J. Phys. Chem. 1982, 86, 914-917
914
Electronic Structure of PH,. Barrier
Effect of Basis Set and Correlation on the Inversion
Dennls S. Marynlck Department of Chemistry, University of Texas at Arlington, Arlington, Texas 76019
and Davld A. Dlxon' Department of Chemistry, Univershy of Mlnnesota, Minneapolis, Mnnesota 55455 (Received: August 17, 1961)
The inversion barrier in PH3 has been calculated using a near Hartree-Fock basis set of Slater type orbitals with and without correlation effects. Correlation effects were incorporated via the technique of configuration interaction (CI) with all single and double excitations from the valence space to the virtual space (c C 9.0 au) included in the CI. An estimate for quadruple corrections was employed yielding a barrier for PH3 of 34.4 kcal/mol. The geometries for the pyramidal and planar forms of PH3were obtained from SCF-CI calculations using a polarized double {basis set. A set of calculations using a near Hartree-Fock basis set was also done for SH3+giving a barrier of 32.8 kcal/mol. The dependence of the inversion barrier of PH3 on basis set size, computational method, and geometry is also presented.
Introduction Molecular inversion barriers are an important part of conformational analysis, especially for group 5B species of the form AX3.1 An important feature of such studies has been the effect of substituents on the inversion barrier.2 It is, therefore, of interest to know the barrier heights for the simplest unsubstituted structures, the hydrides. The barriers for the hydrides, except for NH3,334are quite large {>20 kcal/mol) and have inversion splittings that are so small that they have not yet been measured experimentally. We have previously calculated the inversion barriers for a range of AX3molecules and ions at the HartreeFock level with large polarized basis sets."12 For a number of calculations (mostly ions), correlation effects on the barrier height have been investigated. These results demonstrate that barrier heights can be calculated at the Hartree-Fock level to better than 10% without the inclusion of correlation effects; this result is in agreement with the predictions of Freed's theorem.13 In this paper, we present an SCF-CI study using Slater-type orbitals (STO) of the inversion barrier of PH3 in order to investigate the effects of electron correlation on the calculated barrier. The inversion barrier in PH3 has been calculated by a number of workers at the SCF level using gaussian basis sets.14-" A number of correlated studies on the inversion barrier of PH3 have been made using either small basis sets or approximate CI schemes;lsJ6 however, these results do not yield general conclusions as to the size of the correlation correction to the barrier. We have attempted to resolve this discrepancy by carrying out large basis set calculations on the barrier to PH, at the SCF-CI level. In addition, because calculations on larger molecules are generally done with more limited basis sets, we have examined the dependence of the geometry and barrier height on the basis set size. Calculations All calculations were carried out with Slater orbital basis seta using computer programs that have been previously d e s ~ r i b e d . ~ For ~ J ~the minimum basis (MB) and minimum basis plus polarization functions (3d) on phosphorus (MB + D) set calculations, the geometry and valence shell exponents were chain optimized for both the planar and 'Alfred P. Sloan Foundation Fellow (1977-81). Camille and Henry Dreyfus Teacher-Scholar (1978-83). 0022-3654/82/2O86-O914$01.25/0
TABLE I: Minimum Basis Sets. Optimized Valence Shell" basis/geometryb
P( 3s)
P(3p)
MB ( P Y ~ ) MB (PI) MB + D ( p y r ) MB + D (pl) MB/atom
1.939 1.998 1.931 1.978 1.881
1.777 1.684 1.728 1.662 1.629
P( 3d)
H( 1s)
1.685 1.647
1.089 1.134 1.129 1.180
Inner shell exponents from ref 19: P(1s) = 14.558, P(2s) = 4.904, P(2p) = 5.501. pyr = pyramidal; p l = planar.
r,
TABLE 11: Double Double 5 Plus Polarization, and Near Hartree-Fock Basis Sets DZ basis: Pa 1s 16.1036 1s 12.0245 2s 6.19095 2s 4.74121 2p 8.14488 2p 4.63044 3s 2.36748 3s 1.49875 3p 2.06453 3p 1.22668 DZ basis: Hb 1s 1.331 2s 1.4054
TZ basis: Pe 3s 2.38210 3s 1.48733 4s 2.82619 3p 1.14523 3p 2.05848 4p 1.71188
TZ basis: Hf 1s 2.459 Is 1.325 2s 2.3
polarization functions P(3d) 2.4 P(3d) 1.4 polarization functions H(2p) 1.5d S(3d) 1.885' H(2p) 1.50d From ref 20. Optimized in this work. See text. Optimized in this work. See text. From ref 21. See text. e Optimized in this work for the atom. From ref 22.
