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An SCF and CI study of the properties of the HCl and CI2 molecules
Volume 70, number
1
CHEMICAL
AN SCF AND Cl STUDY
J H WILLIAMS
LETTERS
15 February
1980
OF THE HCI AND Cl, MOLECULES
OF THE PROPERTIES
and R.D. AMOS
Urllr,ersrry Chemrcal Laboratories. Recewed
PHYSICS
12 October
1979,
Cambrdge,
CB2 I EW. UK
m !inal form 3 December
1979
The onc-elcctron propcrtlcs and polarlzabllltxs of the HCI and Cl2 molecules have been calculated using both SCF and Cl wnvcfunctlons Agreement wtb experunental data. where such data east, 1s found to be very good
There have been many ab imtlo studies of the properttes of small molecules. Some of these were performed to obtam values for molecular properties which are difficult or impossible to measure, for example the higher molecular moments (the quadrupole, octopole and hexadecapole moments) Few values for these propertles exist, and those that do cover a wide range of values [I] _Sunllarly there are few experimental results for the hyperpolarlzabihty tensors of even sunple molecules, yet a knowledge of these propertles IS important to the study of non-hnear optics as weU as various intermolecular phenomena [2] _The purpose of the present study is to obtain values of the multipole moments of the hydrogen chloride and chlorme molecules The dipole polarlzabllitles (Y, and, m the case of HCI, the first hyperpolarlzablhty P and the dlpolequsdrupole polarizabihty A, have also been calculated. Addltlonally, the dlamagnetlc contributions to the magnetizability and the nuclear magnetic shleldmg tensors have been obtained The calculations have been made at different levels of sophntlcatlon. Firstly SCF wavefunctlons close to the Hartree-Fock hmlt have been used. CI calculations have also been made, varymg the number and nature of the orbltals correlated The basis set used m these calculations IS H/3Sl p; C1/7sSp2d. The hydrogen basis consists of the 3s set due to Dunning [3], with a two-component STO-2G p function urlth exponent 1 5, which IS the energy-optunised value. The 7s5p part of the chlorine basis IS a set of contracted gaussians due to DUMmg [4], with additionally a set of STO-2G d functions with exponent 2 60 and a set of gausslan d functions wth exponent 0.165. The exponents of these d functions have 162
been optunlsed so that, as far as possible, the energy of the unperturbed molecule and the energy m the presence of a small electric field are smultaneously mimmised. The bond leng’hs used m the present calculations were 2.409 a0 for HCI and 3.757 a0 for Cl,, which are the experunental values. For HCI the SCF energy IS close to that of the definitive calculation by McLean and Yoshunine [5], theu energy berg -460.1 I2 Eh and ours -460.100 E,. There is correspondmgly good agreement between our one-electron properties and those of McLean and Yoshimme, as can be seen from table I. For chlorme our SCF energy is -9 18.976 Eh which 1s close to that of the best SCF calculation by Straub and McLean [8], who obtained -918.99 Eh_ Sunllarly the one-electron properties (table 2) are m agreement with those of Straub and McLean. The polanzablhtles have been obtained usmg the finite-field method [IO] m which the terms representing a small external field are explicitly added to the hamlltoman and the required polarizabtity components are calculated from the mduced dipole moment At the SCF level, this approach 1s completely equivalent, m the limit of small perturbations [ 111, to the coupled Hartree-Fock method [ 121, but has the advan_tage that it is easily extended to the calculation of hyperpolarizabtities, and gibes a simple method of accurateIy calculating polanzablhtles from CI wavefunctions [13,14]. For HCI, McLean and Yoshlmine [5] have CaIculated some of the polarlzablllty components considered here, at the SCF level and using the finite-field method; their results are included in table I _ The only calculation of the polarizabihty of chlorme would ap-
