TOURNAL
J
O F T H E AMERICAN CHEMICAL SOCIETY Registered in L.S. Parent Office.
@ Copyright. 1977, by rhe Anrerican C'heiniral Sorie!j'
VOLUME 99, N U M B E R 14
JULY6, 1977
A Systematic Study of the Ionization Potentials and Electron, Proton, Hydrogen, and Hydride Affinities of OH, Molecules and Ions Roy E. Kari* and Imre G. Csizmadia Contribution f r o m the Departments of Chemistry, Laurentian Unicersity, Sudbury, Ontario, Canada, and the University of Toronto, Toronto, Ontario, Canada. Received November 14. 1974
Abstract: A b initio LCAO-MO-SCF computations with large Gaussian basis sets have been performed on oxjgen hj,drides with one to three hydrogen atoms. Both the bond lengths ( r ) and bond angles (4) were varied to produce energy surfaces E ( r ,4).The resulting energies were used to determine ionization potentials and electron, proton, hydrogen, and hydride affinities.
A knowledge of accurate ionization potentials and electron, proton, hydrogen, and hydride affinities can be obtained by studying the reactions illustrated below. AHn+H=AHn+1
+ A H n m f + H+
avoidable in the calculation of energy differences in processes where closed electronic shells are either created or destroyed as in the electron detachment, attachment process illustrated below:
HzO (5 electron pairs)
A H n m + H- + AHn+ I ( ~ - ' ) ' AHn+]("+')+ AHnnT+ $ AH,("'+I)+ + e-
These energy difference quantities are important for studies in areas such as ion hydration, acid-catalyzed reactions, and electron scattering. Unfortunately, many of the species in the above reactions are not amenable even to experimental detection. It is exactly this kind of problem where theoretical means might be used to their greatest advantage. Although self-consistent molecular orbital theory, with a well defined set of basis functions, gives a generally successful account I - ) of nonenergy one-electron properties such as multipole moments, diamagnetic shielding, etc., the calculation of properties dependent on energy differences have not been as successful. This is because the SCF energy ( E S C Fis) no more than an approximation to the Hartree-Fock energy ( E H F )which , is itself only one component of the electronic energy (E,]) written as: E,I = ESCF + (EHF- E S C F )+ E c
+ ER
where E c is the correlation energy and E R is the relativistic energy. Our ability to compute E,] and resulting energy differences is limited by our knowledge of the last three terms. Since the number of atoms is conserved in chemical reactions, differences in E R can be assumed to be negligible. But, because the correlation energy ( E c ) is generally related to the number of electron pairs in a molecule, systematic errors are un-
+HzO+ (4'/' IP
EA
electron pairs)
+ e-
Estimating the correlation energy changes by comparing calculated results to experimental results, whenever both are reasonably accurate, is a way to reduce the influence of these systematic errors. If in a given system, neither experimental measurements nor theoretically calculated correlation energies of sufficient accuracy exist, a method of making approximate correlation energy corrections is through an extrapolation from similar systems which are better characterized. Both these combinations of circumstances are present in the oxygen hydride situation; that is, only some of the set of oxygen hydrides and their ions have been characterized experimentally and/or theoretically. This paper focuses on the oxygen hydrides for their inherent interest and importance and because it is worthwhile studying the entire set of species in a systematic manner. I n order to transfer correlation energy estimates from one hydride to another, one must be assured that the quantity (EHF - E S C Fis) either known or is of the same relative magnitude for both hydrides. Numerous a b initio LCAO-MO-SCF calculations have been previously performed4-Io to predict energy-dependent properties of some oxygen hydrides. Except for two case^,^,^ these calculations have not been concerned with a comprehensive study of more than a few hydrides, and since it is difficult to estimate (EHF- E S C F for ) these isolated calculations, no correlation energy corrections have been attempted. Also, because the ( E H F- E S C F term ) differs for each calculation, it is impossible to collate their results to determine 4539
4540 trends. Thus, in the present study, a uniform basis set (which included both d and p polarization functions on the oxygen and hydrogen atoms) was employed so as to minimize and reduce fluctuations in ( E H F- E S C F in ) the prediction of a series of ionization potentials (IP) and electron (EA), proton ( A H + ) , hydrogen ( A H ) and , hydride ( A H - )affinities for a few of the monooxygen hydrides. This involved the calculation of equilibrium geometries and energies for the following species, where the ten-electron closed-shell systems are enclosed by the broken line.
