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Calculation of NMR coupling constants with SCF LCGO MO wavefunctions
.‘Volume12,,qumberI .,
:
“.,,
.-
..
.
1 ~cemtw.1971
.~cmmcAtPHYSlCSLmER~ -. ‘.
,a .,.’
‘.
I.
,.
I
CALCULATIONOF NMR m@LING
.’
CONSTANTS’
of the Fermi contact cLlnt&ution to the coup%~ coastants have been curie& wit% kge basis S&C The excited states have been treats@ ‘t;oth with and withaut mnfiguration interaction. In spite of the large and accurate calculations, the agreement between Qkulated and experimental values is rather poor. This is exphtineb by the fact that the perturbation expansion did not converge. Perturbation theory caldations
out for Hz, C2I&, C2N3F and HaO. SCF LOGO MO wavefuncriuns have &?n ~lcu&t~
I.
cited tlipfet state wavefWtctio~Sfor the MdeCUfe. The summation is carried out over alI excited trip’ ‘let states, because the ck_G(r&& operator has zero matrix elements between two singlet states and the ground state is assumed to be singlet [;?I.
Introduction
l.c
The perturbation theory for the caicuIation of nticfear spin-spin coupling constants has been formu; lated by Ramsey fl ] , who showed that they arose by three distinct mechanisms; the d+olar
tnteraction
Expression
the elicfron orbital effect, between the e~eedtron and nu-
(1) can be further
treated with a broad
.range bf difktetit aiprcGmatians_ CaIetiEati01~~ !UV&
clear spin and the Fermi contact interaction. The last of these mechanisms is ove~he~~gly dominant for coupling between protons. Clnly trlis coupling and the Fermi contact ~on~~bution, will be discussed in this : paper. The coupling constant is then given by
been carried out with both moIecu’tarorbital and Mlence bond methods, and wa&functions with different degrees of sophistication for descriptions of the ground ‘stateand the excited states have been used f3-4 al-
SCF LCGO MUground state wavefunctions have been katculated
‘, ;,.-
,’ ‘I
i ‘, .~ ,
with extended
basis sets.
‘.
~o~pu~a~~~~s hati beencaniedtickwiththe lBMOL
Subscripts A andB refer to the nuclei, i &d j to t&e ,eiectrogs, vis the gyromagnetic ratiq, fl the Bohr ~$vqpetpn; S the,eiectro& spin, and 8 is $te Dirac deli -ta fimction; ‘46 tid Q, +e’&ound,state afid nth ex; :
ab.initb
IV prograti with the method descriaed by Clementi and Davis fl 1] . Two’dffferent ways of treating the excited states ha* been ugd. (i) Excited tripW statesware described by single ,. .; .‘.
‘..’
‘.
‘.
..
25
.,~oluma15 number I
CHEMIiSAL PAYSKS
corii’igurations.6btaincd by the transfer of a singIe electron from an occupied to a.vjit-ual orbital_ The coupling &nstant is then given by
x ~~,l~(r,)l~,)i9,la(?~)l~~,~ , (2) where 3AE&i is the energy difference between the excited and the ground state conx’iguration, I), and Gi are molecular orbitals. Indices CI,b, ... denote occupied molecu!ar ortiials, indiczs i, j, . . . virtual orbitals. (ii) Excited triplet states were described by means of the interaction of singly excited configurations.
(%‘} = {3q,i}D
.
(3Qj is the new function set, {3qti+i) is the set of singlyexcited configurations and 0 is the transformation matrix. With this formalism for the excited states, the formulafor the coupling constants becomes
JAB = -$p2hr,y,
.
c (%qJ-’ n
x (~,16(rA)I~j)(~~l~(r,)I~b),
(4)
where 3AE’n is the nth eigznvalue of the CI matrix a;.d di_.; is the.coefficierlt of the 3‘u,_, configuration in!& A FORTRAN program for both types of cakulations has been developed, and can be obtained upon request. The input is essentially the same as to IBMOL IV, completed with the SCF eigenvectors (coefficients of the symmetry orbit& in the molecular orbitals), Fock-matrix eigenvalues and ‘the tape with electron rep&ion integrals computed with IBMOL IV. All one- and two-electron, one- and multi-center integrals are computed exactly. The symmetry profs>rties of molecular integrals are used exterisively.