Volume
1
70. number
Table 1 SCF and CI propertres
CHEMICAL
of hydrogen
E
CI c)
-460
-460.270
-460.3 17
100
Evpenmental
IJ
1.189
1.095
1 096
Q
12 862
12.303
12.335
R
8 808
8 683
8 660
17.274 -44.743
AXd
5.306 141 9
16 222 45.059 5 550 142.0
5.79 f 0 15 [6]
142.1
-144.5
- 144.5
11504
1150 6
1150 5
-144
5
-2.6
-2.6
-148
4 + 25 [6]
2.784
2 822
2 825
3.12
01
2 385
2 439
2.437
2 77 [7]
029
0.138
0.009
Pl
0 017
0 016
0.015
AlI
I 122
1 152
1.160
A,
0.117
0 133
0.133
-0
Table 2 SCF and CI propertres
Q * xd AX d %!I Au&
[7]
and Yoshtmme [S] obtained E = -460 1119E h, cr = 1.215 debye, Q = 12 48 X lo+’ C m*, xd = 44.8 X lO99 J T*, 142 0 ppm, u& = 1150 5 ppm, oar = 2 60 x 10-4~ C* m* I-“, przz = -0 11 X lCiso C3 m3 J-*,A, = 153 X lffso C* m3
b)Sm.gle and double ewtatrons from the valence shell only, 1589 configurations. C)Smgle and double excnations from the valence shell and the chlorme 2p shell, 5708 and polarizabrbtres are referred to the centre of mass as origin
E
* 7 [6]
oil PII
[6]
041 5 539
d!,
-2.3
1.0929 [6] 124 co.4
16.275 45
Aafi “?i Ao&
15 February I980
chlonde CI b)
a
;$=
LETTERS
SCF a)
xd
a)McLean
PHYSICS
CL b)
-918.976
-919.114
106 59 -229
37
23130 1222 5 -99
5
The higher-order
moments
SCF study by Jao et al. [15!, usmg the sum-over-states approximationIn addition to the SCF calculations, we have also used correlated wavefunctions. The CI wavefunctions pear to be a small-scale
of chlonne
SCF a)
1205
confwlatrons.
Experimental
11.90
used were obtained ==14 [9]
tations
by making single and double
exci-
from the SCF wavefunction, e.g. for HCI,
104.70 -23148 231.37 1221
The particular
7
-99.5
“II
6.71
6.73
701c)
Ql
3 19
3.72
4.12
c)
a) Straub and McLean [8], obtamed E = -918 990 Eh, o = 11.27 X 1Cf40 C m*, xd = -228 7 x 10-29 J p, od = 1222.5 ppm b, Valence shell only, 992 configuratrons. c) Bndge and Buckmgham [7], at 6238A.
computational
technique
adopted
is that
due to Roos [ 16) . For HCI the calculations were performed at two levels, firstly just considering correlation of the valence-shell orbitals 40, So, 2~~ and 215, and omitting excitations from the chlorine core, and into the most highly excited virtual orbitals. This generates a total of 1589 configurations of the correct space and spin symmetry, and the result.s.are given in table 1. For HCl, calculations have also been made including excitations from the chlorine 2p shell, i.e. the 30, In, and 163
Volume 70. number 1
la,, orbit&. which generate a total of 5708 space and spin adapted configurations From table 1 it can be seen that correlatmg the chlorine 2p shell makes httle drfference to the one-electron properties Consequently, for the sake of computational economy, rn the calcuiation on the Cl, molecule, only the valence shell was correlated. The lowest energy obtamed for HCI IS that of Bartlett and Srlver [ 171 using many-body perturbation theory. They calculated the valence shell correlatron energy to be -0 2793 Eh, compared to our value of -0.170 1El,. Thus we have obtamed about 60% of the valence-shell correlatron energy for HCl The only other CI calculatron on HCI wluch considers a property other than the energy, IS a calculatron of the drpole moment by Grrmaldr et al. [ 181. There do not appear to be any prevrous Cl calculatrons on the chlorrne molecule. Of the calculated properties of HCI, the one whrch IS most aTenable to comparrson wrth expermrent 1s the dipole moment, for whrch the expernnental value 1s I 0929 D, at the equrhbrrum geometry [6]. The SCF value IS l.lS9 