pyramidal forms at the SCF level. Geometry optimization of both the planar and pyramidal forms was carried out (1) P. W. Payne and L. C. Allen in "Modem Theoretical Chemistry. Applications of Electronic Structure Theory", H. F. Schaefer, 111, Ed., Plenum Press, New York, 1977, Chapter 2. (2) (a) K. Mislow, Tram. N.Y. Acad. Sei., Ser. 2,36,227 (1973); (b) J. M. Lehn, Frotschr. Chem. Forsch., 15, 311 (1970). (3) J. D. Swalen and J. A. Ibers, J. Chem. Phys., 36, 1914 (1962). (4) (a) R. M. Stevens, J. Chem. Phys., 61, 2086 (1974); (b) W. R. Rodwell and L. Radom, ibid., 72, 2205 (1980); (c) N. R. Carlaen, L. Radom, N. V. Riggs, and W. R. Rodwell, J. Am. Chem. SOC., 101,2233 (1979). 0 1982 American Chemical Society
Electronic Structure of PH:,
The Jownal of Physical Chemistry, Vol. 86, No. 6, 1982 915
TABLE 111: Optimized Geometries for PH, calculation MB MB DZ
+D DZ + P DZ + P-CI
CGTO -NHF CGTO-DZ + P CGTO-DZ + P CGTO-DZ + P-PNO-CI CGTO-DZ + P-CEPA-PNO experimental This work. STO basis. Reference 15.
r(pyr), A
e(HW(pyr)
r(pl), A
energy
ref
1.444 1.417 1.422 1.406 1.413 1.421 1.408 1.409 1.413 1.417 1.421
93.9 93.2 96.5 95.16 93.74 93.83 95.78 94.6 92.9 92.5 93.83
1.405 1.384 1.384 1.370 1.377 1.379
-341.6503 - 341.7069 -342.4278 -342.4867 -342.6437 -342.4560 -342.4630 -342.3971 -342.5449 -342.5551 -343.42b
a
a a a a 14 24 25 25 25 24
TABLE IV: Total Energies (in au) basis
SCF(PYr )"
SCF-CI(pyr)
SCF(pl)"
SCF-CI( pl)
M B ~ MB + ~b
-341.65026 -341.70480 -341.58678 -341.63488 -341.70687 -341.81477 - 341.627 16 - 341.74235 DZb - 342.42781 - 342.51086 -342.37924 -342.45950 DZ + Pc - 342.48672 -342.64371 -342.42833 - 342.58548 NHFC -342.48894 -342.65006 -342.43044 -342.59453 MBC -341.64893 - 341.70097 -341.58586 - 341.63202 MB + DC - 341.70688 -341.81449 - 341.62716 -341.74197 DZC -342.42716 -342.50988 -342.37915 -342.45914 pyr = pyramidal; pl = planar. Optimized SCF geometries, Optimized SCF-CI geometry using the DZ t P basis.