Table 1. Computed Total Atomic Energies
Atomic species
State
HH O+ 0
'S 4S
0-
2P
02-
'S
'S
3P
Present -0.405 -0.497 -74.355 -74.793 -74.148 -74.277
Total energy, hartree Hartree-Fock
271 639 627 186 716 585
-0.4878' -0.5 -14,3726' -74,8094' -74.7895d -74.3184
Exptl -0.5245' -0.5 -14.6097' -75.1 101e -15.1639'
a A. W. Weiss, Phys. Reu., 122, 1826 (1961). E. Clementi, J . Chem. Phys., 38, 1001 (1963). E. Clementi et al., Phys. Reu., 127, 161 8 (1962). Reference 25. e Reference 6.
Method For singlet states of molecules, normal closed-shell theory with real molecular orbitals is used, leading to the well-known equations of Roothaan.] For states of higher multiplicity, restricted single determinantI2 theory is used. This method has not been widely used, since iterative convergence of the energy is not always assured. However, no such problems were encountered with the present calculations and it is believed that all of the energies quoted represent the minima obtainable with both methods. Here, the term Hartree-Fock energy ( E H F ) refers to the minimum restricted closed- or open-shell energy which would be obtained with a complete basis set. Correlation energy thus refers to the difference between E H Fand the nonrelativistic energy of the molecular species in question. In a preliminary study13 of the effects of polarization functions on calculated energy differences, it was found that unless these functions were used on both the oxygen and hydrogen atoms, little confidence could be placed on the relative as well as the absolute magnitudes of the calculated energy differences. This is caused by the varying effect that a given polarization function will have on the ( E H F- E S C F energy ) term of each molecular species. For example, the calculated proton affinities of OH- and OH2 changed by - 11.8 and 3.9 kcal/mol, respectively, when polarization functions were added to the basis set. Recent calculations on negative ion^'^-'^ indicate that additional diffuse s and p basis functions are required on the heavier atom to properly describe negative ions. No diffuse basis functions were used in the present calculations and the lack of these diffuse basis functions appears to be only partially offset by the added polarization functions. The actual Gaussian basis sets used in these calculations included a (IOs,5p,ld) basis set on oxygen contracted by a (4s,2p,ld) basis set. The hydrogen atom was described by a (4s, 1 p) basis set contracted to a (2s, 1p) basis set. The oxygen d exponent (0.706 328) was obtained by extrapolating optimized C and N d exponent^.'^ The hydrogen p exponent (0.9) was obtained from previous CI results.'* All other exponents and contraction coefficients were those suggested by Basch et
No distinction was made in the basis sets for ionic or neutral species. The potential surfaces E ( r , @ )generated , by variation of the 0 - H bond length ( r ) and the HOH bond angle (@),were calculated for all of the hydrides listed in the introduction. For economic reasons, these variations were restricted to the following symmetries:
OH: Czr
'
a1.19
For the species investigated, the above basis sets represented the following basis set sizes:
-
0 (31)-+ [16] [21]
OH
(38)
OH2
(45)-
[26]
OH3
(52)
[31]
-
OH*: Dmh and C2L. OH3: D3h and C3r Results and Discussion Total Energies. The calculated total energies for all of the grid points considered are listed in Table I for atoms, Table I 1 for diatomic hydrides, Table 111 for triatomic hydrides, and Table IV for quatratomic hydrides. I n order to economize on the amount of computer time required to compute an energy surface for each species, the increments in both bond angle and bond length variations were deliberately chosen to be quite large. Then, to determine the equilibrium geometries from these surfaces, two methods were employed to determine the significance of the interpolated equilibrium geometries. First, a polynomial of the form
was fitted to the calculated points by means of least-squares fitting. Generally, a,, was found to be significant only for i = 0, 2, and 4 and j varying from 0 to 4. The minimum of the polynomial was then determined. Second, a third-order spline function fitting routine was used to generate a 51-point square interpolated energy surface. The minimum energy computed by each method agreed to four decimals with the exception of H20, where the second method gave an energy 0.0023 hartree hig'ner. The equilibrium bond lengths determined by both methods agreed to three significant figures, whereas the equilibrium bond angles differed by as much as 5 " . Again the largest discrepancy occurred in the calculation of the equilibrium bond angle for HzO. Although the significance of the interpolated equilibrium bond angle could be improved bq computing more energy points near the minimum, this was not done, since we were primarily interested in minimum energies which were reproduced to a sufficient accuracy by both fitting methods. Furthermore, in instances where data points are widely spread, the spline function fitting did not always produce a smooth curve along the whole surface. Thus, the equilibrium energies and geometries listed in the tables and used henceforth were those determined by the polynomial leastsquares fitting method. In Tables V-IX no figures are listed under the heading best MO when it was felt that the present calculations were in fact the best.
