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Bond-orbital study of the angular geometry of small polyatomic molecules
Volume 136, number 3,4
CHEMICAL PHYSICS LETTERS
8 May 1987
BOND-ORBITAL STUDY OF THE ANGULAR GEOMETRY OF SMALL POLYATOMIC MOLECULES Valerio MAGNASCO, Marina RUI and Gian Franc0 MUSS0 Istitutodi Chimica Industrialedell’Universit&16132 Genoa,Italy Received 24 November 1986; in final form 24 February 1987
Ab initio STO-3G bond-orbital (BO) studies of the angular geometry in CH,, NHs, H20, CH*O, CH3F, CH2F2 show that the small second-order delocalization between non-orthogonal SCF BOs is essential to give reasonably accurate results when lone pairs are present on the central atom.
1. Introduction The direct variational construction of non-orthogonal bond orbitals (BOs) has been used to give a convenient description of both intramolecular [ 1] and intermolecular [ 21 interactions. The “chemical” approximation resulting therefrom can be improved by use of perturbation theory by admitting in second order the small pair delocalization between BOs resulting from single excitations from bonding to antibonding orbitals. Ab initio calculation has shown that in such a focal approximation small energy differences such as those occurring in torsional barriers or in intermolecular forces can be obtained with an error which is substantially smaller than the large errors affecting the energies of the individual fragments [ 3 1. In our barrier studies [ 1] the change in conformational energy was studied assuming rigid rotation and experimental geometry. A not very different situation is met in studying the bending of chemical bonds whose length is kept fixed at the experimental value. To explore further the possibilities of our bondorbital approach, we report in this Letter the study of the angular geometry of six small polyatomic molecules (CH*, NH3, HzO, CH20, CH3F, CH2F2) by studying the dependence of the BO molecular energy on the interbond angle 2a (fig. 1) when the bond lengths are frozen to the equilibrium values resulting from experiment. The aim of this paper is twofold. First, we want to
verify the reliability of a minimal basis bond-orbital description of the angular geometry in simple molecules and, second, to study the importance that delocalization effects have in determining the optimum geometry. There are good reasons for believing that delocalization, describing small charge-transfer effects between localized bonds [4], can at least in part compensate for the lack of polarization functions in the basis set.
2. Method and results Details of the method can be found elsewhere [ 1,2]. The energy is given by the non-orthogonal
Epstein-Nesbet expansion E=E’O’+E’Z’
,
where
is the energy in the one-configuration mation, and E’*’ = -i
K
IZ-f,, -H,,oSKo 1*/(H,,
BO approxi-
-Hoe)
is the second-order correction arising from the interconfigurational mixing due to single excitations to antibonding orbitals. w. is the one-determinant
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
303
Volume 136, number 3,4
a May 1987
CHEMICAL PHYSICS LETTERS
wavefunction (wf) of doubly occupied BOs whose form is determined by variational optimization of all disposable parameters in E(O), while the wKare singly excited wavefunctions coupled to singlet states. E(O) results from the “chemical” description of the molecule in terms of non-orthogonal bonds, lone pairs and inner shells, whereas Ec2) describes in terms of polarization and delocalization components [ 3,4] the energy lowering associated with the distortion of the bond orbitals by the molecular environment. The interbond angle 2cu subjected to bond-orbital energy optimization is defined in fig. 1, which also gives the coordinate axis used in the calculations together with the specification of the interhybrid angle 19~and the orientation o of the local axis system for the peripheral heavy atoms. The hybridization parameters 8x and w (fig. lb) are variational parameters occurring in the orthogonal transforma-
tion matrix connecting the atomic orbital basis to the hybrid basis in which the orbitals are directed in space. 13~in CH20 and 19~are the angles between the two equivalent sp’(C,) hybrids; 8c in CH3F is the interhybrid angle between any of the three equivalent sp3(C3”) hybrids and the remaining one; 8o in CH2FZ is the angle between the two equivalent sp3( C,,) hybrids pertaining to the CF bonds; w is an angle specifying the orientation of the whole local hybrid system on F. The polarity parameter A gives the mixing of the atomic hybrids forming the bond described by the bond orbital @=N(K~+&,). The following geometrical relations exist between bond angles: CH3X
sin/3=tfisin
CHzX2 cos y= -(;
2a, ‘l+;;;22$2.