at the SCF level for the double C (DZ) and double C plus polarization (DZ P) basis sets and at the SCF-CI level for the DZ + P basis. Configuration interaction calculations were performed including all single and double excitations from the occupied valence space to the fullvirtual space except for the calculations with the largest basis set. For these latter calculations, all virtual orbitals with eigenvalues greater than 9.0 au were excluded from the CI. The orbitals used in the CI calculations were taken from the single SCF configuration. The basis sets are summarized in Tables I and 11. The inner shell exponents for the MB and MB + D basis sets for phosphorus were taken from Clementi and Raimondi,l9while the DZ exponents were taken from Roetti and Clementim The H(1s) and H(2s) exponents were optimized at the DZ level and the polarization functions on H(2p) were taken as the weighted average of the 2p, and 2p, exponents determined for PH.21 The 3d polarization function on phosphorus was optimized
+
(5)D. S.Marynick and D. A. Dixon, Faraday Discuss. C ~ MSoc., . 62, 47 (1977). (6)D. S.Marynick and D. A Dixon, R o c . Natl. Acad. Sci. U.S.A.,74, 410 (1977). (7)D. A. Dixon and D. S. Marynick, J. AM. Chern. SOC.,99,6101 (1977). (8)D. S.Marynick and D. A. Dixon, J. C h e M . Phys., 69,498(1978). (9)D. A. Dixon and D. S. Marynick, J. Chern. Phys., 71,2860(1979). (10)(a) R. A. Eadea and D. A. Dixon, J. Chern. Phys., 72,3309(1980); (b) R.A. Eadea, D. A. Weil, D. A. Dixon, and C. H. D o u g h , Jr., J. Phys. CheM., 85, 976 (1981). (11).(a) D. S. Marynick, J. Chem. Phys., 73,3939 (1980); (b) D. S. Marylllck, ibid., 74,5186(1981);(c) D.S.Marynick, CheM. Phys. Lett., 71,101 (1980);76,550 (1980); (d) D. 5.Marynick, J. Mol. Struct., in preas. (12)For other work we: (a) C. E. Dykstra, M. Hereld, R. R. Luccheae, H. F. Schaefer, III, and W. Meyer, J. Chern. Phys., 67,4071 (1977); (b) H.Lischka and V. Dyczmons, C ~ MPhys. . Lett., 23,167(1973);(c) W. R.Rodwell and L. Radom, J. A M . Chern. SOC.,103,2886 (lg81); (d) F. Keil and R. Ahlrichs, C ~ MPhys., . 8,384 (1975); (e) G.H.F.Dierckeen, W. P. Kraemer, and B. 0. €Low, Theor. Chirn. Acta, 36, 249 (1975). (13)K. F. Freed,Chern. Phya. Lett., 2, 255 (1968). (14)J. M. Lehn and B. Munsch, Mol. Phys., 23, 91 (1972). (15)R.Ahlrichs, F.Keil, H. Lischka, W. Kutzelniig, and V. Staemmler, J. Chern. Phys., 63,455 (1975). (16)J. M.Scott and B. T. Sutcliffe, Theor. Chirn. Acta, 41,141(1976). (17)J. D. Petke and J. L. Whitten, J . Chern. Phya., 59,4865(1973). (18)(a) R. M. Stevens, J. Chern. Phys., 66, 1725 (1971). (19)E.Clementi and D. L. Raimondi, J. CheM. Phys., 88,2686 (1963). (20)C. Roetti and E. Clementi, J. Chern. Phys., 60,4725 (1974). (21)P. E.Cade and W. Huo, J. Chern. Phys., 47,649 (1967).
for pyramidal PH3 with the DZ + P basis set at the SCF level. The largest basis set (see Table 11) had a DZ inner shell for P with a triple { valence shell and two sets of polarization functions on P. The valence shell exponents on P were optimized for the atom. A triple f basis set and one set of polarization functions was used for H.22 The CI calculations were carried out for the SCF optimized structures and for the optimum structures obtained from the DZ P-CI calculations. The effect of quadruple excitations can be estimated through the use of Davidson's formula
+
AE, = (1- C 0 2 ) A E D where Cois the leading coefficient of the CI expansion and A E D is the CI energy due to double excitation^.^^
Results and Discussion The optimum values for the h4B valence shell exponents are significantly larger than the corresponding optimum atomic values (see Table I). At the level of the MB set, the P(3s) orbital contracts while the P(3p) orbitals expand on going from the pyramidal to the planar form. Concomitant with expansion of the P(3p) orbitals in the planar form, the H(1s) orbitals contract. The same general effects are observed for addition of a set of 3d functions to P to yield the MB + D basis. The P(3s) exponent shows little change on the addition of a set of 3d orbitals. The P(3p) orbitals become more diffuse and the H(1s) orbitals contract. For the pyramidal structure, the H(1s) exponents are significantly more diffuse than the value of 1.2 typically used in many molecular calculations. The P(3d) orbital exponent is found to increase on inversion. The general conclusions observed for PH3 are also found in calculations on H3S+,except that in the case of the ion, the changes are smaller? We note for H3S' that S(3d) contracts on inversion in contrast to the result found for PH8. The optimum geometry with the MB set is in reasonable agreement with experimenta except that the bond length (22)J. Bicerano, D. S. Marynick, and W. N. Lipscomb, J. AM.Chern. Soc., 100,732 (1978). (23)S . R. Langhoff and E. R. Davidson, Int. J . Quantum Chern., 8, 61 (1974).
