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Anisotropy of electron-density distribution around atoms in molecules: N, P, O and S atoms
Journal of Molecular Structure (Theo&em), 205 (1990) 191-201 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
191
ANISOTROPY OF ELECTRON-DENSITY DISTRIBUTION AROUND ATOMS IN MOLECULES: N, P, 0 AND S ATOMS
SHIGERU IKUTA General Education Department, Tokyo 152 (Japan)
Tokyo Metropolitan
University,
Yakumo, Meguro-ku,
(Received 24 April 1989)
ABSTRACT Electron densities around N, P, 0 and S atoms in HCN, HCP, OCHx and SCHz molecules were calculated at various distances from the nuclei in two or three directions by using the HartreeFock method with the 6-311G (2d,p) and MC-311G (2d,p) basis sets. Van der Waals radii (in the isolated molecules) were estimated at the position where the electron density is 0.005 a.u. Theoretical radii are in fairly good agreement with the experimental values in the crystals estimated by Nyburg and Fareman. Smaller polar flattening is obtained in the 0 atom of OCHx and larger polar flattening is confirmed in the S atom of SCH2. The electron densities in the minor direction are larger than those in the major direction in both the N atom of HCN and the P atom of HCP at over the wide range of the distance from the nuclei. Negative polar flattening was found for the P atom of the HCP molecule.
INTRODUCTION
Van der Waals radii of non-bonded atoms in molecules are one of the basic physical properties of chemical compounds [ 11.These radii are often used as one of the parameters in the analytical potential to compute the interaction energies between the molecules, where the spherical radii are used [ 21. Nyburg and Fareman [ 31 estimated the van der Waals radii using the crystallographic data of the atoms bonded to the carbon atom. These authors pointed out that some atoms (bonded to carbon) have two different radii: the major ( rs) and minor radii (rh). The radius in the major direction is usually larger than that in the minor one; this behaviour is called polar flattening. Bader et al. [4] pointed out that the atoms and bonds in molecules are uniquely defined by the topology of the molecular electron-density distribution, and recently proposed the volume of an atom in a molecule [ 51. However, there are few reports which quantitatively discuss the anisotropy of van der Waals radii and electron-density distribution around atoms in molecules. Recently, the present author [ 61 clearly indicated that an anisotropy of electron-density distribution exists around halogen atoms in molecules (HX and 0166-1280/90/$03.50
0 1990 Elsevier Science Publishers B.V.
192
CH3X) and that the repulsion energies of HX dimers (in sideways-on and head-on contacts) reflect its anisotropy. He also pointed out that the major ( rs) and minor (r,,) radii of atoms in molecules may be predicted by the position where the electron density is 0.005 a.u. The main purpose of the present study was to determine the electron-density distribution around N, P, 0 and S atoms in HCN, HCP, OCHz and SCH, molecules, respectively. Anisotropy of both electron-density distribution and van der Waals radii was obtained except for the N atom. In the P atom of the HCP molecule, the minor radius (r,J is 0.03 A larger than the major one (rJ; this result is very special and limited being contrary to those of other atoms (0, S and halogen atoms) in molecules. Electron densities around 0 and S atoms will be calculated in three directions: one relates to the minor radius ( rh) and the other two relate to the major radii (r, and r; ); a hyperconjugation due to a CH2 group is present in the f, direction.
I
x ->major
1 X4
or P
X-0
or
S
METHOD
Electron densities around atoms (N, P, 0 and S) in molecules (HCN, HCP, OCHz and SCH2, respectively) were calculated at the Hartree-Fock level of theory using the 6-311G (24~) basis set for the first-row atoms [7] and the MC-311G (24 basis set for the second-row atoms [8]. The HF/6-31G (d,p) method was used to optimize the geometries of the molecules, which are shown in Fig. 1. The electron densities around the N atom of HCN and the P atom of HCP were calculated in two directions relating to the major ( rs) and minor radii ( rh). The densities around the 0 atom of OCHz and S atom of SCH2 molecules were computed in three directions (r,, r: and rh). One of the three relates to the minor radius (rh) and the other two to the major radii (r, and r; ) . Electron densities in the r: direction may reflect a hyperconjugation due to the CH, group especially in the SCH, molecule. All the calculations were performed using the North-Dakota version of the GAMESS programme package [ 9,101.
193 1.059
1.063
1.133
H-C-N (0.268)
CO.1 17)
E=-92.877
H,
’ CL’
1.515
H-C-P C-0.386)
I38
(0.1194X-0.326X0.133)
(I.“.
,,“.r;m
Er379.107438
(
p2~’
a.”
~*>,4:,‘“’ (-0.282)
I
1.597
0 (-0.431)
E=- 1 13.869743
5 (-0.0576)
a.“.
E=-436.509953
a.“.