H
(a)
H
H (b)
Fig. 1. (a) Interbond angles 2cxsubjected to bond-orbital energy optimization, and (b) definition of interhybrid angles Ox and orientation of the local axis system w.
304
Volume 136, number 3,4
CHEMICAL PHYSICS LETTERS
For CH2F2, which has two independent angular variables, 28 was fixed to the experimental value ( 113.7 o ) , while 2a was varied so as to reach the minimum in the molecular energy. The bond lengths (A) of the six molecules were kept fixed at their experimental values: CH= 1.093 for CH, [5], NHz1.012 for NH3 [6], OH=0.957 forH20 [7],CH=1.1161 andCO=1.2078forCHz0 [8], CH=1.095 and CF=11.382 for CHSF [9], CH= 1.0934 and CF= 1.3574 for CHzFz [lo]. Using experimental values for the bond lengths already accounts for the effects of the different molecular environment on the same bond in different molecules. A minimal STO-3G Gaussian basis [ 111 was used in all calculations, since it is known that angular geometry is usually quite well represented by MO calculations in this basis [ 12 1. In the single-zeta (SZ) approximation the bond orbitals were constructed from suitably directed hybrids in the valence shell, retaining orthogonality at the same centre and the local symmetry of each chemical group [ 11. sp3 hybrids were used for the central atom in CH4 (symmetry Td), CH3X and NH3 (C,,) and for the C atom in CH2X2 (C,,), whereas sp*x: hybrids of C, symmetry were used in the remaining cases. The best values for hybridization and polarity parameters resulting from the one-configuration BO SCF calculation at the equilibrium bond angles 2a,, where the molecular energy has a minimum (see fig. 2 and table 2 later in the paper) have been collected in table 1. We see from table 1 that: (i) the polarities of the single bonds reflect the usually accepted Mulliken electronegativity scale and some dependence on hybridization, with a polarity enhanced for the CT bond of the carbonyl group in CH,O: with respect to other minimal bases [ 2,13 ] the polarities appear to be somewhat underestimated, reflecting a peculiarity of the STO-3G basis; (ii) the hybridization reveals the small sp mixing obtained for N and 0 with a SZ basis without scale factors [ 131 and the large deviations from the ideal value of 120” obtained for sp* hybridization on 0 and F, as well as the regular decrease in s content resulting in the sp3 hybridization on the C atom when gradually introducing F atoms in CH,.
8 May 1987
Table 1 Best values for hybridization (0) and polarity (J.) parameters resulting from the one-configuration BO SCF calculation at the equilibrium bond angles 2ar, CH, ox (deg) &or
6~ (deg) 6% (deg) &-I z:.
109.5 0.957
NH3 94.3 0.868
Hz0 91.4 0.849
CH20
CH,F
CHsF,
119.8 156.2 0.917 1.242 1.024
108.7 167.0 0.934 1.201
106.8 167.1 =’ 0.903 1.198
a) The best orientation of the local axis system on F gives w = 38”.
The dependence of the molecular energy (atomic units, E,,) on 2a is graphically illustrated in fig. 2 for both E(O) (full curves) and E”)+E(*’ (open circles) in the case of the three hydrides and CH20. The values at the minimum, marked with a vertical bar on the plots, have been collected in table 2 and compared with the experimental bond angles in the last column of the table. In the case of CH, the trigonal distortion preserving the C3, symmetry of the methyl group along the z axis (fig. 1) was studied. It is apparent from both fig. 2 and table 2 that the second-order correction brings the minimum geometry into better agreement with experiment, with the exception of CH3F. In CH4 the optimum geometry is dictated by symmetry and delocalization has no effect on it, although lowering the energy. All 2a, values calculated in second order are close to the corresponding MO results not reported in table 2 (CH, = 109.5 ‘, NH,= 105.2”, H20= lOl.O”, CH20= 114.2”, CH3F = 110.6”, CH2F2= 108.7”) *. Hybridization is small in Hz0 and NH3, but the equilibrium bond angle is always much larger than the interhybrid angle, denoting sensible bent bonds in these molecules [ 2,13,15,16]. It is not clear how much this does depend on the basis set, but previous calculations for Hz0 [2] show that there is no substantial difference among various minimal sets (STO3G, MINI-l, MEDIUM), hybridization being only Pople’s tabulated MO data [ 141 show that no better results can be expected when using optimized STG-3G bond lengths instead of the experimental ones used here.