3. Results Calculations have been carried out for moIecu!ar 26
LETTER&
”
”
1 December
1971
hydrc.gen, ethylene, ffuoroethylene and water, Calculation .of _moIecuIar orbitah for hydrogen were done with ?-very !Fge basis set including 10 gaussian-type, orbita!; (GTO) of s-type with exponents optimized by Htinaga [12], 3 p-type GTO% and one of each d.&,‘dyY, d,, type. No contraction was applied. The total pound state ene%y, -1 .I 335950 au corresponds cIoseI!l to the Harpee-Fock limit for Hz. The results of coupling constant calculations have nevertheless been rather poor. Computation without configuration interaction gave J= 114.46 Hz. The corresponding value obtained with the CI procedure was 200.27 Hz. The experimental value is 280 Hz [ 131. Calculations for ethy!ene have been done with two basis sets of similar type, both by including and by omitting the polarization functions -p-type CTO’s on the.hydrogens. Using symbol (A/n,, n , nd) to denote the numbers of gaussian functions o F s, p and d (if any) type, centered
MI ;ttom A, the basis sets can be described as
(C/7,3)(H/4,1) and (C/7,3)(H/4)- The contraction has been used; appropriate linear combinations with constant coefficients (calculated for atoms) have been introduced instead of groups of individual gaussians. With the symbol (A/N,, N , Nd) for description of contracted basis, the ethy Hene basis sets are (C/4,2) (H/2,1 j and (C/4,2) @II/Z)respectively. Exponents and contraction coefficients for the carbon functions have been taken from Raos and Siegbahn [143. Molecular orbitals for fhroroethylene, calculated with an analogous basis set without polarization functions, have been obtained from Meza and Wahlgren [I 51, some molecular property calculations -led out by those authors, with the same molecular wavefunctions as used in this study, for ethylene and fluoroethy!ene agree rather well with experiment, However, the results of our study can hardly be considered satisfactory, although the internal order of the coupling constants, calculated with the CI procedure is correct and the experimentally observed decrease of the respective values in fluoroethylene compared with those in ethylene is reproduced. The results are presented in table 1;together with the results obtained by Armour and Stone [7] with the minimal basis set of SIater orbitals and the experimental dataRather extensive cslculations have been carried out for the_Hz0 molecule. Six different sets of &JO’shave been calculated; using different basis sets. barge-basis calculations have been done with exponents and con-
:I .. .
Volume 12, number 1
CriEMiCALPHYSICSLETTERS
I
December 1971
.
_; ~.
C&i&
‘.,
Ta@IeL ;
coptants
in: ethylene (Xj
1. and fiudioethyicne
Thiswotk : .:
:
;;m JBtrans
With:poh.riiation
Without pawi..
functions
wtiori functions
(B), all
V3ftGtl in Hz
Armour and Stone
Expe&zenfai
171
[L6,2Sj
SCF
CI
SC?
Ci
SCF
CI
2.24 3.12 5.67
2.11 6.67 10.90
2.11 3.14 5.54
2.61’ 6.89 11.10
12.90 6.15 14.86
9.30 9.60 20.1I
3.29
‘BP”
l.1.S -19.1
0.54 .’ : 2.77
0.44 3.78
Jt.rans
: 25
-3.2 4.6 f2.8
6,90
TabIc 2
Comparisonof different calculationsfor water ~~~up~ constants ti Hz) Unmntracred
basis
Contracted basis
Groundstate
Couplii
energy (au)
SCF
constantsa) CI
G&‘7,3)(H/41
10/4,2t cx?fZt
-7S.B7SO
~0~7,3,l~fJm,l~ (O/9,5) (H/4,11 (0/9,5,X) w4,u (c)/i I,71 m/w
(0/4,2,1)ffi/2,I> @o/4,2> (H/2, I) (0/4,2,I>CH/2,1>
-75.9219
5.26 I.88
-76.0285
2.89
-1.81
-76.0374
2A8
@3/6,43 M/5)
-76.G189
2.40
-2.26 -1.82
(0~6,4~~~~5,~~
-76.0454
1.86
-2.05
co/l I ,?I Gw, Xl
a} Experimental
-0.47
-2.51
Mlue: -7.2 Hz.