Fig. 1. GeoFetries of the study compounds optimized using the HF/6-31G (dg) method (bond lengths in A and bond angles in degrees). Total energies and Mulliken atomic charges are also shown. RESULTS AND DISCUSSION
N atom in HCN molecule Electron densities at various distances from the N nucleus in the minor direction, calculated at the Hartree-Fock level of theory with several basis sets [ 11-131, are listed in Table 1. Electron density at the position of the N nucleus (0.0 A in Table 1) computed using the HF/6-31G (dg) method [11,12] is somewhat smaller than those obtained using other methods; a quite extended basis set is indispensable when obtaining the exact electron density at the nucleus position. The data at other positions are quite similar to one another. The computed electron densities in the major direction are summarized in Table 2. The values at the same distance from the nucleus are also very similar to one another. These results clearly indicate that the basis-set dependency is negligible if the extended basis set can be used. Boyd and Wang [ 141 and the present author [ 61 have recently pointed out that the electron correlation has almost no effect on the electron-density distribution. Electron densities in both major and minor directions, computed using the HF/6-311G (2&p) method [ 71, are plotted in Fig. 2 as a function of the distance (I> 1.0 A) from the N nucleus. Electron densities in the minor direction are slightly larger than those in the major direction over the wide range of the distance from_the nucleus, and both values in two directions are equal (0.005 a.~. ) at 1.50 A from the nucleus (I= 1.5 A). The position having an electron density of 0.005 a.u. can be used to estimate the van der Waals radii of nonbonded atoms in isolated molecules [ 61. Thus, both the major and the minor radii of the N atom in the HCN molecule are 1.50 A indicating no anisotropy of van der Waals radii. These radii may be compared with the values obtained experimentally by Nyburg and Fareman [ 31; they estimated van der Waals (major and minor) radii of several non-bonded atoms bonded to a carbon atom using many crystallographic data. Their experimental major and minor radii
194 TABLE 1 Electron densities computed with different basis sets and at various distances (I) from the N nucleus of the HCN molecule in the minor direction (in a.u.) Z (A) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Basis set 6-31G (d,p)
DV95G (d,p )
6-311G (c&p)
6-311G (2d,p)
6-311G (3d,2p)
192.4069 15.4566 1.7905 0.7518 0.5628 0.4026 0.2702 0.1760 0.1128 0.0713 0.0449 0.0284 0.0182 0.0119 0.0078 0.0051 0.0033 0.0021 0.0013 0.0008 0.0005
195.1927 15.4617 1.7612 0.7546 0.5571 0.4003 0.2701 0.1750 0.1119 0.0716 0.0459 0.0294 0.0186 0.0118 0.0074 0.0047 0.0029 0.0019 0.0012 0.0007 0.0005
194.9309 15.4792 1.7900 0.7664 0.5613 0.3990 0.2668 0.1734 0.1117 0.0717 0.0459 0.0294 0.0189 0.0122 0.0080 0.0052 0.0034 0.0022 0.0014 0.0009 0.0005
194.9311 15.4769 1.7849 0.7572 0.5555 0.3982 0.2687 0.1757 0.1133 0.0723 0.0458 0.0289 0.0183 0.0118 0.0076 0.0050 0.0033 0.0021 0.0014 0.0009 0.0005
194.8310 15.4761 1.7799 0.7560 0.5555 0.3974 0.2668 0.1735 0.1117 0.0717 0.0458 0.0291 0.0185 0.0118 0.0076 0.0049 0.0031 0.0020 0.0012 0.0008 0.0005
are both 1.60 A, which are only 0.1 A larger than the present theoretical value. It is very important to note that no anisotropy of van der Waals radii of the N atom exists, but that small anisotropy of electron-density distribution is present. The fact that the electron densities in the minor direction are larger than those in the major one (over the wide range of the distances from the nucleus)is contrary to the results obtained for halogen atoms in molecules [ 61, where the densities in the major direction are always larger. P atom in HCP nwkcule Computed electron densities around the P atom in the HCP molecule are summarized in Table 3; the densities in both the major and the minor directions are listed. The densities are plotted in Fig. 2 as a function of the distance from the P nucleus. As noted above for the HCN molecule, the electron densities in the minor direction are larger than those in the major one over the wide range of distance from the nucleus. Minor and major densities become
195 TABLE 2 Electron densities computed with different basis sets and at various distances from the N nucleus of the HCN molecule in the major direction (in a.u.) Z (A,
Basis set 6-31G (d,p)
DV95G (d,p)
6-311G (c&p)
6-311G (2d,p)
6-311G (3d,2p)
0.0
192.4069
195.1927 15.4779
194.9309 15.4713 1.5716 0.5356 0.3902 0.2880 0.1999 0.1339 0.0883 0.0576 0.0374 0.0243 0.0159 0.0106 0.0071 0.0048 0.0033 0.0023 0.0015 0.0010 0.0007
194.9311 15.4676 1.5707 0.5331 0.3896 0.2892 0.2017 0.1356 0.0897 0.0588 0.0384 0.0250 0.0165 0.0109 0.0074 0.0050 0.0034 0.0023 0.0016 0.0010 0.0007
194.8310 15.4718 1.5711 0.5342 0.3896 0.2887 0.2007 0.1345 0.0887 0.0581 0.0380 0.0248 0.0163 0.0109 0.0073 0.0050 0.0034 0.0023 0.0016 0.0011 0.0007
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
15.4668 1.5858 0.5304 0.3906 0.2891 0.2010 0.1351 0.0889 0.0577 0.0373 0.0242 0.0159 0.0107 0.0072 0.0049 0.0033 0.0022 0.0015 0.0009 0.0006
1.5708 0.5370 0.3901 0.2887 0.2012 0.1345 0.0884 0.0579 0.0379 0.0247 0.0161 0.0105 0.0069 0.0045 0.0030 0.0020 0.0014 0.0009 0.0006
Fig. 2. Electron densities of the N atom in HCN and the P atom in HCP computed in two directions plotted versus the distance from the nucleus. 0, Major direction; 0, minor direction.