D, about 9% too large, whereas the CI value of 1 096 D IS very close to the experrmental result. There 1s also an experrmental value for the quadrupole moment of HCI, from molecular-beam spectroscopy [6],whrch1sO=(1247+040)X 1040Cn1* (u = 0). Given that the CI values of p and 0 are m agreement wrth expenment, it can reasonably be assumed that the values for the octopole and hexadecapole moments of HCI, and of the quadrupole and hexadecapole moments of chlorme, are also accurate There IS an experimental value for the octopole moment of HCI, from collisronal hne broadenmg [ 19]_ and of the quadrupole moment of chlorine. from vrrral coeffrcrent data [9], but these values are of necessrty approxrmate. The magnetrzabrhty tensor of a molecule has dramagnetic and paramagnetrc parts. The dramagnetrc part is obtamed drrectly m these calculatrons. The paramagnetic part may be obtamed vra rts relatronshrp to the rotationalg-factor [20], which has been measured for HCI [6], from whrch X!x = (6.12 f 0.12) X IO-29 J T-2. Combmmg this value of X!& wrth the measured value of the magnetic anisotropy [6], Ax = (-0 32 + 0 1) X 10mZg J T-I, grves an experimental value for Axd of (5 8 + 0 2) X 1O-7g J T-‘, for the ground vrbratronal state. The calculated value (table 1) IS m good agreement wth this result. Usmg the experimental value for xP together with the calculated value for Xd gives a good 164
15 February 1980
CHLhlICAL PHYSICS LETl-ERS
estunate of the total magnetrzabrhty, X = 40 9 X 1O-2g J T-?. Like the magnetrzabrhty, the nuclear magnetic shreld. mg tensor e has dramagnetrc and paramagnetrc parts. The paramagnetlc component is related to the spm-rotation constant [20] _ Usmg the experimental values for the spin-rotation constants rn HCl [21] , then, for the equihbrmm bond length, (02)~
= -166.0
ppm
= -299.9
ppm
and (o$,)ct
Therefore, usrng the calculated values for c$, and a$, from table 1, we obtam absolute shreldmg values oH = -3 1 4 ppm and uCi = -950 6 ppm This last result wrll be of use ur estabhshmg an absolute shieldmg scale for 13Cl NMR. The amsotropres m the shrelding tensors are, by the same means, Au,
= 2.15 ppm
and Au,,
= 297 S ppm.
The experimental values [6] are AOH = 2 I f 5 ppm and Au,, = 300 + 24 ppm A simrlar analysrs cannot be made for the magnetic properties of Cl2 as no expenmental values are available for the rotatronal g-factor or the spur-rotation constant. One property whrch has been more extensrvely rnvestrgated 1s the molecular polarrzablhty 01 Brrdge and Buckmgham [7] gave expenmental values of OL= 2 893 and Acr = 0.346 X 1040 C* m* J-l for HCI, and Q!= 5.13 and Acu = 2 89 X 1O-4o C’ m* J-l for Cl,. These are dynamrc polanzabrlitres, at 6328 A; the experimental values of the statrc polarizabrhtres, obtained by extrapolatmg the refractrve index data of Landolt and Bornstem [22] to zero frequency, are 01= 2.867 X lo40 C* rn2 JO* for HCl and Q!= 4.99 X 1040 C* m* J-1 for Cl,. Our calculated values are statrc polarrzabrhtres. The results for Cl,, (Y= 4.72 and A(Y = 3.01 X 1Oe40 C* m2 J-1, are m good agreement wrth the expenmental data. The results for HCl, OL= 2.566 and Ao = 0.383 X lOA C2 m2 J-l, are shghtly more III error, possrbly due to omission of “polanzatron” basis functions on the hydrogen rn HCl. Nevertheless the results are the most accurate calculated values for the polarrzabrhties of HCI. There are no experimental val-
Volume 70, number 1
CHEMICAL PHYSICS LETTERS