traction coefficients of SaIez and VeriUard [17] and Huzirqa [I 21, the medium- and small-basis molecaIEr orbitais have been tho& of Roos and Siegbahn f181. Thi results of the mlcutatiotis are’presented in ta51e 2. The Hartree-Fock energy for water is approximat‘efy -76.07 au,as reported by Neumann and MoSkowitz/l9]. Some of the ~o~Rd~stat~ functions used can therefore be considered satisfactory. The experiment& value obtained by Holmes et a1. [ZO] is 7.2 Hz. The sign of the coupling constantwas not experimentally determined. &cording to calculations by Popfe et al. [2f 1, a tiiigzitiv-ssigignis highfy probable. The agreekent between the cafcufarett and o’tjseerved valces of the coupling c&stani: is also here rather poor, The results &e gh%&d against the gtoind stak total
,‘_ vopuni
12, num*r
:
,.
.,
cgmI&4LPHysx+~-~E~s,.‘~
. ,.: ..'_ .I','_,, .'. ,: .;, -_, :..,: _'. energy’
:..
. '.
.'
’
‘..
:.
‘_. +Fmti
_:_ _-' ..,,',.
1971 ,'
SCF MO; the results of the pert~rb~~io~ .. &nation o:i” i ‘expa&on ,are h&&!y unceitain, TI& is probably : :,?,ly highly watifuncti@n dependent; For_example ri: : ‘I,- cause >y .the factcthat neither the GTG basis rior the sin&excited ~~~f~ra~~ns form a complete +et. ‘c+&on t$ polarization functions in the.amall basis set Final&, ode’sh&!d be a?varethat the Hart@-Foek has a &i&r ef&i. &the ~calculated.coupling~coti: 1 m&&gives wavefunctions that do not take account ‘.stants than _would be expetied. Y’,’ : of e~ec~ol~,corr~~tion.The infhrence of this phenom‘. enon on the hype&me effects, ai indirect nuclear I.. spm-spin cou$ng, may be considerable. 4. Disdon “Y ’‘. ,, . ‘, :.
_‘
:
..
:.
:
as a’pro,of of&ativzly
-.._
’
The resultsof the ~~culatitions&‘the e~~~r~enta~ results rather’pooriy althOugh the ground state wavefunctions us&dare &tively good (within the H&t-. ree$Fock ap~r~~~~tioR}. E-venthe energies of the, lower,trijietstates (calculated witil’C1)are not .too, far from th;e observed values; this cou:r! be interpreted .’
.‘..
’
Adcnowk&ements
The authors would like to tkauk Dr. $aia Meti and F.K. Ulf Wah.Ig.renfor access to their unpublished results. We would also like to than$ 7.K. Ulf Wahlgren and FL Jan AImIof for assistance wrth the programming and Dr. Kelvin Roberts for revising the English of the marmscriRt.
correct desqript;on of rho=.