equal at about 2.10 A from the P nucleus. The distances having an electron density of 0.005 a.u. are 1.74 A in the major direction and 1.77 A in the minor one; the minor radius (Q, ) is 0.03 A larger than the major one (r,) . The present
196 TABLE 3 Electron densities computed at various distances (I) from the P nucleus of the HCP molecule in the major and minor directions (in a.u.)a I (A)
Minor direction
Major direction
0.0
2118.4078 24.4549 9.0470 2.7569 0.7474 0.2564 0.1521 0.1242 0.1052 0.0853 0.0660 0.0493 0.0359 0.0258 0.0183 0.0129 0.0091 0.0064 0.0045 0.0031 0.0022 0.0015 0.0010
2118.4078 24.1459 8.9192 2.7456 0.7457 0.2410 0.1274 0.0973 0.0805 0.0651 0.0507 0.0384 0.0286 0.0210 0.0154 0.0112 0.0081 0.0058 0.0042 0.0030 0.0021 0.0015 0.0011
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
%-31lG (2d,p) basis set for H and C and MC-3llG
(2d) basis set for P.
radii cannot be compared with the experimental values in the crystals, since Nyburg and Fareman did not report the van der Waals radii of a P atom bonded to a carbon atom. However, it is very interesting to note that the minor radius (rh) is larger than the major one (r8) and that this is the first case indicating a negative polar flattening. (Usually r, is larger than r,,. ) 0 atom in OCH, molecule Electron densities around the 0 atom in the OCH, molecule were calculated in three (r,, r: and rh) directions as shown in the Introduction. The rhdirection relates to the minor radius, and r, and ri to the major one. The hyperconjugation due to the CH, group may be present in the r: direction. Electron densities computed using the HF/6-311G (2dg) method are summarized in Table 4, and are plotted in Fig. 3 as a function of the distance from the nucleus. Near the 0 nucleus the electron density in the r: direction is the largest due
197 TABLE 4 Computed electron densities at various distances from the 0 nucleus of the 0CH2 molecule in three directions (in a.u.)’ Z
rh
rs
rL
295.3107 16.2728 1.8391 1.0007 0.6993 0.4489 0.2734 0.1630 0.0960 0.0561 0.0329 0.0196 0.0120 0.0074 0.0046 0.0029 0.0018 0.0010 0.0006 0.0003 0.0002
295.3107 16.2983 1.6083 0.7933 0.5681 0.3774 0.2382 0.1478 0.0912 0.0562 0.0349 0.0221 0.0143 0.0094 0.0062 0.0041 0.0027 0.0017 0.0011 0.0007 0.0004
295.3107 16.6402 2.0275 1.1139 0.7806 0.5073 0.3145 0.1925 0.1170 0.0707 0.0428 0.0262 0.0163 0.0103 0.0065 0.0041 0.0025 0.0015 0.0009 0.0005 0.0003
6,
0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
“6-311G (2&p) basis set was used. For the three directions, see the illustration in the Introduction.
I
0.020
\
Distance
‘0 \ \
from
the
nucleus
(A)
Fig. 3. Electron densities of the 0 atom of OCHz and the S atom of SCH, computed in three directions plotted versus the distance from the nucleus. 0, rh direction; 0, r, direction; a, r: direction.
198
to the hyperconjugation of CH2, and the value approaches that in the r, direction at about 1.5 A from the nucleus. The electron densities in the minor direction are larger than those in the r, direction only near the nucleus, and both values cross at about 0.9 A. The computed electron density is 0.005 a.u. at 1.46 and 1.45 A from the nucleus in the ri and r, major directions, respectively, and at 1.39 A in the minor direction. Although the polar flattening is very small (0.07-0.06 A), it is certainly present in the 0 atom of the isolated OCHp molecule. The present radii (1.46, 1.45 and 1.39 A) are slightly smaller (by 0.14-0.11 A) than those predicted for the N atom of the isolated HCN molecule noted above. This behaviour [ r( 0) < r(N) ] is in good agreement with the experimental findings [ 31 th$ the radius of the 0 atom (1.54 A) is 0.06 A smaller than the radius (1.60 A) of the N atom. The polar flattening of the 0 atom bonded to the carbon atom was not observed in the crystals [3], and thus the small polar flattening theoretically obtained in the isolated OCHz molecule might be reduced by the addition of the surrounding molecules in the crystals. S atom in SCH, molecule Electron densities around the S atom in the SCH, molecule were calculated in three directions (rs, r: and r,.,) by using the Hartree-Fock method with the 6-311G (2&p) (for H and C atoms [7]) and MC-311G (2d) (for S atom [S]) basis sets. The computed densities are listed in Table 5, and plotted in Fig. 3 as a function of the distance from the nucleus. The computed electron densities in the r: direction are larger than those in the rh and r, directions at all distances from the nucleus; this fact indicates the presence of a quite large hyperconjugation due to CH,. The electron density in the minor direction is 0.005 a.u. at 1.64 A from the nucleus and at 1.70 A in the r, major direction. In another ri major direction this position is 1.83 A, reflecting the large hyperconjugation. The presence of the anisotropy of both van der Waals radii and electrondensity distribution was clearly confirmed in the present study, and the average value of the present theoretical radii (1.64,1.70 and 1.83 A) is quite close to the spherical radius (1.74 A) reported by Bondi [ 151. Nyburg and Fareman [3], however, reported a larger major radius (2.03 A) and a very large polar flattening (rk - r, = 0.43 A) ; the present theoretical polar flattening is less than half the experimental value. Experimental van der Waals radii were estimated by using many crystallographic data of S atoms bonded to a carbon atom. Therefore, the experimental radii and its polar flattening may not be compared directly with the results obtained for a simple molecule like the present SCH2, but may be compared with those for a larger molecule like SC (CR) (CR’ ), where a larger hyperconjugation will be present.