Journal of the American Chemical Society / 99:14 / July 6 , I977
4541 Table 11. Computed Total Energies of Diatomic Oxygen Hydrides Diatomic species
0H
+
OH OH-
Bond length, bohr State
I .7
1.8
I .9
2.0
32:
-14.910 281 -75.395 631 -15.362 818
-74.979 682 -75.399 762 -75.366 488
-74.982 651 -75.391 644 -75.364 261
-14.981 145 -15.391 203 -15.358 129
*n '2
Table 111. Computed Total Energies for H2O- (2Z- and 2AI), H 2 0 (!& and !A!), and HzO+ (211and 2 B ~ ) Bond angle, deg
Species
1 .l
Bond length, bohr
180.000 000
HzO-
-15.164 339 -15.987 121 -15.589 613 -75.191 005 -76.022 428 -75.615 910 -75.196 838 -76.029 288 -15.620 180 -16.032 041 -75.805 716 -75.613 564 -15.199 231 -76.01 5 142
H2
0
HzO+ H2 0 -
132.120 120
y20 H*O+ HzOHzO H20+ H2O H2O-
124.392 864 120.000 000 109.41I 202 95.842 912 82.952 420
HzO+ HzO-
H2
0
I .9
1 .a
-15.788 -75.987 -75.602 -75.812 -16.025 -15.628 -75.811 -16.032 -15.633 -76.036 -15.824 -75.628 -15.819 -16.024
-75.802 -15.915 -15.602 -15.824 -16.016 -15.629 -75.828 -16.024 -75.634 -76.021 -75.833 -75.631 -75.828 -76.020
691 198 I01 770 304 8 16 583 868 331 013 890 119 535 552
2. I 158 482 616 526 309 455 006 488 108 969 108 158 602 193
-75.813 431 -75.581 519 -15.828 681 -75.607 99 1 -75.830 256 -75.612 618 -15.830 205 -75.611 815 -15.826 519
Table IV. Computed Total Energies for H 3 0 - ( ' A ! ) , H3O ( 2 A ~ )H, 3 0 + ( ' A I ) , and H@'+ ( * A I ) Bond angle, deg 120.0
117.5
115.0
110.0
105.0
95.0
Species
I .7
1 .a
H3OH30 H3O+ H 3O*+ H 30H30 H3O+ H30*+ H3OH30 H3O+ H302+ H3OH30 H3O+ H302+ H3OH@ H3O+ H302+ H3OH3O H30+ H3O2+
-76.176 517
-76.222 128 -16 420 923 -76.321 396 -15.480 436 -76.223 221 -76.422 098 -16.322 484 -15.473 390 -76.224 221 -16.422 932 -76.322 925 -75.466 028 -76.225 281 -76.423 514 -76.321 737 -75.448 945 -76.226 484
-76.308 506 -75.442 910 -76.178 594 -16.309 096 -75.436 031 -76.180 467 -76.309 017 -15.428 300 -76.1 83 386 -76.306 701 -15.411 100
Bond length, bohr 1.9 -16.252 650 -76.434 554 -16.3 16 005 -15.498 115 -16.252 609 -16.435 394 -16.31 7 518 -15.492 225 -16.252 593 -16.435 931 -76.318 401 -75.484 891 -76.252 483 -16.436 094 -76.318 161 -75.461 966 -76.252 001 -76.434 91 9 -76.31 5 073 -75.448 219 -16.241 460 -16.421 998
-16.311 584 -75.428 312
Ionization Potentials and Electron Affinities. The adiabatic ionization potential (Ia)for a molecule or ion (M) is defined as the energy absorbed when an electron is removed from a parent molecule or ion while the electron affinity (EA) is defined as the energy released when an electron is captured by a molecule or ion (M). In order to avoid confusion, the thermodynamic conventions will be used to specify energy differences. Thus, all endothermic processes will show a positive energy difference, while exothermic processes will show a negative energy difference. In the following two reactions
2.0
2.2