‘statee.‘Tl&Mghet energy levels are probably not ao satisfactorily desaibed. The-largediscrepancy observed night be caused.by. ffre, fact’&& GTO’s maynot cor&tly describe the elect& den&yat,the nuclei. Howelier, it is probable, 1that the GTO’s can be r&ale &en at the nuclei. The due at the proton was calculated for optimized contracted GTG’s of H+naga~for the H atpni [lij . The eriei for different numbers ofGTB’s converges rather quickly to the valueonly 03% below the value of the exact 1s function. The‘basis .st.used for H, and the large sets for H20 should therefore give’s reasonably good expectation value of ,&$(rkII). The r&e 0.470247’obtained in’ti$s c&ulation~for Ha ._
References [I ] NE, Rsmssy, phys. Rev. 91 (1953) 303. [Z] 39, Motiory, Quantum theory of magnetic resonance p&amcters (McGraw-HJJi, New York, 1968). [3] J& PopleandD+P.Santry, Mol. Phys. 8 (1964)1. j4f P. Lo&w and ,L;Salem, J. Chem. Phys. 43 (1965) 3402. fg].C, Barhier and G. Bertl&r,Theoret. Chim. Acta 14
(1969)71. 161R. DitchfiEld and J.N. Munell, M&. Phys. i4 (1968) 481. 17J E.A.G. timour and A.J. Stone, Proc.Roy. !ioc.A302 (1967) 25. [8] M. Bart’ieki, J. Chem; Phys. 49 (1968) 2145. [9] M. Qarpfus and DH. Andersoh, J. Chem. Phys. 30
may’+ comparedwith 0.457ji33 calculatedfrom the very dccurate wavefunctiorrof K&OSand Rocth~aaan [22; lo!. The situatidn may of c3grse be different for t& exdted states, An important phenol~len#n, especiail~ r~rn~~b~~ i? H, and,large-basisIQ0 calculations, is the complete lack of convergence, This fact is not changed by the iric+sipn of Ct treatment, ~h~ch.othe~~ apparent@ imprqvea,the results; Th%lack of ,convergence’. for.si.milarcaiculatio~s for HF (carried.out with STO*s~wit&out CI) ha% been reported,by %ato abd Saika j231 and Adam et al. ‘1241..The highly enegetjc &ate+give uery high, apparently urir&o&b.ble cone ~~utions..The ~~~.o~ hydrogen and water moleii+i.catise~
,tie‘;fatesto
(1959)6. [lo] E. Armour, J. Chem. Phys. 49 (1968) 5445.. [If 1 E. Cfementi and D.R. Davis, J. Comput. Phys. 2 11967) .’ 223. [12] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [13] 2. Dayan, G. Wjden~cher and M. Ckiagneau, Compt. Rend, Acad. @i. [Paris) 257’(i963) 2455. [J.4]-3; Roes and P. Siegbahn, Theoret.‘Chim. Acta I7 (1970)‘109. iIls] S, heza and
pub&he&
..
U;~ah&eq~&ewet.
C&n, A&, to $B
‘.
.[16] R.M. L}-nde.il-Bell and ti; h~e&y.cd, ROC RbY. Sot’ :
sppeiq& @tire $@ch aC ‘j.;,
,most The hick of qw&gen& is a ., .,:, can,!.&ch,o’~er. +r* serious fa~lt;it $teans,t.+ at th&X&e!of appycix: ‘. ., .; .. . ; _... ,.: ,,: ” ;., ‘. ;. : ‘.,C.,, -28:1:...:. ;.: ‘.. - ., 1,:. :;,._,,;-:: .: _,; ,_.. “: ; ;. :;,:..;‘._ ., .y: ; : _ .. I: ,:. (, _. ‘,. ),,
Volume
12. number
1
CHEMICAL
[I91 D. Neumann and J.W. Moskowitz, J. Chem. Phys. 49 (1968) 2056, [ZO] J.R Holmes, lk F’hys. 37 (1962) (211 J-k Pople, J.W. Phys. 49 (19682
Kivekon and W.C. Drinka.& 150.
J. Chem.
Mciver and N.S. Cktlund, J. Chem. 2965. [22J W. Koibs and C.C.J. Roothaan, Rev. Mod. Phys. 32 (1960) 219.
PHYSICS LEITERS
1 D-xember
1971
(231 Y. Kate and A. Saika, I. Chem. F%ys. 46 (1967) 1975. [ 241 W. Adam, A. Grirnkon and P.A. Sprangle, Thcoret. Cl&n. Acta 18 (1970) 365. [ 25 1 C.N. Banwell, N. Sheppard and J 6. Turner, Spectcochim. Acta 16 (1960) 794.