199 TABLE 5 Computed electron densities at various distances (I) from the S nucleus of the SCH, molecule in three directions (in a.~. )”
z 6)
rh
rs
r:
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
2589.0013 27.8327 9.7486 2.5182 0.6256 0.2484 0.1756 0.1436 0.1129 0.0838 0.0595 0.0412 0.0280 0.0189 0.0127 0.0086 0.0058 0.0039 0.0026 0.0017 0.0012 0.0008 0.0005
2589.0013 27.5495 9.6495 2.5168 0.6261 0.2393 0.1632 0.1327 0.1055 0.0801 0.0587 0.0422 0.0300 0.0212 0.0149 0.0104 0.0072 0.0050 0.0035 0.0024 0.0016 0.0011 0.0008
2589.0013 28.0165 9.7480 2.5150 0.6462 0.2879 0.2224 0.1894 0.1535 0.1178 0.0872 0.0632 0.0454 0.0323 0.0229 0.0162 0.0114 0.0080 0.0056 0.0039 0.0028 0.0019 0.0014
“6-311G (2d,p) basis set for C and H atoms and MC-311G (2d) basis set for the S atom. For the three directions see the illustration in the Introduction.
Polarfluttening The position from the nucleus having the electron density of 0.005 a.u. is considered to be a good parameter for estimating the van der Waals radii of an atom in a molecule [ 61. Such predicted radii of N, P, 0 and S atoms in HCN, HCP, OCH, and SCH, are compared with the experimental values estimated from crystallographic data [ 31 in Table 6. (The experimental van der Waals radii of the P atom have not been reported.) The predicted van der Waals radii of the N atom in HCN and the 0 atom in OCHz lie within 0.1 A of the experimental values [ 31. Negative polar flattening ( rh> rJ was first observed for the P atom of the isolated HCP molecule. The electron densities around the P and N atoms in the minor directions are larger than those in the major one over the wide range of distance from the nuclei. Although the difference between the major and
200 TABLE 6 Comparison of theoretical and experimental radii (in A) Atom
r,,
r,
rk
Theoretical N P 0 S
radii” 1.50 1.74 1.39 1.64
1.50 1.77 1.45 1.70
1.46 1.83
rh
r, or r:
Spherical radii’
1.60
1.60
1.70
1.54 1.60
1.54 2.03
1.50 1.74
Experimental radiib N P 0 S
“Predicted values in the present study. bRef. 3. ‘Refs. 15 and 16.
minor radii is not very large, polar flattening is really present in the 0 atom of the isolated OCHz molecule. The minor van der Waals radius of the S atom (1.64 A) is in fairly good agreement with tht experimtntal value of 1.60 A, but the major radius (r: ) of the S atom (1.83 A) is 0.2 A smaller than the experimental one. The larger experimental radius in the major direction might be compared with the theoretical results obtained for a larger molecule like SC (CR) (CR’ ) where a larger hyperconjugation is present, To compare the present theoretical values completely with the experimental ones, the environmental effect on the van der Waals radii of atoms in isolated molecules might need be considered. ACKNOWLEDGEMENT
The author thanks Dr. Mike Schmidt, North-Dakota State University, for use of the North-Dakota version of the GAMESS program.
REFERENCES L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 1939. See, for example, (a) M. Billeter, A.E. Howard, I.D. Kuntz and P.A. Kollman, J. Am. Chem. Sot., 110 (1988) 8385. (b) H.J. Bohm and A. Ahlrichs, Mol. Phys., 54 (1985) 1261. S.C. Nyburg and C.H. Fareman, Acta Crystahogr., Sect. B, 41 (1985) 274. R.F.W. Bader, W.H. Henneker and P.E. Cade, J. Chem. Phys., 46 (1967) 3341. R.F.W. Bader, M.T. Carroll, J.R. Cheeseman and C. Chang, J. Am. Chem. Sot., 109 (1987) 7968.
201 6 8 9 10 11 12 13 14 15 16
S. Ikuta, J. Am. Chem. Sot., in press. R. Krishnan, J.S. Binkley, R. Seeger and J.A. Pople, J. Chem. Phys., 72 (1980) 650. A.D. McLean and G.S. Chandler, J. Chem. Phys., 72 (1980) 5639. M. Dupuis, D. Spangler and J.J. Wendolski, NRCC Software Catalog (QGOl), 1981. M. Schmidt, North-Dakota State University, 1987. W.J. Hehre, R.D. Ditchfield and J.A. Pople, J. Chem. Phys., 56 (1972) 2257. P.C. Hariharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. T.H. Dunning and P.J. Hay, Methods of Electronic Structure Theory, Plenum Press, New York, 1977. R.J. Boyd and L.-C. Wang, J. Comput. Chem., 10 (1989) 367. A. Bondi, J. Phys. Chem., 68 (1964) 441. A. Bondi, Physical Properties of Molecular Crystals, Liquids, and Glasses, Wiley, New York, 1968.