The Journal of Physical Chemistry, Vol. 86, No. 6, 7982
916
is too long by 0.02 A. The geometry determined using the MB + D set is in excellent agreement with the experimental values, although this agreement is probably somewhat fortuitous. Still, a similar effect is observed in H3S+.9 The worst geometry is found with the DZ basis, where the bond angle is too large by 2.7’. This is a typical feature of the DZ basis and of any large unpolarized set. The DZ + P basis gives a geometry with a bond distance that is too short by -0.02 A and a bond angle that is too large by 2O. These features are coupled since a shorter bond distance (due to an excess of density between P and H)increasesthe repulsions between the hydrogens, leading to an increased bond angle. The geometry determined at the DZ P-CI level predicts a bond length 0.008 8, less than experiment24and a bond angle that is low by 0.1O. This agreement is excellent considering both the size of the basis and the errors in the experiments. A number of other workers have determined the geometry of PH3with large basis sets14*25728 and, in one instance, with correlation effects included;26these results are also given in Table 111. We note that our SCF total energy is the best yet reported for PH3. (See Table IV.) Our energy is very close to the estimated Hartree-Fock limit of -342.4960 a d 5 and is almost 0.01 au better than the previous “best”SCF energy of -342.4787 au.15 Using a DZ P CGTO basis, Walker25 finds a geometry in good agreement with our DZ + P result. Using a slightly larger CGTO basis with 2 sets of 3d functions on P, Lehn and Munsch14 find a geometry in excellent agreement with experiment which is somewhat surprising considering the well-known deficiencies of Hartree-Fock wave functions for giving exact bond distances. Kutzelnigg and Wallmeier26used a DZ + P CGTO basis and find an SCF geometry in reasonable agreement with our structure and that of Walker.25 They also included correlation effects using the PNO-CI and CEPA-PNO scheme~.~’Their PNO-CI geometry is in good agreement with our result except their bond angle is ~ 0 . larger. 2 ~ The CEPA-PNO structure shows slightly better agreement with experiment than does our structure for the bond length but is worse for the bond angle. The CEPA-PNO geometry has a longer bond length and smaller bond angle than the DZ + P-CI geometry. The geometries for the planar form show a decrease in bond length as compared to the pyramidal structure. This is typically observed for most molecules that invert, especially for those with central atoms from beyond the first row. The decreases range from 0.033 A at the DZ P level to the shortening of 0.039 A found for the MB set. The DZ P-CI result is intermediate. A similar decrease in bond length for the planar form was found by Lehn and Munsch.14 The inversion barriers uncorrected for zero-point effects are shown in Table V. The values depend strongly on the quality of the basis set. The most reliable value for the inversion barrier in PH3 is the SCF-CI value determined with our NHF basis and corrected for the effect of quadrupole excitations. This gives a barrier of 34.4 kcal/mol for PH3. We will compare all values to this standard quantity. The minimum basis set at the SCF level does
+
+
+
+
~~~
(24)(a) C.A. Burrus, Jr., A. Jache, and W. Gordy, Phys. Reu., 95,700 (1954),microwave; (b) V.M. McConaghie and H. H. Nieleen, J. Chern. Phys., 21, 1836 (1963),infrared; (c) see ala0 M. H. Sirvetz and R. E. Weston, Jr., ibid., 21, 898 (1953),who obtain r(P-H) = 1.418 A and B(H-P-H) = 93.37. (25)W. Walker, J. Chem. Phys., 59, 1537 (1973). (26)W.Kutzelnigg and H. Wallmeier, Theor. Chirn. Acta, 51, 261 (1979). (27)W. Kutzelnigg, in “Methods of Electronic Structure Theory”, H. F.Schaefer, 111, Ed., Plenum Press, New York, 1977,p 129.