ues for any of the elements of b or A for HCI As can be seen from table 1 the calculated values of p,, = fizz= vary considerably, possibly due to numerical difficulties, and may not be reliable. The values obtamed for the other components of fi and A should be reasonably accurate The present calculation IS the most comprehensive ab initlo study of the one-electron properties of the hydrogen chloride and chlorme molecuIes The results obtained should be sufficiently accurate to provide useful values for quantities such as the tigher electromc moments of HCl and Cl, for which there are no expenmental results AddItionally, the calculations have provided accurate values for the magnetlzabihty and the NMR shielding constants m hydrogen chloride. The authors thank the Sctence Research Councd for the award of a studentshtp (JHW) and a postdoctoral fellowship
References [ 1 ] S Klehch, m DieIectrtc and related molecular processes, Vol 1, Chemtcal Society Spectahst Penodxal Reports
(1972) ch 7. [2] A D Buckmgham, m Intermolecular mtoractions from dlatomlcs to btopolymcrs, ed B Pullman Whey. New York, 1978), ch. 1. 131 T H. Dunnm_e,J Cbem Phys 55 (1971) 716
15 February
1980
[4] T H. Dunning, Chem. Phys. Letters 7 (1970) 423. [S 1 A.D. McLean and M. Yoshimine, J. Chem. Phyo- 47 (1967) 3256. 161 F. de Leeuw and A. Dynamus. J. Mol. Spectry. 48 (1973) 427. [7] N.J. Bridge and A.D. Buckingham, Proc. Roy. Sot. A 295 (1966) 334. [S] P-A. Straub and A D. McLean. Theoret Chim. Acta 32 (1974) 227. [9J A.D. Kmg,J.Chem.Phys.Sl (1969) 1262. [ 101 H D. Cohen and CC J. Roothaan, J. Chem. Phys 43 (1965) S34. [ll] J A Pople, J.W. Mclver and N.S. Ostlund, J. Chem. Wys. 49 (1968) 2960. [12] R M Stevens, R.hI. Pttzer and W.N. Lipscomb. I. Chem. Phys 38 (1963) 550. [13) R D. Amos, Mol. Phys 38 (1978) 33. [ 141 H-J Werner and W. Meyer, Mol. Phys. 31 (1976) 855. [151 T C Jao, N H-F. Beebe, W.B. Person and J.R. Sabii. Chem Phys. Letters 26 (1974) 474. 1161 B Roos, Chem. Phys. Letters 15 (1972) 153. 1171 R J. Bartlett and D M. Sdver, J. Chem. Phys. 64 (1976) 4578. 1181 F. Cnmaldl, A Lecourt and C. Moser, Symp. Faraday Sot. 2 (1968) 59. I191 P. Isnard, C. Boulet and A. Levy, J. Quant Specky. Radiative Transfer 13 (1973) 1433. 1201 N-F. Ramsey, Molecular beams (Oxford Univ. Press, London, 1956) 1211 F J. Lovas and E. Tlemann, J. Phys. Chem. Ref. Data 3 (1974) 609. Zahlenwerte und Funkttonen aus 1221 Landolt-Bomstein, Physlk, Chemie, Astronomte, Geophysik und Technik. Band II, Ted 8 (Springer, Berlin, 1962)
1
CHEMICAL
AN SCF AND Cl STUDY
J H WILLIAMS
LETTERS
15 February
1980
OF THE HCI AND Cl, MOLECULES
OF THE PROPERTIES
and R.D. AMOS
Urllr,ersrry Chemrcal Laboratories. Recewed
PHYSICS
12 October
1979,
Cambrdge,
CB2 I EW. UK
m !inal form 3 December
1979
The onc-elcctron propcrtlcs and polarlzabllltxs of the HCI and Cl2 molecules have been calculated using both SCF and Cl wnvcfunctlons Agreement wtb experunental data. where such data east, 1s found to be very good
There have been many ab imtlo studies of the properttes of small molecules. Some of these were performed to obtam values for molecular properties which are difficult or impossible to measure, for example the higher molecular moments (the quadrupole, octopole and hexadecapole moments) Few values for these propertles exist, and those that do cover a wide range of values [I] _Sunllarly there are few experimental results for the hyperpolarlzabihty tensors of even sunple molecules, yet a knowledge of these propertles IS important to the study of non-hnear optics as weU as various intermolecular phenomena [2] _The purpose of the present study is to obtain values of the multipole moments of the hydrogen chloride and chlorme molecules The dipole polarlzabllitles (Y, and, m the case of HCI, the first hyperpolarlzablhty P and the dlpolequsdrupole polarizabihty A, have also been calculated. Addltlonally, the dlamagnetlc contributions to the magnetizability and the nuclear magnetic shleldmg tensors have been obtained The calculations have been made at different levels of