-16.212 125 -16.436 625 -16.298 147 -75.503 959 -16 271 293 -16 436 949 -16.299 924 -15.491 433 -76.270 092 -76.437 100 -76.301 135 -75.490 324 -16 268 160 -76.436 183 -76.301 706 -15.413 906 -16.266 301 -16.435 362 -76.299 51 8 -15.454 599 -16.260 755 -16.428 901
-76.288 587 -76.416 563
-15.406 371
-75.391 099
-75.489 500 -16 285 492 -76.416 580 -75.482 340 -76.282 513 -76.416 353 -75.476 360 -16 211 3 I2 -76.415 242 -15.461 140 -76.212 11 1 -16.413 308 -15.443 810 -76.265 006 -76.407 262
M+M++eand M+e-+Msince the electronic energy of a bare electron is zero, one may define the following: I , ( M ) = E"+(Re) - E M ( R e ) EA(M) = EM-(Re) - EM(Re) Subdividing the total energies into Hartree-Fock, correlation,
Kari, Csizmadia
/ Hydride Affinities of OH, Molecules and Ions
4542 Table V. Equilibrium S C F Energies for Oxygen Hydrides As Determined by Least-Squares Polynomial Fitting
Species
Best MO
Present
O H + (32-) O H (2n) O H - (IZg) OH2+ ('BI) OH2 ( ' A i ) OH2- ( * A i ) OH3?+ ( 2 A i ) OH3+ At ) OH3 ( * A I ) OH3- ( I A I )
S C F energies, hartree Hartree-Fock"
-75.0004 '
-14.9827 -75.3998 -75.3665 -15.6375 -16.0410 -15.8342 -75.5039 -16.3233 -76.4380 -76.2886f
EXPtl - 7 5.300 -75.180' -75.847h
-75.001 -75.422 -75.418 -75.668 -76.068 -75.865 -75.534 -76.350 -76.468
-15.421 3h -75.4175c -76.066d
-76.3433e
-76.385
Hartree-Fock energies are estimated from either best M O or present results. Reference 6 . Reference 7 . H. Popkie, H . Kistenmacher, and E. Clementi, J . Chem. Phys., 59, 1325 (1973). e Reference 8. /Calculated at r = 2.2 bohr and 6 = 120°. Table VIII. Inversion Barriers for Nonplanar Oxygen Hydrides
Table VI. Bond Lengths for Oxygen Hydrides r e , bohr Theoretical Present Best MO
M 01ecu le
OH+(~Z-) OH(2n) OH-(' q ) OHl+('Bi) O H ? (' A i ) OH>-('Ai) O H AI) O H i + (' A i ) OH3(*Ai) OH~-('AI)
1.909 1.811 1.806 1.86 1.79 1.95 2.00 1.82 1.96
1.7950 1.795" 1.781'
ExDtl OH*+ OH2 OH>OH3+ OH?
1.9443 1.8342 1.834 1.89f 1.81
1 .77aC
a
I .823d
Inversion barrier, kcal/mol Present Best M O
Molecule
1.91'
20.6 31.6 13.1 1.2 0.6
1.50
Table V, footnote e .
Table IX. Hartree-Fock Ionization Potentiels of Oxygen Hydrides
m
Molecule
Table V, footnote b. Table V, footnote il Table V , footnote a . d . Reference IO. ' T. H. Dunning, R. M. Pitzer, and S. Aung, J . Chem. Phys.. 57, 5044 (1972). f H . Lew and I. Heiber, ibid.,58, 1246 (1973).
Theoretical, eV Present Best M O
OH OH2 OH,+ OH3
I I .4"
11.3 11.0 22.3 3.1
Exptl, eV 13.36 12.65
Table VII. Bond Angles ( 6 ) for Oxygen Hydrides Table V, footnote b. (1973).
4,deg Molecule
Present
OH2+ OH2 OHzOH3?+ OH3+ OH3 OH3-
113.4 105.2 105.4 120.0 114.2 113.0 120.0
Theoret ica I Best M O
Exptl 1 10.50d
106.6"
104.Sh 1 10.4c
a Table V, footnote d . Table V, footnote e . L. Basile, P. LaBonville, J. R. Ferraro, and J. M. Williams, J . Chem. Phys., 60, 198 1 (1974). Table VI, footnotef.