:
“.,,
.-
..
.
1 ~cemtw.1971
.~cmmcAtPHYSlCSLmER~ -. ‘.
,a .,.’
‘.
I.
,.
I
CALCULATIONOF NMR m@LING
.’
CONSTANTS’
of the Fermi contact cLlnt&ution to the coup%~ coastants have been curie& wit% kge basis S&C The excited states have been treats@ ‘t;oth with and withaut mnfiguration interaction. In spite of the large and accurate calculations, the agreement between Qkulated and experimental values is rather poor. This is exphtineb by the fact that the perturbation expansion did not converge. Perturbation theory caldations
out for Hz, C2I&, C2N3F and HaO. SCF LOGO MO wavefuncriuns have &?n ~lcu&t~
I.
cited tlipfet state wavefWtctio~Sfor the MdeCUfe. The summation is carried out over alI excited trip’ ‘let states, because the ck_G(r&& operator has zero matrix elements between two singlet states and the ground state is assumed to be singlet [;?I.
Introduction
l.c
The perturbation theory for the caicuIation of nticfear spin-spin coupling constants has been formu; lated by Ramsey fl ] , who showed that they arose by three distinct mechanisms; the d+olar
tnteraction
Expression
the elicfron orbital effect, between the e~eedtron and nu-
(1) can be further
treated with a broad
.range bf difktetit aiprcGmatians_ CaIetiEati01~~ !UV&
clear spin and the Fermi contact interaction. The last of these mechanisms is ove~he~~gly dominant for coupling between protons. Clnly trlis coupling and the Fermi contact ~on~~bution, will be discussed in this : paper. The coupling constant is then given by
been carried out with both moIecu’tarorbital and Mlence bond methods, and wa&functions with different degrees of sophistication for descriptions of the ground ‘stateand the excited states have been used f3-4 al-
SCF LCGO MUground state wavefunctions have been katculated
‘, ;,.-
,’ ‘I
i ‘, .~ ,
with extended
basis sets.
‘.
~o~pu~a~~~~s hati beencaniedtickwiththe lBMOL
Subscripts A andB refer to the nuclei, i &d j to t&e ,eiectrogs, vis the gyromagnetic ratiq, fl the Bohr ~$vqpetpn; S the,eiectro& spin, and 8 is $te Dirac deli -ta fimction; ‘46 tid Q, +e’&ound,state afid nth ex; :
ab.initb
IV prograti with the method descriaed by Clementi and Davis fl 1] . Two’dffferent ways of treating the excited states ha* been ugd. (i) Excited tripW statesware described by single ,. .; .‘.
‘..’
‘.
‘.
..
25
.,~oluma15 number I
CHEMIiSAL PAYSKS
corii’igurations.6btaincd by the transfer of a singIe electron from an occupied to a.vjit-ual orbital_ The coupling &nstant is then given by
x ~~,l~(r,)l~,)i9,la(?~)l~~,~ , (2) where 3AE&i is the energy difference between the excited and the ground state conx’iguration, I), and Gi are molecular orbitals. Indices CI,b, ... denote occupied molecu!ar ortiials, indiczs i, j, . . . virtual orbitals. (ii) Excited triplet states were described by means of the interaction of singly excited configurations.
(%‘} = {3q,i}D
.
(3Qj is the new function set, {3qti+i) is the set of singlyexcited configurations and 0 is the transformation matrix. With this formalism for the excited states, the formulafor the coupling constants becomes
JAB = -$p2hr,y,
.
c (%qJ-’ n
x (~,16(rA)I~j)(~~l~(r,)I~b),
(4)
where 3AE’n is the nth eigznvalue of the CI matrix a;.d di_.; is the.coefficierlt of the 3‘u,_, configuration in!& A FORTRAN program for both types of cakulations has been developed, and can be obtained upon request. The input is essentially the same as to IBMOL IV, completed with the SCF eigenvectors (coefficients of the symmetry orbit& in the molecular orbitals), Fock-matrix eigenvalues and ‘the tape with electron rep&ion integrals computed with IBMOL IV. All one- and two-electron, one- and multi-center integrals are computed exactly. The symmetry profs>rties of molecular integrals are used exterisively.