sophntlcatlon. Firstly SCF wavefunctlons close to the Hartree-Fock hmlt have been used. CI calculations have also been made, varymg the number and nature of the orbltals correlated The basis set used m these calculations IS H/3Sl p; C1/7sSp2d. The hydrogen basis consists of the 3s set due to Dunning [3], with a two-component STO-2G p function urlth exponent 1 5, which IS the energy-optunised value. The 7s5p part of the chlorine basis IS a set of contracted gaussians due to DUMmg [4], with additionally a set of STO-2G d functions with exponent 2 60 and a set of gausslan d functions wth exponent 0.165. The exponents of these d functions have 162
been optunlsed so that, as far as possible, the energy of the unperturbed molecule and the energy m the presence of a small electric field are smultaneously mimmised. The bond leng’hs used m the present calculations were 2.409 a0 for HCI and 3.757 a0 for Cl,, which are the experunental values. For HCI the SCF energy IS close to that of the definitive calculation by McLean and Yoshunine [5], theu energy berg -460.1 I2 Eh and ours -460.100 E,. There is correspondmgly good agreement between our one-electron properties and those of McLean and Yoshimme, as can be seen from table I. For chlorme our SCF energy is -9 18.976 Eh which 1s close to that of the best SCF calculation by Straub and McLean [8], who obtained -918.99 Eh_ Sunllarly the one-electron properties (table 2) are m agreement with those of Straub and McLean. The polanzablhtles have been obtained usmg the finite-field method [IO] m which the terms representing a small external field are explicitly added to the hamlltoman and the required polarizabtity components are calculated from the mduced dipole moment At the SCF level, this approach 1s completely equivalent, m the limit of small perturbations [ 111, to the coupled Hartree-Fock method [ 121, but has the advan_tage that it is easily extended to the calculation of hyperpolarizabtities, and gibes a simple method of accurateIy calculating polanzablhtles from CI wavefunctions [13,14]. For HCI, McLean and Yoshlmine [5] have CaIculated some of the polarlzablllty components considered here, at the SCF level and using the finite-field method; their results are included in table I _ The only calculation of the polarizabihty of chlorme would ap-
Volume
1
70. number
Table 1 SCF and CI propertres
CHEMICAL
of hydrogen
E
CI c)
-460
-460.270
-460.3 17
100
Evpenmental
IJ
1.189
1.095
1 096
Q
12 862
12.303
12.335
R
8 808
8 683
8 660
17.274 -44.743
AXd
5.306 141 9
16 222 45.059 5 550 142.0
5.79 f 0 15 [6]
142.1
-144.5
- 144.5
11504
1150 6
1150 5
-144
5
-2.6
-2.6
-148
4 + 25 [6]
2.784
2 822
2 825
3.12
01
2 385
2 439
2.437
2 77 [7]
029
0.138
0.009
Pl
0 017
0 016
0.015
AlI
I 122
1 152
1.160
A,
0.117
0 133
0.133
-0
Table 2 SCF and CI propertres
Q * xd AX d %!I Au&
[7]
and Yoshtmme [S] obtained E = -460 1119E h, cr = 1.215 debye, Q = 12 48 X lo+’ C m*, xd = 44.8 X lO99 J T*, 142 0 ppm, u& = 1150 5 ppm, oar = 2 60 x 10-4~ C* m* I-“, przz = -0 11 X lCiso C3 m3 J-*,A, = 153 X lffso C* m3
b)Sm.gle and double ewtatrons from the valence shell only, 1589 configurations. C)Smgle and double excnations from the valence shell and the chlorme 2p shell, 5708 and polarizabrbtres are referred to the centre of mass as origin
E
* 7 [6]
oil PII
[6]
041 5 539
d!,
-2.3
1.0929 [6] 124 co.4
16.275 45
Aafi “?i Ao&
15 February I980
chlonde CI b)
a
;$=
LETTERS
SCF a)
xd
a)McLean
PHYSICS
CL b)
-918.976
-919.114
106 59 -229
37
23130 1222 5 -99
5
The higher-order
moments
SCF study by Jao et al. [15!, usmg the sum-over-states approximationIn addition to the SCF calculations, we have also used correlated wavefunctions. The CI wavefunctions pear to be a small-scale
of chlonne
SCF a)
1205
confwlatrons.