305
E.7UEh
Exptl
80
L so
I ‘O”
Exptt t 110
&I/
-073 ( 100
I 110
2aP
E’SSIEt,
Fig. 2. Effect of interbond delocalization (open circles) in determining the equilibrium bond angles 2cuin the SCF bond-orbital description of the ‘A, ground states of H20, NH3, CH4 and C&O.
CHEMICAL PHYSICS LETTERS
Volume 136, number 3,4
8 May 1987
Table 2 One-configuration and multiconfiguration STO-3G bond-orbital energies determining the best bond angles 2a in some polyatomic molecules when bond distances are fixed to their experimental values. A is the difference of the second-order result from the corresponding MO SCF value
CH,
NH3 f-N
CHzO CH,F CHzF,
E”’ (E,,)
2a0
- 39.70060 -55.41999 - 74.94880 - 112.29201 -137.11662 -234.53124
109.5 99.9 96.9 119.2 108.6 105.7
(deg)
E’“‘+E’2’
(E,,)
- 39.72063 - 55.45228 - 74.96308 -112.34561 -137.16174 -234.61231
enhanced by energy optimization of the scale factors of the Gaussian orbitals in the single-zeta basis [ 131 or when the basis itself is split as in recent DZ bondorbital calculations [ 171. The latter two bases, however, exaggerate electrostatic effects yielding too large molecular dipole moments and bond angles which are only readjusted by introducing polarization functions on the heavy atom [ 131. This means that the STO-3G basis is a fairly balanced SZ basis set, which can be used with some confidence for a first evaluation of the angular geometries. Improving the quality of the SZ basis improves the overall second-order result +.
3. Conclusions In the BO approach one can construct the molecular wf step by step, improving by perturbation theory the chemical description resulting from variational optimization of the one-configuration energy. Since the second-order result is quite close to the corresponding MO result, the bond-orbital method allows, in a sense, for an energy investigation of what is essentially a molecular-orbital wavefunction. The first approximation in terms of inner shells, bonds and lone pairs incorporating in an optimum way such important chemical concepts as bond polarities and hybridization, is seen to yield an angu-
A (IO-)E,)
L-I (deg)
Exp.
5.90 1.96 0.37 8.17 7.30 12.58
109.5 105.2 101.0 115.8 110.5 107.0
109.5 106.7 104.5 116.5 108.5 108.3
Ref.
151
[61 [71
181 ]91
1101
lar geometry which is not unreasonable (column 2 in table 2) but evidently fails in the presence of lone pairs on the central atom (NH3 and, particularly, H20). The second approximation accounting for delocalization between polarized bond orbitals improves substantially the latter case, giving angular geometries which are well within the corresponding MO geometries and differ on the average by no more than 1% from the experimental ones. The only anomaly, for which we have no explanation, seems to be CHSF, but the same result is also found in the corresponding MO calculation. The little distortion of the charge distribution of each localized bond by the molecular remainder, accounted for in second-order perturbation theory, seems to play an essential role for a correct description of the angular geometry in the minimal basis. This is in line with what we have already found for barriers [ 1] and for the H bond in the linear water dimer [ 21.
Acknowledgement We acknowledge support by the Italian Ministry of Public Education (MPI 40% and 60%) and by the National Research Council (CNR) under grants in Theoretical Chemistry.
References As an example, the basis MEDIUM used elsewhere [ 2,131 gives for Hz0 2ao=99.7” and 2a= 104.1 a after second-order correction. This basis is however much more expensive in terms of computer time.