191
ANISOTROPY OF ELECTRON-DENSITY DISTRIBUTION AROUND ATOMS IN MOLECULES: N, P, 0 AND S ATOMS
SHIGERU IKUTA General Education Department, Tokyo 152 (Japan)
Tokyo Metropolitan
University,
Yakumo, Meguro-ku,
(Received 24 April 1989)
ABSTRACT Electron densities around N, P, 0 and S atoms in HCN, HCP, OCHx and SCHz molecules were calculated at various distances from the nuclei in two or three directions by using the HartreeFock method with the 6-311G (2d,p) and MC-311G (2d,p) basis sets. Van der Waals radii (in the isolated molecules) were estimated at the position where the electron density is 0.005 a.u. Theoretical radii are in fairly good agreement with the experimental values in the crystals estimated by Nyburg and Fareman. Smaller polar flattening is obtained in the 0 atom of OCHx and larger polar flattening is confirmed in the S atom of SCH2. The electron densities in the minor direction are larger than those in the major direction in both the N atom of HCN and the P atom of HCP at over the wide range of the distance from the nuclei. Negative polar flattening was found for the P atom of the HCP molecule.
INTRODUCTION
Van der Waals radii of non-bonded atoms in molecules are one of the basic physical properties of chemical compounds [ 11.These radii are often used as one of the parameters in the analytical potential to compute the interaction energies between the molecules, where the spherical radii are used [ 21. Nyburg and Fareman [ 31 estimated the van der Waals radii using the crystallographic data of the atoms bonded to the carbon atom. These authors pointed out that some atoms (bonded to carbon) have two different radii: the major ( rs) and minor radii (rh). The radius in the major direction is usually larger than that in the minor one; this behaviour is called polar flattening. Bader et al. [4] pointed out that the atoms and bonds in molecules are uniquely defined by the topology of the molecular electron-density distribution, and recently proposed the volume of an atom in a molecule [ 51. However, there are few reports which quantitatively discuss the anisotropy of van der Waals radii and electron-density distribution around atoms in molecules. Recently, the present author [ 61 clearly indicated that an anisotropy of electron-density distribution exists around halogen atoms in molecules (HX and 0166-1280/90/$03.50
0 1990 Elsevier Science Publishers B.V.
192
CH3X) and that the repulsion energies of HX dimers (in sideways-on and head-on contacts) reflect its anisotropy. He also pointed out that the major ( rs) and minor (r,,) radii of atoms in molecules may be predicted by the position where the electron density is 0.005 a.u. The main purpose of the present study was to determine the electron-density distribution around N, P, 0 and S atoms in HCN, HCP, OCHz and SCH, molecules, respectively. Anisotropy of both electron-density distribution and van der Waals radii was obtained except for the N atom. In the P atom of the HCP molecule, the minor radius (r,J is 0.03 A larger than the major one (rJ; this result is very special and limited being contrary to those of other atoms (0, S and halogen atoms) in molecules. Electron densities around 0 and S atoms will be calculated in three directions: one relates to the minor radius ( rh) and the other two relate to the major radii (r, and r; ); a hyperconjugation due to a CH2 group is present in the f, direction.
I
x ->major
1 X4
or P
X-0
or
S
METHOD
Electron densities around atoms (N, P, 0 and S) in molecules (HCN, HCP, OCHz and SCH2, respectively) were calculated at the Hartree-Fock level of theory using the 6-311G (24~) basis set for the first-row atoms [7] and the MC-311G (24 basis set for the second-row atoms [8]. The HF/6-31G (d,p) method was used to optimize the geometries of the molecules, which are shown in Fig. 1. The electron densities around the N atom of HCN and the P atom of HCP were calculated in two directions relating to the major ( rs) and minor radii ( rh). The densities around the 0 atom of OCHz and S atom of SCH2 molecules were computed in three directions (r,, r: and rh). One of the three relates to the minor radius (rh) and the other two to the major radii (r, and r; ) . Electron densities in the r: direction may reflect a hyperconjugation due to the CH, group especially in the SCH, molecule. All the calculations were performed using the North-Dakota version of the GAMESS programme package [ 9,101.
193 1.059
1.063
1.133
H-C-N (0.268)
CO.1 17)
E=-92.877
H,
’ CL’
1.515
H-C-P C-0.386)
I38
(0.1194X-0.326X0.133)
(I.“.
,,“.r;m
Er379.107438
(
p2~’
a.”
~*>,4:,‘“’ (-0.282)
I
1.597
0 (-0.431)
E=- 1 13.869743
5 (-0.0576)
a.“.
E=-436.509953
a.“.