3. Results Calculations have been carried out for moIecu!ar 26
LETTER&
”
”
1 December
1971
hydrc.gen, ethylene, ffuoroethylene and water, Calculation .of _moIecuIar orbitah for hydrogen were done with ?-very !Fge basis set including 10 gaussian-type, orbita!; (GTO) of s-type with exponents optimized by Htinaga [12], 3 p-type GTO% and one of each d.&,‘dyY, d,, type. No contraction was applied. The total pound state ene%y, -1 .I 335950 au corresponds cIoseI!l to the Harpee-Fock limit for Hz. The results of coupling constant calculations have nevertheless been rather poor. Computation without configuration interaction gave J= 114.46 Hz. The corresponding value obtained with the CI procedure was 200.27 Hz. The experimental value is 280 Hz [ 131. Calculations for ethy!ene have been done with two basis sets of similar type, both by including and by omitting the polarization functions -p-type CTO’s on the.hydrogens. Using symbol (A/n,, n , nd) to denote the numbers of gaussian functions o F s, p and d (if any) type, centered
MI ;ttom A, the basis sets can be described as
(C/7,3)(H/4,1) and (C/7,3)(H/4)- The contraction has been used; appropriate linear combinations with constant coefficients (calculated for atoms) have been introduced instead of groups of individual gaussians. With the symbol (A/N,, N , Nd) for description of contracted basis, the ethy Hene basis sets are (C/4,2) (H/2,1 j and (C/4,2) @II/Z)respectively. Exponents and contraction coefficients for the carbon functions have been taken from Raos and Siegbahn [143. Molecular orbitals for fhroroethylene, calculated with an analogous basis set without polarization functions, have been obtained from Meza and Wahlgren [I 51, some molecular property calculations -led out by those authors, with the same molecular wavefunctions as used in this study, for ethylene and fluoroethy!ene agree rather well with experiment, However, the results of our study can hardly be considered satisfactory, although the internal order of the coupling constants, calculated with the CI procedure is correct and the experimentally observed decrease of the respective values in fluoroethylene compared with those in ethylene is reproduced. The results are presented in table 1;together with the results obtained by Armour and Stone [7] with the minimal basis set of SIater orbitals and the experimental dataRather extensive cslculations have been carried out for the_Hz0 molecule. Six different sets of &JO’shave been calculated; using different basis sets. barge-basis calculations have been done with exponents and con-
:I .. .
Volume 12, number 1
CriEMiCALPHYSICSLETTERS
I
December 1971
.
_; ~.
C&i&
‘.,
Ta@IeL ;
coptants
in: ethylene (Xj
1. and fiudioethyicne
Thiswotk : .:
:
;;m JBtrans
With:poh.riiation
Without pawi..
functions
wtiori functions
(B), all
V3ftGtl in Hz
Armour and Stone
Expe&zenfai
171
[L6,2Sj
SCF
CI
SC?
Ci
SCF
CI
2.24 3.12 5.67
2.11 6.67 10.90
2.11 3.14 5.54
2.61’ 6.89 11.10
12.90 6.15 14.86
9.30 9.60 20.1I
3.29
‘BP”
l.1.S -19.1
0.54 .’ : 2.77
0.44 3.78
Jt.rans
: 25
-3.2 4.6 f2.8
6,90
TabIc 2
Comparisonof different calculationsfor water ~~~up~ constants ti Hz) Unmntracred
basis
Contracted basis
Groundstate
Couplii
energy (au)
SCF
constantsa) CI
G&‘7,3)(H/41
10/4,2t cx?fZt
-7S.B7SO
~0~7,3,l~fJm,l~ (O/9,5) (H/4,11 (0/9,5,X) w4,u (c)/i I,71 m/w
(0/4,2,1)ffi/2,I> @o/4,2> (H/2, I) (0/4,2,I>CH/2,1>
-75.9219
5.26 I.88
-76.0285
2.89
-1.81
-76.0374
2A8
@3/6,43 M/5)
-76.G189
2.40
-2.26 -1.82
(0~6,4~~~~5,~~
-76.0454
1.86
-2.05
co/l I ,?I Gw, Xl
a} Experimental
-0.47
-2.51
Mlue: -7.2 Hz.