[ 1] G.F. Musso and V. Magnasco, Mol. Phys. 53 (1984) 615. [ 21 V. Magnasco, G.F. Musso, C. Costa and G. Figari, Mol. Phys. 56 (1985) 1249.
Volume 136, number 3,4
CHEMICAL PHYSICS LETTERS
[ 31 V. Magnasco, G.F. Musso, G. Figari, M. Rui and C. Costa, Gazz. Chim. Ital. 116 (1986)) to be published. [4] V. Magnasco and G.F. Musso, Chem. Phys. Letters 87 (1982) 447. [ 51K. Kuchitsu and L.S. Bartell, J. Chem. Phys. 36 (1962) 2470. [ 61 W.S. Benedict and E.K. Plyler, Can. J. Phys. 35 (1957) 1235. [7] W.S. Benedict, N. Gailar and E.K. Plyler, J. Chem. Phys. 24 (1956) 1139. [8] K. Takagi andT. Oka, J. Phys. Sot. Japan 18 (1963) 1174. [ 91 J.L. Duncan, J. Mol. Struct. 6 (1970) 447. [lo] E. Hirota, T. Tanaka, A. Sakakibara, Y. Ohashi and Y. Morino, J. Mol. Spectry. 34 (1970) 222. [ 111 W.J. Hehre, R.F. Stewart and J.A. Pople, J. Chem. Phys. 5 1 (1969) 2657.
308
8 May 1981
[ 121 J.A. Pople, in: Applications of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) pp. 9-11. [ 131 G.F. Musso, C. Costa and V. Magnasco, J. Mol. Struct. THEOCHEM 135 (1986) 267. [ 141 R.A. Whiteside, M.J. Frisch, J.S. Binkley, D.J. De Frees, H.B. Schlegel, K. Raghavachari and J.A. Pople, CamegieMellon Quantum Chemistry Archive, Pittsburgh (198 1). [ 151 R.G.A.R. Maclagan and G.W. Schnuelle, Theoret. Chim. Acta (1977) 165. [ 161 R.G.A.R. Maclagan, Mol. Phys. 41 (1980) 1471. [ 171 G.F. Musso and V. Magnasco, unpublished results (1986).
CHEMICAL PHYSICS LETTERS
8 May 1987
BOND-ORBITAL STUDY OF THE ANGULAR GEOMETRY OF SMALL POLYATOMIC MOLECULES Valerio MAGNASCO, Marina RUI and Gian Franc0 MUSS0 Istitutodi Chimica Industrialedell’Universit&16132 Genoa,Italy Received 24 November 1986; in final form 24 February 1987
Ab initio STO-3G bond-orbital (BO) studies of the angular geometry in CH,, NHs, H20, CH*O, CH3F, CH2F2 show that the small second-order delocalization between non-orthogonal SCF BOs is essential to give reasonably accurate results when lone pairs are present on the central atom.
1. Introduction The direct variational construction of non-orthogonal bond orbitals (BOs) has been used to give a convenient description of both intramolecular [ 1] and intermolecular [ 21 interactions. The “chemical” approximation resulting therefrom can be improved by use of perturbation theory by admitting in second order the small pair delocalization between BOs resulting from single excitations from bonding to antibonding orbitals. Ab initio calculation has shown that in such a focal approximation small energy differences such as those occurring in torsional barriers or in intermolecular forces can be obtained with an error which is substantially smaller than the large errors affecting the energies of the individual fragments [ 3 1. In our barrier studies [ 1] the change in conformational energy was studied assuming rigid rotation and experimental geometry. A not very different situation is met in studying the bending of chemical bonds whose length is kept fixed at the experimental value. To explore further the possibilities of our bondorbital approach, we report in this Letter the study of the angular geometry of six small polyatomic molecules (CH*, NH3, HzO, CH20, CH3F, CH2F2) by studying the dependence of the BO molecular energy on the interbond angle 2a (fig. 1) when the bond lengths are frozen to the equilibrium values resulting from experiment. The aim of this paper is twofold. First, we want to
verify the reliability of a minimal basis bond-orbital description of the angular geometry in simple molecules and, second, to study the importance that delocalization effects have in determining the optimum geometry. There are good reasons for believing that delocalization, describing small charge-transfer effects between localized bonds [4], can at least in part compensate for the lack of polarization functions in the basis set.
