeO3 -101100,HFeO2 -100900,CsCl -100500,CrOH++ -99900,NaOH -99800,VOH+ -99250,LiCl -98340,HSeO3- -98300,ZnCl2 -97870,RbCl -97400,HSbO2 -97300,HSnO2- -97300,MnOH+ -97016,InF++ -96240,HAsO2 -95430,KCl -95400,HFeO2- -94610,CsBr -93290,ZnO2-- -93250,RhCl4-- -92910,NaCl -92800,CrO+ -92250,CO2 -91210,PtCl4-- -91157,FeF+ -91100,GaOH++ -91010,RbBr -90550,Be++ -90010,KBr -89963,CuCl3-- -89730,RuCl4- -88400,SeO3-- -88000,FeO2- -87373,CdF+ -86600,GaO+ -86500,HCdO2- -86290,MnCl+ -85610,NaBr -84851,CdCl2 -83900,RuCl4-- -83650,AsO2- -83600,Ti+++ -83460,CsI -83400,HCoO2- -82710,AgCl3-- -82400,SbO2- -81980,HNiO2- -81732,CoF+ -81500,MnO -81190,ZnOH+ -81000,HPbO2- -79768,NiF+ -79645,FeF++ -79300,HBiO2 -78900,RbI -77740,KI -77700,La++ -77500,RhCl4- -75860,PbF+ -75338,CuCl3- -75216,TlF -75100,Ti++ -74600,InOH++ -74504,HgCl3- -73480,FeCl2 -72900,NaI -71980,SO2 -71662,HF -71600,RuO4-- -71200,PbCl2 -69933,Li+ -69810,PdCl3- -69710,Cs+ -69400,InO+ -67811,AuCl3-- -67800,Rb+ -67510,K+ -67420,ZnO -67340,F- -67300,CdO2-- -66850,ZnCl+ -65850,FeOH+ -65550,TlOH -64200,NiO2-- -63530,RhCl3- -63200,CoO2-- -62591,Na+ -61700,BiO2- -61500,CdOH+ -60100,HCuO2- -59226,InCl++ -58600,SnOH+ -58560,RuCl3 -58038,CuCl2- -57900,V+++ -57800,FeOH++ -57760,PtCl3- -57600,HTlO2 -56690,H2O -56025,CoOH+ -55100,Mn++ -54380,RuCl3- -53950,PbOH+ -53739,CuF+ -53600,SnO -53100,FeO+ -53030,FeCl+ -52850,NiOH+ -52627,CdCl+ -52000,V++ -51560,AgCl2- -50720,FeO -49459,AgF -49300,Cr+++ -47500,CdO -46190,RhCl3 -46142,CuCl2 -45200,HHgO2- -45157,CoCl+ -44000,CoO -42838,HgCl2 -41600,TlO2- -41200,CuO2-- -40920,NiCl+ -39815,TlCl -39400,Cr++ -39350,PbO -39340,NiO -39050,PbCl+ -38000,Ga+++ -37518,FeCl++ -36781,AuCl2- -35332,AuCl4- -35200,Zn++ -35160,PdCl2 -33970,RhCl2 -32300,BiOH++ -31700,HIO3 -31379,Cl- -30600,IO3- -30410,HCl -30204,HgF+ -30200,CuOH+ -29300,BiO+ -28682,CO -26507,NO3- -26440,RuCl2+ -25590,Br3- -25060,RuCl2 -24870,Br- -24730,HNO3 -23700,HIO -23400,In+++ -23280,OCN- -23000,CoOH++ -22608,CuCl -22290,PtCl2 -21900,AgOH -21870,Fe++ -20800,CuO -20300,Mn+++ -20058,Pb(HS)2 -19700,HBrO -19100,HClO -19100,ScOH++ -18990,NH4+ -18971,Pb(HS)3- -18560,Cd++ -18290,Rh(OH)+ -17450,AgCl -16250,CuCl+ -14780,RhCl2+ -14000,IO4- -13130,Pd(OH)+ -13000,Co++ -12700,HgOH+ -12410,I- -12300,I3- -12190,Ru(OH)2++ -12100,HNO2 -11500,PdO -10900,Ni++ -10470,Ru(OH)+ -10450,RuO+ -9200,IO- -8900,HgO -8800,ClO- -8000,BrO- -7740,Tl+ -7738,AgNO3 -7700,NO2- -7220,RhO -6673,H2S -6570,Sn++ -6383,NH3 -5710,Pb++ -5500,AgO- -4500,TlOH++ -4120,Fe+++ -3380,RhCl+ -3200,TlO+ -3184,AuCl -2155,HgCl+ -2040,ClO4- -1900,ClO3- -1130,PtO -820,Rh(OH)++ 0,Ag(HS)2- 0,H+ 230,RuO 1400,HClO2 1560,Pt(OH)+ 2429,Au(HS)2- 2500,PdCl+ 2860,HS- 3140,RhO+ 3215,Xe 3554,Kr 3890,Ar 4100,ClO2- 4347,N2 4450,BrO3- 4565,Ne 4658,He 5210,RuCl+ 7100,RuCl++ 8600,H2N2O2 9375,TlCl++ 10500,HSe- 11950,Cu+ 15675,Cu++ 15700,S5-- 16500,S4-- 17600,S3-- 18200,HN2O2- 18330,RhCl++ 18380,PtCl+ 18427,Ag+ 19000,S2-- 19500,SeCN- 19700,N2H5+ 21100,N2H6++ 22160,SCN- 22880,Bi+++ 27700,Rh++ 28200,BrO4- 28600,HCN 32000,Co+++ 33200,N2O2-- 35900,Ru++ 36710,Hg2++ 39360,Hg++ 41200,CN- 41440,Ru+++ 42200,Pd++ 51300,Tl+++ 52450,Rh+++ 61600,Pt++ 64300,Ag++ 103600,Au+++"""