traction coefficients of SaIez and VeriUard [17] and Huzirqa [I 21, the medium- and small-basis molecaIEr orbitais have been tho& of Roos and Siegbahn f181. Thi results of the mlcutatiotis are’presented in ta51e 2. The Hartree-Fock energy for water is approximat‘efy -76.07 au,as reported by Neumann and MoSkowitz/l9]. Some of the ~o~Rd~stat~ functions used can therefore be considered satisfactory. The experiment& value obtained by Holmes et a1. [ZO] is 7.2 Hz. The sign of the coupling constantwas not experimentally determined. &cording to calculations by Popfe et al. [2f 1, a tiiigzitiv-ssigignis highfy probable. The agreekent between the cafcufarett and o’tjseerved valces of the coupling c&stani: is also here rather poor, The results &e gh%&d against the gtoind stak total
,‘_ vopuni
12, num*r
:
,.
.,
cgmI&4LPHysx+~-~E~s,.‘~
. ,.: ..'_ .I','_,, .'. ,: .;, -_, :..,: _'. energy’
:..
. '.
.'
’
‘..
:.
‘_. +Fmti
_:_ _-' ..,,',.
1971 ,'
SCF MO; the results of the pert~rb~~io~ .. &nation o:i” i ‘expa&on ,are h&&!y unceitain, TI& is probably : :,?,ly highly watifuncti@n dependent; For_example ri: : ‘I,- cause >y .the factcthat neither the GTG basis rior the sin&excited ~~~f~ra~~ns form a complete +et. ‘c+&on t$ polarization functions in the.amall basis set Final&, ode’sh&!d be a?varethat the Hart@-Foek has a &i&r ef&i. &the ~calculated.coupling~coti: 1 m&&gives wavefunctions that do not take account ‘.stants than _would be expetied. Y’,’ : of e~ec~ol~,corr~~tion.The infhrence of this phenom‘. enon on the hype&me effects, ai indirect nuclear I.. spm-spin cou$ng, may be considerable. 4. Disdon “Y ’‘. ,, . ‘, :.
_‘
:
..
:.
:
as a’pro,of of&ativzly
-.._
’
The resultsof the ~~culatitions&‘the e~~~r~enta~ results rather’pooriy althOugh the ground state wavefunctions us&dare &tively good (within the H&t-. ree$Fock ap~r~~~~tioR}. E-venthe energies of the, lower,trijietstates (calculated witil’C1)are not .too, far from th;e observed values; this cou:r! be interpreted .’
.‘..
’
Adcnowk&ements
The authors would like to tkauk Dr. $aia Meti and F.K. Ulf Wah.Ig.renfor access to their unpublished results. We would also like to than$ 7.K. Ulf Wahlgren and FL Jan AImIof for assistance wrth the programming and Dr. Kelvin Roberts for revising the English of the marmscriRt.
correct desqript;on of rho=.