Fig. 1. GeoFetries of the study compounds optimized using the HF/6-31G (dg) method (bond lengths in A and bond angles in degrees). Total energies and Mulliken atomic charges are also shown. RESULTS AND DISCUSSION
N atom in HCN molecule Electron densities at various distances from the N nucleus in the minor direction, calculated at the Hartree-Fock level of theory with several basis sets [ 11-131, are listed in Table 1. Electron density at the position of the N nucleus (0.0 A in Table 1) computed using the HF/6-31G (dg) method [11,12] is somewhat smaller than those obtained using other methods; a quite extended basis set is indispensable when obtaining the exact electron density at the nucleus position. The data at other positions are quite similar to one another. The computed electron densities in the major direction are summarized in Table 2. The values at the same distance from the nucleus are also very similar to one another. These results clearly indicate that the basis-set dependency is negligible if the extended basis set can be used. Boyd and Wang [ 141 and the present author [ 61 have recently pointed out that the electron correlation has almost no effect on the electron-density distribution. Electron densities in both major and minor directions, computed using the HF/6-311G (2&p) method [ 71, are plotted in Fig. 2 as a function of the distance (I> 1.0 A) from the N nucleus. Electron densities in the minor direction are slightly larger than those in the major direction over the wide range of the distance from_the nucleus, and both values in two directions are equal (0.005 a.~. ) at 1.50 A from the nucleus (I= 1.5 A). The position having an electron density of 0.005 a.u. can be used to estimate the van der Waals radii of nonbonded atoms in isolated molecules [ 61. Thus, both the major and the minor radii of the N atom in the HCN molecule are 1.50 A indicating no anisotropy of van der Waals radii. These radii may be compared with the values obtained experimentally by Nyburg and Fareman [ 31; they estimated van der Waals (major and minor) radii of several non-bonded atoms bonded to a carbon atom using many crystallographic data. Their experimental major and minor radii
194 TABLE 1 Electron densities computed with different basis sets and at various distances (I) from the N nucleus of the HCN molecule in the minor direction (in a.u.) Z (A) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Basis set 6-31G (d,p)
DV95G (d,p )
6-311G (c&p)
6-311G (2d,p)
6-311G (3d,2p)
192.4069 15.4566 1.7905 0.7518 0.5628 0.4026 0.2702 0.1760 0.1128 0.0713 0.0449 0.0284 0.0182 0.0119 0.0078 0.0051 0.0033 0.0021 0.0013 0.0008 0.0005
195.1927 15.4617 1.7612 0.7546 0.5571 0.4003 0.2701 0.1750 0.1119 0.0716 0.0459 0.0294 0.0186 0.0118 0.0074 0.0047 0.0029 0.0019 0.0012 0.0007 0.0005
194.9309 15.4792 1.7900 0.7664 0.5613 0.3990 0.2668 0.1734 0.1117 0.0717 0.0459 0.0294 0.0189 0.0122 0.0080 0.0052 0.0034 0.0022 0.0014 0.0009 0.0005
194.9311 15.4769 1.7849 0.7572 0.5555 0.3982 0.2687 0.1757 0.1133 0.0723 0.0458 0.0289 0.0183 0.0118 0.0076 0.0050 0.0033 0.0021 0.0014 0.0009 0.0005
194.8310 15.4761 1.7799 0.7560 0.5555 0.3974 0.2668 0.1735 0.1117 0.0717 0.0458 0.0291 0.0185 0.0118 0.0076 0.0049 0.0031 0.0020 0.0012 0.0008 0.0005
are both 1.60 A, which are only 0.1 A larger than the present theoretical value. It is very important to note that no anisotropy of van der Waals radii of the N atom exists, but that small anisotropy of electron-density distribution is present. The fact that the electron densities in the minor direction are larger than those in the major one (over the wide range of the distances from the nucleus)is contrary to the results obtained for halogen atoms in molecules [ 61, where the densities in the major direction are always larger. P atom in HCP nwkcule Computed electron densities around the P atom in the HCP molecule are summarized in Table 3; the densities in both the major and the minor directions are listed. The densities are plotted in Fig. 2 as a function of the distance from the P nucleus. As noted above for the HCN molecule, the electron densities in the minor direction are larger than those in the major one over the wide range of distance from the nucleus. Minor and major densities become
195 TABLE 2 Electron densities computed with different basis sets and at various distances from the N nucleus of the HCN molecule in the major direction (in a.u.) Z (A,
Basis set 6-31G (d,p)
DV95G (d,p)
6-311G (c&p)
6-311G (2d,p)
6-311G (3d,2p)
0.0
192.4069
195.1927 15.4779
194.9309 15.4713 1.5716 0.5356 0.3902 0.2880 0.1999 0.1339 0.0883 0.0576 0.0374 0.0243 0.0159 0.0106 0.0071 0.0048 0.0033 0.0023 0.0015 0.0010 0.0007
194.9311 15.4676 1.5707 0.5331 0.3896 0.2892 0.2017 0.1356 0.0897 0.0588 0.0384 0.0250 0.0165 0.0109 0.0074 0.0050 0.0034 0.0023 0.0016 0.0010 0.0007
194.8310 15.4718 1.5711 0.5342 0.3896 0.2887 0.2007 0.1345 0.0887 0.0581 0.0380 0.0248 0.0163 0.0109 0.0073 0.0050 0.0034 0.0023 0.0016 0.0011 0.0007
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
15.4668 1.5858 0.5304 0.3906 0.2891 0.2010 0.1351 0.0889 0.0577 0.0373 0.0242 0.0159 0.0107 0.0072 0.0049 0.0033 0.0022 0.0015 0.0009 0.0006
1.5708 0.5370 0.3901 0.2887 0.2012 0.1345 0.0884 0.0579 0.0379 0.0247 0.0161 0.0105 0.0069 0.0045 0.0030 0.0020 0.0014 0.0009 0.0006
Fig. 2. Electron densities of the N atom in HCN and the P atom in HCP computed in two directions plotted versus the distance from the nucleus. 0, Major direction; 0, minor direction.