Marynick and Dixon
TABLE V: Inversion Barriers of PH, (in kcal/mol) basis set
SCF
MB MB + D DZ DZ + P NHF~ M B ~ MB + ~b DZb CGTO-NHF CGLobe-DZ + P CGTO-NHFC CGTO-NHF~
39.8 50.0 30.5 36.6 36.7 39.6 50.0 30.1 36.7 40.1 37.6 37.8
CGTO-DZ CGTO-DZ+ D
22.8 34.4
CI
ref
43.9 45.4 32.2 36.5 34.8 (34.4)e 43.3 45.5 31.8
a
a a
a a a a
a 14 17 15 15 15 15 16 16
34.5 (1EPA)f 35.6 (PNO-CI)‘ 34.9 ( C E P A ) ~ 22.6 30.2
a This work. STO basis. At optimized geometry from SCF-CI calculation with a DZ + P basis. Large Smaller NHF basis. Includes 1 set o f f orbitals on P. NHF basis. Includes 1 set of f orbitals o n P. e Value obtained after correcting for the effect of a quadruple excitations. f Localized and canonical orbitals. Localized orbitals. Use of canonical orbitals gives 35.7. Localized orbitals. Use of canonical orbitals gives 35.4.
quite well in predicting the barrier for PH3, giving a result that is high by 16%. In contrast, inclusion of correlation effects via CI at this level almost doubles the error, giving a barrier that is 28% too high. Since the lone pair belongs to a unique symmetry species (valence shell only) in the planar form, it is essentially uncorrelated, leading to a destabilization of the planar geometry. The MB D basis set gives a significant error, being 45% high at the SCF level; this error is partly compensated for by the inclusion of CI, where the error is reduced to 32%. The DZ basis set gives a barrier that is low by 11%. Such behavior is typical of this basis set in predicting inversion barriers in these compounds. Inclusion of CI at the DZ level brings the barrier into better agreement with the standard value (6% error). The barrier at the DZ + P level is high by 6% at the SCF level and there is essentially no CI effect at this level. The barrier determined with the SCF method with the NHF basis is in good agreement with the SCF barrier determined with the DZ P basis showing the basis set convergence at this computational level. The SCF barrier using the NHF basis is too high by 7% as compared to the standard value. The barrier determined by Munsch and Lehn14 using a CGTO basis of NHF quality yields a barrier at the SCF level in exact agreement with our result. The barrier determined by Petke and Whitten” is too high as compared to other SCF values with the error most likely being due to their contraction scheme. The barrier determined by Ahlrichs et al.15 at the SCF level is 1 kcal/mol higher than our SCF result and that of Lehn.14 This is somewhat surprising since the only significant difference in the basis seta is the presence of a set of f orbitals in the work of Ahlrichs et al.15 A contribution of 2.5% seems quite large to attribute to the presence off orbitals in the basis set at the SCF level. The CI studies of Ahlrichs et were carried out with a slightly smaller basis set than employed in their best SCF calculations and the best method (CEPA) gives results in reasonable agreement with our CI results. The CEPA results depend somewhat on the orbital basis set employed and the calculation which employed a localized basis set show the best agreement with our standard result. Scott and Sutcliffelehave also carried out a study of the M i set dependence of the inversion M e r in PH3 using CGTO basis sets with SCF and SCF-CI
+
+
917
J. Phys. Chem. 1002, 86,917-921
TABLE VI: Correlation Effects on Molecular Inversion Barriers (in kcal/mol) molecule SCF CI A Ea ref CH,CH,“3
“3
H30+ H,O+ SiH3PH, SH3+ a AE
2.0 1.5 5.6 6.2 2.3 2.0 26.2 34.4 32.8
1.7 1.7 5.2 5.9 1.5
1.3 27.3 36.7 33.6
= E(C1) - E(SCF).
t0.2 -0.2 t0.4 + 0.3 + 0.8 t 0.7 -1.1 -2.3 -0.8
6 12a 12c 4a 12c 12e 12d b b
This work.