and AEZpv(Re) are negligible and can be ignored. Thus, considering the known experimental ionization potentials of OH and O H 1 and the Hartree-Fock energies listed in Table V, AEcM(Re) may be estimated as 1.90 eV for OH and 1.77 eV for OHz. Based on these results, the ionization potentials listed in Table IX and illustrated in Figure 1 may be considered to differ from the experimental values by approximately 1.75 f 0.25 eV. The electron affinity of a molecule (M) may be subdivided into energy differences in a manner analogous to the subdivision of the ionization potential. EA(M) = AEHF(')(Re)
relativistic, and zero-point energy contributions, the I , of a molecule may be written as
I,(M) = AEHF'(Re)
+ AEcM(Re) -k AERM(Re)
+ AEzpM(Re)
where and where the remaining energy differences are written in an analogous manner. For a stable molecule (M), it is generally assumed that both AEHF'(Re) and AEc'(Re) are both greater than zero. For the present discussion, it will be assumed that both hER'(Re)
Journal of the American Chemical Society
W . L. Smith, Mol. Phys., 26, 361
+ AEc(M)(Re) + AER(M)(Re)+ AEZp(")(Re)
where AEAHF(')(Re)
= EHF('-)(Re)
- EHF(')(Re)
and where the other total energy component differences are defined similarly. As before, we shall assume that A E R ( ~Re) )( and AEzp(')(Re) are negligible. For a stable negative ion to be formed in this electron capture process, AEHF(')(Re) must generally be a negative number or a small positive number. In the event that EHF(M)(Re)is positive and the negative ion is stable, then the binding energy of the excess electron must be attributed to correlation, relativistic, and zero-point energy contributions.
1 99:14 1 July 6,1977
4543 Unfortunately, few experimental oxygen hydride proton affinities have been determined to reasonable accuracies. Thus, the formulation of A H + in terms of theoretical components is of little use for the determination of exact molecular correlation and relativistic energy corrections. However, if one determines a single correlation-relativistic correction for the hydride series, then, assuming the hEc+R'(Re) remains constant for each increased oxygen-hydrogen bond, one can make an effort to more exactly approximate experimental A H + from approximate Hartree- Fock calculations. One of the more recent experimental determinations22of the proton affinity of OH2 lists a value of - 166 f 2.3 kcal/mol. The zero-point energy difference between OH3+ and OH2 has been previously estimated23as 8.8 kcal/mol. Using these values and the Hartree-Fock energies, A E c + R ( O ~may ~ ) be calculated to be 2.2 kcal/mol. For the reaction
1
i
z 0
oc
I
O-
1
I
$;-
-I
0 -200
OH-400
Figure 1. Ionization potentials of oxygen and its simple hydrides
The electron affinities (eV) calculated from the S C F energies listed in Tables I and V are 2.5 I , 1.2 I , 0.9 I , and 5.63 for H, 0,O H , and OH2, respectively, and a number IEc(H20)I > IEc(H3Of)l
A recent C1 c a l c ~ l a t i o ngives ~ ~ numerical confirmation to the
above statement for the H*O-H30+ pair. The proton affinities listed in Table X and illustrated in Figure 2 are computed without including any contributions due to correlation and relativistic effects. It is understood that these A H + will be less than the experimental A H +by a t least I O kcal/mol. Hydrogen and Hydride Affinities. The hydrogen ( A H )and hydride affinities ( A H - )can be defined for the reactions M+H+MH and M
+ H--
MH-
in a manner analogous to the definition of proton affinities. For both cases, the relativistic energy differences will be assumed to be negligible and hEc+R(M)(Re) may he reduced to A E c ( ~ )Re). ( For hydrogen affinities, since the bare hydrogen atom possesses no correlation energy, AEc(M)(Re)will in general be a negative number. A reliable estimate to the correlation energy contribution to the A H of a molecule M can be made by
Kari, Csizmadia
/
Hydride Affinities of OH,, Molecules and Ions
4544 Table X. Proton Affinities of Oxygen and Its Hydrides
Theoretical, kcal/mol Present Hartree-Fock
Species
0 0-
-119 -409 -684 -149 -423 84 -177 -379
02-
OH OHOH2 OH1 OH2-
Estimated.
Table XI. Hydrogen Affinities of Oxygen Hydrides
Exptl or best estimate, kcal/mol
-120 -397
-107" -384"
-154 -408 84 -177 -379
O+ 0 0OH+ OH OHOH>+ OH2 OH>-
-395" -166h
Reference 20.
Theoretical, kcal/mol Present Hartree-Fock
Exptl or best estimate
-80.7 -71.5 -80.7 -104 -9 1.6 33.3 -1 15 62.8
-80.7 -69.2 -76.1 -99.2 -90.1 18.8 - I I8 63.2