2. Method and results Details of the method can be found elsewhere [ 1,2]. The energy is given by the non-orthogonal
Epstein-Nesbet expansion E=E’O’+E’Z’
,
where
is the energy in the one-configuration mation, and E’*’ = -i
K
IZ-f,, -H,,oSKo 1*/(H,,
BO approxi-
-Hoe)
is the second-order correction arising from the interconfigurational mixing due to single excitations to antibonding orbitals. w. is the one-determinant
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
303
Volume 136, number 3,4
a May 1987
CHEMICAL PHYSICS LETTERS
wavefunction (wf) of doubly occupied BOs whose form is determined by variational optimization of all disposable parameters in E(O), while the wKare singly excited wavefunctions coupled to singlet states. E(O) results from the “chemical” description of the molecule in terms of non-orthogonal bonds, lone pairs and inner shells, whereas Ec2) describes in terms of polarization and delocalization components [ 3,4] the energy lowering associated with the distortion of the bond orbitals by the molecular environment. The interbond angle 2cu subjected to bond-orbital energy optimization is defined in fig. 1, which also gives the coordinate axis used in the calculations together with the specification of the interhybrid angle 19~and the orientation o of the local axis system for the peripheral heavy atoms. The hybridization parameters 8x and w (fig. lb) are variational parameters occurring in the orthogonal transforma-
tion matrix connecting the atomic orbital basis to the hybrid basis in which the orbitals are directed in space. 13~in CH20 and 19~are the angles between the two equivalent sp’(C,) hybrids; 8c in CH3F is the interhybrid angle between any of the three equivalent sp3(C3”) hybrids and the remaining one; 8o in CH2FZ is the angle between the two equivalent sp3( C,,) hybrids pertaining to the CF bonds; w is an angle specifying the orientation of the whole local hybrid system on F. The polarity parameter A gives the mixing of the atomic hybrids forming the bond described by the bond orbital @=N(K~+&,). The following geometrical relations exist between bond angles: CH3X
sin/3=tfisin
CHzX2 cos y= -(;
2a, ‘l+;;;22$2.
H
(a)
H
H (b)
Fig. 1. (a) Interbond angles 2cxsubjected to bond-orbital energy optimization, and (b) definition of interhybrid angles Ox and orientation of the local axis system w.
304
Volume 136, number 3,4
CHEMICAL PHYSICS LETTERS
For CH2F2, which has two independent angular variables, 28 was fixed to the experimental value ( 113.7 o ) , while 2a was varied so as to reach the minimum in the molecular energy. The bond lengths (A) of the six molecules were kept fixed at their experimental values: CH= 1.093 for CH, [5], NHz1.012 for NH3 [6], OH=0.957 forH20 [7],CH=1.1161 andCO=1.2078forCHz0 [8], CH=1.095 and CF=11.382 for CHSF [9], CH= 1.0934 and CF= 1.3574 for CHzFz [lo]. Using experimental values for the bond lengths already accounts for the effects of the different molecular environment on the same bond in different molecules. A minimal STO-3G Gaussian basis [ 111 was used in all calculations, since it is known that angular geometry is usually quite well represented by MO calculations in this basis [ 12 1. In the single-zeta (SZ) approximation the bond orbitals were constructed from suitably directed hybrids in the valence shell, retaining orthogonality at the same centre and the local symmetry of each chemical group [ 11. sp3 hybrids were used for the central atom in CH4 (symmetry Td), CH3X and NH3 (C,,) and for the C atom in CH2X2 (C,,), whereas sp*x: hybrids of C, symmetry were used in the remaining cases. The best values for hybridization and polarity parameters resulting from the one-configuration BO SCF calculation at the equilibrium bond angles 2a,, where the molecular energy has a minimum (see fig. 2 and table 2 later in the paper) have been collected in table 1. We see from table 1 that: (i) the polarities of the single bonds reflect the usually accepted Mulliken electronegativity scale and some dependence on hybridization, with a polarity enhanced for the CT bond of the carbonyl group in CH,O: with respect to other minimal bases [ 2,13 ] the polarities appear to be somewhat underestimated, reflecting a peculiarity of the STO-3G basis; (ii) the hybridization reveals the small sp mixing obtained for N and 0 with a SZ basis without scale factors [ 131 and the large deviations from the ideal value of 120” obtained for sp* hybridization on 0 and F, as well as the regular decrease in s content resulting in the sp3 hybridization on the C atom when gradually introducing F atoms in CH,.