equal at about 2.10 A from the P nucleus. The distances having an electron density of 0.005 a.u. are 1.74 A in the major direction and 1.77 A in the minor one; the minor radius (Q, ) is 0.03 A larger than the major one (r,) . The present
196 TABLE 3 Electron densities computed at various distances (I) from the P nucleus of the HCP molecule in the major and minor directions (in a.u.)a I (A)
Minor direction
Major direction
0.0
2118.4078 24.4549 9.0470 2.7569 0.7474 0.2564 0.1521 0.1242 0.1052 0.0853 0.0660 0.0493 0.0359 0.0258 0.0183 0.0129 0.0091 0.0064 0.0045 0.0031 0.0022 0.0015 0.0010
2118.4078 24.1459 8.9192 2.7456 0.7457 0.2410 0.1274 0.0973 0.0805 0.0651 0.0507 0.0384 0.0286 0.0210 0.0154 0.0112 0.0081 0.0058 0.0042 0.0030 0.0021 0.0015 0.0011
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
%-31lG (2d,p) basis set for H and C and MC-3llG
(2d) basis set for P.
radii cannot be compared with the experimental values in the crystals, since Nyburg and Fareman did not report the van der Waals radii of a P atom bonded to a carbon atom. However, it is very interesting to note that the minor radius (rh) is larger than the major one (r8) and that this is the first case indicating a negative polar flattening. (Usually r, is larger than r,,. ) 0 atom in OCH, molecule Electron densities around the 0 atom in the OCH, molecule were calculated in three (r,, r: and rh) directions as shown in the Introduction. The rhdirection relates to the minor radius, and r, and ri to the major one. The hyperconjugation due to the CH, group may be present in the r: direction. Electron densities computed using the HF/6-311G (2dg) method are summarized in Table 4, and are plotted in Fig. 3 as a function of the distance from the nucleus. Near the 0 nucleus the electron density in the r: direction is the largest due
197 TABLE 4 Computed electron densities at various distances from the 0 nucleus of the 0CH2 molecule in three directions (in a.u.)’ Z
rh
rs
rL
295.3107 16.2728 1.8391 1.0007 0.6993 0.4489 0.2734 0.1630 0.0960 0.0561 0.0329 0.0196 0.0120 0.0074 0.0046 0.0029 0.0018 0.0010 0.0006 0.0003 0.0002
295.3107 16.2983 1.6083 0.7933 0.5681 0.3774 0.2382 0.1478 0.0912 0.0562 0.0349 0.0221 0.0143 0.0094 0.0062 0.0041 0.0027 0.0017 0.0011 0.0007 0.0004
295.3107 16.6402 2.0275 1.1139 0.7806 0.5073 0.3145 0.1925 0.1170 0.0707 0.0428 0.0262 0.0163 0.0103 0.0065 0.0041 0.0025 0.0015 0.0009 0.0005 0.0003
6,
0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
“6-311G (2&p) basis set was used. For the three directions, see the illustration in the Introduction.
I
0.020
\
Distance
‘0 \ \
from
the
nucleus
(A)
Fig. 3. Electron densities of the 0 atom of OCHz and the S atom of SCH, computed in three directions plotted versus the distance from the nucleus. 0, rh direction; 0, r, direction; a, r: direction.
198
to the hyperconjugation of CH2, and the value approaches that in the r, direction at about 1.5 A from the nucleus. The electron densities in the minor direction are larger than those in the r, direction only near the nucleus, and both values cross at about 0.9 A. The computed electron density is 0.005 a.u. at 1.46 and 1.45 A from the nucleus in the ri and r, major directions, respectively, and at 1.39 A in the minor direction. Although the polar flattening is very small (0.07-0.06 A), it is certainly present in the 0 atom of the isolated OCHp molecule. The present radii (1.46, 1.45 and 1.39 A) are slightly smaller (by 0.14-0.11 A) than those predicted for the N atom of the isolated HCN molecule noted above. This behaviour [ r( 0) < r(N) ] is in good agreement with the experimental findings [ 31 th$ the radius of the 0 atom (1.54 A) is 0.06 A smaller than the radius (1.60 A) of the N atom. The polar flattening of the 0 atom bonded to the carbon atom was not observed in the crystals [3], and thus the small polar flattening theoretically obtained in the isolated OCHz molecule might be reduced by the addition of the surrounding molecules in the crystals. S atom in SCH, molecule Electron densities around the S atom in the SCH, molecule were calculated in three directions (rs, r: and r,.,) by using the Hartree-Fock method with the 6-311G (2&p) (for H and C atoms [7]) and MC-311G (2d) (for S atom [S]) basis sets. The computed densities are listed in Table 5, and plotted in Fig. 3 as a function of the distance from the nucleus. The computed electron densities in the r: direction are larger than those in the rh and r, directions at all distances from the nucleus; this fact indicates the presence of a quite large hyperconjugation due to CH,. The electron density in the minor direction is 0.005 a.u. at 1.64 A from the nucleus and at 1.70 A in the r, major direction. In another ri major direction this position is 1.83 A, reflecting the large hyperconjugation. The presence of the anisotropy of both van der Waals radii and electrondensity distribution was clearly confirmed in the present study, and the average value of the present theoretical radii (1.64,1.70 and 1.83 A) is quite close to the spherical radius (1.74 A) reported by Bondi [ 151. Nyburg and Fareman [3], however, reported a larger major radius (2.03 A) and a very large polar flattening (rk - r, = 0.43 A) ; the present theoretical polar flattening is less than half the experimental value. Experimental van der Waals radii were estimated by using many crystallographic data of S atoms bonded to a carbon atom. Therefore, the experimental radii and its polar flattening may not be compared directly with the results obtained for a simple molecule like the present SCH2, but may be compared with those for a larger molecule like SC (CR) (CR’ ), where a larger hyperconjugation will be present.