Experimental
11.90
used were obtained ==14 [9]
tations
by making single and double
exci-
from the SCF wavefunction, e.g. for HCI,
104.70 -23148 231.37 1221
The particular
7
-99.5
“II
6.71
6.73
701c)
Ql
3 19
3.72
4.12
c)
a) Straub and McLean [8], obtamed E = -918 990 Eh, o = 11.27 X 1Cf40 C m*, xd = -228 7 x 10-29 J p, od = 1222.5 ppm b, Valence shell only, 992 configuratrons. c) Bndge and Buckmgham [7], at 6238A.
computational
technique
adopted
is that
due to Roos [ 16) . For HCI the calculations were performed at two levels, firstly just considering correlation of the valence-shell orbitals 40, So, 2~~ and 215, and omitting excitations from the chlorine core, and into the most highly excited virtual orbitals. This generates a total of 1589 configurations of the correct space and spin symmetry, and the result.s.are given in table 1. For HCl, calculations have also been made including excitations from the chlorine 2p shell, i.e. the 30, In, and 163
Volume 70. number 1
la,, orbit&. which generate a total of 5708 space and spin adapted configurations From table 1 it can be seen that correlatmg the chlorine 2p shell makes httle drfference to the one-electron properties Consequently, for the sake of computational economy, rn the calcuiation on the Cl, molecule, only the valence shell was correlated. The lowest energy obtamed for HCI IS that of Bartlett and Srlver [ 171 using many-body perturbation theory. They calculated the valence shell correlatron energy to be -0 2793 Eh, compared to our value of -0.170 1El,. Thus we have obtamed about 60% of the valence-shell correlatron energy for HCl The only other CI calculatron on HCI wluch considers a property other than the energy, IS a calculatron of the drpole moment by Grrmaldr et al. [ 181. There do not appear to be any prevrous Cl calculatrons on the chlorrne molecule. Of the calculated properties of HCI, the one whrch IS most aTenable to comparrson wrth expermrent 1s the dipole moment, for whrch the expernnental value 1s I 0929 D, at the equrhbrrum geometry [6]. The SCF value IS l.lS9 D, about 9% too large, whereas the CI value of 1 096 D IS very close to the experrmental result. There 1s also an experrmental value for the quadrupole moment of HCI, from molecular-beam spectroscopy [6],whrch1sO=(1247+040)X 1040Cn1* (u = 0). Given that the CI values of p and 0 are m agreement wrth expenment, it can reasonably be assumed that the values for the octopole and hexadecapole moments of HCI, and of the quadrupole and hexadecapole moments of chlorme, are also accurate There IS an experimental value for the octopole moment of HCI, from collisronal hne broadenmg [ 19]_ and of the quadrupole moment of chlorine. from vrrral coeffrcrent data [9], but these values are of necessrty approxrmate. The magnetrzabrhty tensor of a molecule has dramagnetic and paramagnetrc parts. The dramagnetrc part is obtamed drrectly m these calculatrons. The paramagnetic part may be obtamed vra rts relatronshrp to the rotationalg-factor [20], which has been measured for HCI [6], from whrch X!x = (6.12 f 0.12) X IO-29 J T-2. Combmmg this value of X!& wrth the measured value of the magnetic anisotropy [6], Ax = (-0 32 + 0 1) X 10mZg J T-I, grves an experimental value for Axd of (5 8 + 0 2) X 1O-7g J T-‘, for the ground vrbratronal state. The calculated value (table 1) IS m good agreement wth this result. Usmg the experimental value for xP together with the calculated value for Xd gives a good 164