8 May 1987
Table 1 Best values for hybridization (0) and polarity (J.) parameters resulting from the one-configuration BO SCF calculation at the equilibrium bond angles 2ar, CH, ox (deg) &or
6~ (deg) 6% (deg) &-I z:.
109.5 0.957
NH3 94.3 0.868
Hz0 91.4 0.849
CH20
CH,F
CHsF,
119.8 156.2 0.917 1.242 1.024
108.7 167.0 0.934 1.201
106.8 167.1 =’ 0.903 1.198
a) The best orientation of the local axis system on F gives w = 38”.
The dependence of the molecular energy (atomic units, E,,) on 2a is graphically illustrated in fig. 2 for both E(O) (full curves) and E”)+E(*’ (open circles) in the case of the three hydrides and CH20. The values at the minimum, marked with a vertical bar on the plots, have been collected in table 2 and compared with the experimental bond angles in the last column of the table. In the case of CH, the trigonal distortion preserving the C3, symmetry of the methyl group along the z axis (fig. 1) was studied. It is apparent from both fig. 2 and table 2 that the second-order correction brings the minimum geometry into better agreement with experiment, with the exception of CH3F. In CH4 the optimum geometry is dictated by symmetry and delocalization has no effect on it, although lowering the energy. All 2a, values calculated in second order are close to the corresponding MO results not reported in table 2 (CH, = 109.5 ‘, NH,= 105.2”, H20= lOl.O”, CH20= 114.2”, CH3F = 110.6”, CH2F2= 108.7”) *. Hybridization is small in Hz0 and NH3, but the equilibrium bond angle is always much larger than the interhybrid angle, denoting sensible bent bonds in these molecules [ 2,13,15,16]. It is not clear how much this does depend on the basis set, but previous calculations for Hz0 [2] show that there is no substantial difference among various minimal sets (STO3G, MINI-l, MEDIUM), hybridization being only Pople’s tabulated MO data [ 141 show that no better results can be expected when using optimized STG-3G bond lengths instead of the experimental ones used here.
305
E.7UEh
Exptl
80
L so
I ‘O”
Exptt t 110
&I/
-073 ( 100
I 110
2aP
E’SSIEt,
Fig. 2. Effect of interbond delocalization (open circles) in determining the equilibrium bond angles 2cuin the SCF bond-orbital description of the ‘A, ground states of H20, NH3, CH4 and C&O.
CHEMICAL PHYSICS LETTERS
Volume 136, number 3,4
8 May 1987
Table 2 One-configuration and multiconfiguration STO-3G bond-orbital energies determining the best bond angles 2a in some polyatomic molecules when bond distances are fixed to their experimental values. A is the difference of the second-order result from the corresponding MO SCF value
CH,
NH3 f-N
CHzO CH,F CHzF,
E”’ (E,,)
2a0
- 39.70060 -55.41999 - 74.94880 - 112.29201 -137.11662 -234.53124
109.5 99.9 96.9 119.2 108.6 105.7
(deg)
E’“‘+E’2’
(E,,)
- 39.72063 - 55.45228 - 74.96308 -112.34561 -137.16174 -234.61231
enhanced by energy optimization of the scale factors of the Gaussian orbitals in the single-zeta basis [ 131 or when the basis itself is split as in recent DZ bondorbital calculations [ 171. The latter two bases, however, exaggerate electrostatic effects yielding too large molecular dipole moments and bond angles which are only readjusted by introducing polarization functions on the heavy atom [ 131. This means that the STO-3G basis is a fairly balanced SZ basis set, which can be used with some confidence for a first evaluation of the angular geometries. Improving the quality of the SZ basis improves the overall second-order result +.