199 TABLE 5 Computed electron densities at various distances (I) from the S nucleus of the SCH, molecule in three directions (in a.~. )”
z 6)
rh
rs
r:
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
2589.0013 27.8327 9.7486 2.5182 0.6256 0.2484 0.1756 0.1436 0.1129 0.0838 0.0595 0.0412 0.0280 0.0189 0.0127 0.0086 0.0058 0.0039 0.0026 0.0017 0.0012 0.0008 0.0005
2589.0013 27.5495 9.6495 2.5168 0.6261 0.2393 0.1632 0.1327 0.1055 0.0801 0.0587 0.0422 0.0300 0.0212 0.0149 0.0104 0.0072 0.0050 0.0035 0.0024 0.0016 0.0011 0.0008
2589.0013 28.0165 9.7480 2.5150 0.6462 0.2879 0.2224 0.1894 0.1535 0.1178 0.0872 0.0632 0.0454 0.0323 0.0229 0.0162 0.0114 0.0080 0.0056 0.0039 0.0028 0.0019 0.0014
“6-311G (2d,p) basis set for C and H atoms and MC-311G (2d) basis set for the S atom. For the three directions see the illustration in the Introduction.
Polarfluttening The position from the nucleus having the electron density of 0.005 a.u. is considered to be a good parameter for estimating the van der Waals radii of an atom in a molecule [ 61. Such predicted radii of N, P, 0 and S atoms in HCN, HCP, OCH, and SCH, are compared with the experimental values estimated from crystallographic data [ 31 in Table 6. (The experimental van der Waals radii of the P atom have not been reported.) The predicted van der Waals radii of the N atom in HCN and the 0 atom in OCHz lie within 0.1 A of the experimental values [ 31. Negative polar flattening ( rh> rJ was first observed for the P atom of the isolated HCP molecule. The electron densities around the P and N atoms in the minor directions are larger than those in the major one over the wide range of distance from the nuclei. Although the difference between the major and
200 TABLE 6 Comparison of theoretical and experimental radii (in A) Atom
r,,
r,
rk
Theoretical N P 0 S
radii” 1.50 1.74 1.39 1.64
1.50 1.77 1.45 1.70
1.46 1.83
rh
r, or r:
Spherical radii’
1.60
1.60
1.70
1.54 1.60
1.54 2.03
1.50 1.74
Experimental radiib N P 0 S
“Predicted values in the present study. bRef. 3. ‘Refs. 15 and 16.
minor radii is not very large, polar flattening is really present in the 0 atom of the isolated OCHz molecule. The minor van der Waals radius of the S atom (1.64 A) is in fairly good agreement with tht experimtntal value of 1.60 A, but the major radius (r: ) of the S atom (1.83 A) is 0.2 A smaller than the experimental one. The larger experimental radius in the major direction might be compared with the theoretical results obtained for a larger molecule like SC (CR) (CR’ ) where a larger hyperconjugation is present, To compare the present theoretical values completely with the experimental ones, the environmental effect on the van der Waals radii of atoms in isolated molecules might need be considered. ACKNOWLEDGEMENT
The author thanks Dr. Mike Schmidt, North-Dakota State University, for use of the North-Dakota version of the GAMESS program.
REFERENCES L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 1939. See, for example, (a) M. Billeter, A.E. Howard, I.D. Kuntz and P.A. Kollman, J. Am. Chem. Sot., 110 (1988) 8385. (b) H.J. Bohm and A. Ahlrichs, Mol. Phys., 54 (1985) 1261. S.C. Nyburg and C.H. Fareman, Acta Crystahogr., Sect. B, 41 (1985) 274. R.F.W. Bader, W.H. Henneker and P.E. Cade, J. Chem. Phys., 46 (1967) 3341. R.F.W. Bader, M.T. Carroll, J.R. Cheeseman and C. Chang, J. Am. Chem. Sot., 109 (1987) 7968.
201 6 8 9 10 11 12 13 14 15 16
S. Ikuta, J. Am. Chem. Sot., in press. R. Krishnan, J.S. Binkley, R. Seeger and J.A. Pople, J. Chem. Phys., 72 (1980) 650. A.D. McLean and G.S. Chandler, J. Chem. Phys., 72 (1980) 5639. M. Dupuis, D. Spangler and J.J. Wendolski, NRCC Software Catalog (QGOl), 1981. M. Schmidt, North-Dakota State University, 1987. W.J. Hehre, R.D. Ditchfield and J.A. Pople, J. Chem. Phys., 56 (1972) 2257. P.C. Hariharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. T.H. Dunning and P.J. Hay, Methods of Electronic Structure Theory, Plenum Press, New York, 1977. R.J. Boyd and L.-C. Wang, J. Comput. Chem., 10 (1989) 367. A. Bondi, J. Phys. Chem., 68 (1964) 441. A. Bondi, Physical Properties of Molecular Crystals, Liquids, and Glasses, Wiley, New York, 1968.