15 February 1980
CHLhlICAL PHYSICS LETl-ERS
estunate of the total magnetrzabrhty, X = 40 9 X 1O-2g J T-?. Like the magnetrzabrhty, the nuclear magnetic shreld. mg tensor e has dramagnetrc and paramagnetrc parts. The paramagnetlc component is related to the spm-rotation constant [20] _ Usmg the experimental values for the spin-rotation constants rn HCl [21] , then, for the equihbrmm bond length, (02)~
= -166.0
ppm
= -299.9
ppm
and (o$,)ct
Therefore, usrng the calculated values for c$, and a$, from table 1, we obtam absolute shreldmg values oH = -3 1 4 ppm and uCi = -950 6 ppm This last result wrll be of use ur estabhshmg an absolute shieldmg scale for 13Cl NMR. The amsotropres m the shrelding tensors are, by the same means, Au,
= 2.15 ppm
and Au,,
= 297 S ppm.
The experimental values [6] are AOH = 2 I f 5 ppm and Au,, = 300 + 24 ppm A simrlar analysrs cannot be made for the magnetic properties of Cl2 as no expenmental values are available for the rotatronal g-factor or the spur-rotation constant. One property whrch has been more extensrvely rnvestrgated 1s the molecular polarrzablhty 01 Brrdge and Buckmgham [7] gave expenmental values of OL= 2 893 and Acr = 0.346 X 1040 C* m* J-l for HCI, and Q!= 5.13 and Acu = 2 89 X 1O-4o C’ m* J-l for Cl,. These are dynamrc polanzabrlitres, at 6328 A; the experimental values of the statrc polarizabrhtres, obtained by extrapolatmg the refractrve index data of Landolt and Bornstem [22] to zero frequency, are 01= 2.867 X lo40 C* rn2 JO* for HCl and Q!= 4.99 X 1040 C* m* J-1 for Cl,. Our calculated values are statrc polarrzabrhtres. The results for Cl,, (Y= 4.72 and A(Y = 3.01 X 1Oe40 C* m2 J-1, are m good agreement wrth the expenmental data. The results for HCl, OL= 2.566 and Ao = 0.383 X lOA C2 m2 J-l, are shghtly more III error, possrbly due to omission of “polanzatron” basis functions on the hydrogen rn HCl. Nevertheless the results are the most accurate calculated values for the polarrzabrhties of HCI. There are no experimental val-
Volume 70, number 1
CHEMICAL PHYSICS LETTERS
ues for any of the elements of b or A for HCI As can be seen from table 1 the calculated values of p,, = fizz= vary considerably, possibly due to numerical difficulties, and may not be reliable. The values obtamed for the other components of fi and A should be reasonably accurate The present calculation IS the most comprehensive ab initlo study of the one-electron properties of the hydrogen chloride and chlorme molecuIes The results obtained should be sufficiently accurate to provide useful values for quantities such as the tigher electromc moments of HCl and Cl, for which there are no expenmental results AddItionally, the calculations have provided accurate values for the magnetlzabihty and the NMR shielding constants m hydrogen chloride. The authors thank the Sctence Research Councd for the award of a studentshtp (JHW) and a postdoctoral fellowship
References [ 1 ] S Klehch, m DieIectrtc and related molecular processes, Vol 1, Chemtcal Society Spectahst Penodxal Reports
(1972) ch 7. [2] A D Buckmgham, m Intermolecular mtoractions from dlatomlcs to btopolymcrs, ed B Pullman Whey. New York, 1978), ch. 1. 131 T H. Dunnm_e,J Cbem Phys 55 (1971) 716
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1980
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