3. Conclusions In the BO approach one can construct the molecular wf step by step, improving by perturbation theory the chemical description resulting from variational optimization of the one-configuration energy. Since the second-order result is quite close to the corresponding MO result, the bond-orbital method allows, in a sense, for an energy investigation of what is essentially a molecular-orbital wavefunction. The first approximation in terms of inner shells, bonds and lone pairs incorporating in an optimum way such important chemical concepts as bond polarities and hybridization, is seen to yield an angu-
A (IO-)E,)
L-I (deg)
Exp.
5.90 1.96 0.37 8.17 7.30 12.58
109.5 105.2 101.0 115.8 110.5 107.0
109.5 106.7 104.5 116.5 108.5 108.3
Ref.
151
[61 [71
181 ]91
1101
lar geometry which is not unreasonable (column 2 in table 2) but evidently fails in the presence of lone pairs on the central atom (NH3 and, particularly, H20). The second approximation accounting for delocalization between polarized bond orbitals improves substantially the latter case, giving angular geometries which are well within the corresponding MO geometries and differ on the average by no more than 1% from the experimental ones. The only anomaly, for which we have no explanation, seems to be CHSF, but the same result is also found in the corresponding MO calculation. The little distortion of the charge distribution of each localized bond by the molecular remainder, accounted for in second-order perturbation theory, seems to play an essential role for a correct description of the angular geometry in the minimal basis. This is in line with what we have already found for barriers [ 1] and for the H bond in the linear water dimer [ 21.
Acknowledgement We acknowledge support by the Italian Ministry of Public Education (MPI 40% and 60%) and by the National Research Council (CNR) under grants in Theoretical Chemistry.
References As an example, the basis MEDIUM used elsewhere [ 2,131 gives for Hz0 2ao=99.7” and 2a= 104.1 a after second-order correction. This basis is however much more expensive in terms of computer time.
[ 1] G.F. Musso and V. Magnasco, Mol. Phys. 53 (1984) 615. [ 21 V. Magnasco, G.F. Musso, C. Costa and G. Figari, Mol. Phys. 56 (1985) 1249.
Volume 136, number 3,4
CHEMICAL PHYSICS LETTERS
[ 31 V. Magnasco, G.F. Musso, G. Figari, M. Rui and C. Costa, Gazz. Chim. Ital. 116 (1986)) to be published. [4] V. Magnasco and G.F. Musso, Chem. Phys. Letters 87 (1982) 447. [ 51K. Kuchitsu and L.S. Bartell, J. Chem. Phys. 36 (1962) 2470. [ 61 W.S. Benedict and E.K. Plyler, Can. J. Phys. 35 (1957) 1235. [7] W.S. Benedict, N. Gailar and E.K. Plyler, J. Chem. Phys. 24 (1956) 1139. [8] K. Takagi andT. Oka, J. Phys. Sot. Japan 18 (1963) 1174. [ 91 J.L. Duncan, J. Mol. Struct. 6 (1970) 447. [lo] E. Hirota, T. Tanaka, A. Sakakibara, Y. Ohashi and Y. Morino, J. Mol. Spectry. 34 (1970) 222. [ 111 W.J. Hehre, R.F. Stewart and J.A. Pople, J. Chem. Phys. 5 1 (1969) 2657.
308
8 May 1981
[ 121 J.A. Pople, in: Applications of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) pp. 9-11. [ 131 G.F. Musso, C. Costa and V. Magnasco, J. Mol. Struct. THEOCHEM 135 (1986) 267. [ 141 R.A. Whiteside, M.J. Frisch, J.S. Binkley, D.J. De Frees, H.B. Schlegel, K. Raghavachari and J.A. Pople, CamegieMellon Quantum Chemistry Archive, Pittsburgh (198 1). [ 151 R.G.A.R. Maclagan and G.W. Schnuelle, Theoret. Chim. Acta (1977) 165. [ 161 R.G.A.R. Maclagan, Mol. Phys. 41 (1980) 1471. [ 171 G.F. Musso and V. Magnasco, unpublished results (1986).