techniques. They used the experimental geometry for PH3(pyr) and the same experimental bond distance for PH,(pl) and performed only a partial CI. They also studied the barrier using an MB D STO basis set and found results virtually identical with ours. The best calculations (Basis Set DZ02 of ref 16) are shown in Table V with no polarization functions and with polarization functions only on P(DZ D). The DZ results at the SCF level are very low compared to our standard value and with our DZ results. The DZ + D result at the SCF level is in reasonable agreement with the DZ + P result showing that the polarization functions on H play a smaller role than the polarization functions on the central atom. A similar result has been previously observed for amines.’Ob The trends that we observed at the CI level are reproduced by Scott and Sutcliffe’s calculations; CI increases the barrier at the DZ level and decreases it at the DZ + D level. The effects are, however, much larger than we observed. Comparison of these results using CGTO basis sets with our STO calculations demonstrates the importance of obtaining a properly contracted basis set in order to reproduce calculations using an STO basis. The size of the correlation correction to the inversion barrier using the NHF basis is surprising considering the magnitude of the correlation correction at the DZ P level. Although a 5% correction due to correlation effects is
+
+
+
small, the magnitude, 2.3 kcal/mol, is of chemical importance. This magnitude is larger than what has previously been observed for other hydrides. The barriers and correlation effects in other hydrides are shown in Table VI. Since a large correlation effect was found for PH3, we calculated the inversion barrier in SH3+using the same size basis set as employed in the PH3 calculations.28 The total SCF energies are SH,+(pyr) = -398.99622 au and SH,+(pl) = 398.94274 au, while the SCF-CI energies are SH,+(pyr) = -399.16892 au and SH3+(pl)= -399.11644 au. This yields barriers to inversion of 33.6 and 32.9 kcal/mol at the SCF and SCF-CI levels, respectively. Correcting for the effect of quadrupole excitations yields a barrier of 32.8 kcal/mol for SH3+. Thus, correlation lowers the barrier in SH3+by 0.8 kcal/mol using an NHF basis. This is in contrast to the result found with a DZ P basis where correlation corrections increase the barrier by 0.6 kcal/mol. The correlation corrections show certain trends. For inversion barriers of compounds containing second row ( n = 2) atoms, most calculations show that correlation increases the barrier, with the largest correction being found for H30+. (The exception is the calculation for CH< using SCEP). The barriers for compounds containing third row atoms show the opposite effect with correlation corrections decreasing the size of the inversion barrier. The effect in this row is largest for PHB. In conclusion, we have calculated the inversion barrier in PH3 to be 34.4 kcal/mol and the inversion barrier in SH3+to be 32.8 kcal/mol. A moderate sized correlation effect is observed on the inversion barrier. This correlation effect is shown to be quite basis set dependent and is found only when very large basis sets are employed.
+
Acknowledgment. D. S. Marynick acknowledges the Robert A. Welch Foundation (Grant Y-743) and the Organized Research Fund of the University of Texas at Arlington for partial support of this work. (28) The baais set is taken from ref 22. The geometries are the SCFCI optimized structures obtained with a DZ + P basis given in ref 9.
Electron Spin Resonance Monitorlng of Ligand Ejection Reactions Following Solid-state Reduction of Cobalt Globin and Cobalt Protoporphyrln Complexes L. Charles Dlcklnson’ Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 0 1003
and M. C. R. Symons Department of chemistry, University of Leicester, Leicester, England LE 1 7RH (Received: April 4, 198 1; In Final Form: October 29, 198 1)
Cobaltihemoglobin, isolated a and 6 chains, and cobaltimyoglobin in aqueous solution at neutral pH were irradiated at 77 K with 3 Mrd of @ C ‘o y-rays. These diamagnetic Co(II1) species are converted to paramagnetic Co(I1) species in high yield. The EPR spectra are identical with those of authentic six-coordinate cobalt(I1) porphyrins. Upon partial annealing of the species, the EPR spectrum transforms irreversibly to that of a five-coordinatespecies, indicating that at 77 K these cobaltiglobins are “cobaltichromes”in analogy to the hemichromes of the native iron species. Differences are seen among all of the six-coordinate,reduced protein ligated species. This ejection of the sixth ligand with thermal annealing after addition of one electron to the d,2 orbital of the cobalt porphyrin also occurs in aqueous glasses of cobalt protoporphyrin IX in pyridine, n-butylamine, or quinuclidine. The five-coordinate species in aqueous media are stable with annealing to room temperature.
A number of approaches have been made toward an understanding of the bonding of ligands to hemoglobin. 0022-3654/82/2086-0917$01.25/0
Although X-ray crystallography offers a clear, static picture of geometry and bonding, other techniques contribute to 0 1982 American Chemical Society