‘statee.‘Tl&Mghet energy levels are probably not ao satisfactorily desaibed. The-largediscrepancy observed night be caused.by. ffre, fact’&& GTO’s maynot cor&tly describe the elect& den&yat,the nuclei. Howelier, it is probable, 1that the GTO’s can be r&ale &en at the nuclei. The due at the proton was calculated for optimized contracted GTG’s of H+naga~for the H atpni [lij . The eriei for different numbers ofGTB’s converges rather quickly to the valueonly 03% below the value of the exact 1s function. The‘basis .st.used for H, and the large sets for H20 should therefore give’s reasonably good expectation value of ,&$(rkII). The r&e 0.470247’obtained in’ti$s c&ulation~for Ha ._
References [I ] NE, Rsmssy, phys. Rev. 91 (1953) 303. [Z] 39, Motiory, Quantum theory of magnetic resonance p&amcters (McGraw-HJJi, New York, 1968). [3] J& PopleandD+P.Santry, Mol. Phys. 8 (1964)1. j4f P. Lo&w and ,L;Salem, J. Chem. Phys. 43 (1965) 3402. fg].C, Barhier and G. Bertl&r,Theoret. Chim. Acta 14
(1969)71. 161R. DitchfiEld and J.N. Munell, M&. Phys. i4 (1968) 481. 17J E.A.G. timour and A.J. Stone, Proc.Roy. !ioc.A302 (1967) 25. [8] M. Bart’ieki, J. Chem; Phys. 49 (1968) 2145. [9] M. Qarpfus and DH. Andersoh, J. Chem. Phys. 30
may’+ comparedwith 0.457ji33 calculatedfrom the very dccurate wavefunctiorrof K&OSand Rocth~aaan [22; lo!. The situatidn may of c3grse be different for t& exdted states, An important phenol~len#n, especiail~ r~rn~~b~~ i? H, and,large-basisIQ0 calculations, is the complete lack of convergence, This fact is not changed by the iric+sipn of Ct treatment, ~h~ch.othe~~ apparent@ imprqvea,the results; Th%lack of ,convergence’. for.si.milarcaiculatio~s for HF (carried.out with STO*s~wit&out CI) ha% been reported,by %ato abd Saika j231 and Adam et al. ‘1241..The highly enegetjc &ate+give uery high, apparently urir&o&b.ble cone ~~utions..The ~~~.o~ hydrogen and water moleii+i.catise~
,tie‘;fatesto
(1959)6. [lo] E. Armour, J. Chem. Phys. 49 (1968) 5445.. [If 1 E. Cfementi and D.R. Davis, J. Comput. Phys. 2 11967) .’ 223. [12] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [13] 2. Dayan, G. Wjden~cher and M. Ckiagneau, Compt. Rend, Acad. @i. [Paris) 257’(i963) 2455. [J.4]-3; Roes and P. Siegbahn, Theoret.‘Chim. Acta I7 (1970)‘109. iIls] S, heza and
pub&he&
..
U;~ah&eq~&ewet.
C&n, A&, to $B
‘.
.[16] R.M. L}-nde.il-Bell and ti; h~e&y.cd, ROC RbY. Sot’ :
sppeiq& @tire $@ch aC ‘j.;,
,most The hick of qw&gen& is a ., .,:, can,!.&ch,o’~er. +r* serious fa~lt;it $teans,t.+ at th&X&e!of appycix: ‘. ., .; .. . ; _... ,.: ,,: ” ;., ‘. ;. : ‘.,C.,, -28:1:...:. ;.: ‘.. - ., 1,:. :;,._,,;-:: .: _,; ,_.. “: ; ;. :;,:..;‘._ ., .y: ; : _ .. I: ,:. (, _. ‘,. ),,
Volume
12. number
1
CHEMICAL
[I91 D. Neumann and J.W. Moskowitz, J. Chem. Phys. 49 (1968) 2056, [ZO] J.R Holmes, lk F’hys. 37 (1962) (211 J-k Pople, J.W. Phys. 49 (19682
Kivekon and W.C. Drinka.& 150.
J. Chem.
Mciver and N.S. Cktlund, J. Chem. 2965. [22J W. Koibs and C.C.J. Roothaan, Rev. Mod. Phys. 32 (1960) 219.
PHYSICS LEITERS
1 D-xember
1971
(231 Y. Kate and A. Saika, I. Chem. F%ys. 46 (1967) 1975. [ 241 W. Adam, A. Grirnkon and P.A. Sprangle, Thcoret. Cl&n. Acta 18 (1970) 365. [ 25 1 C.N. Banwell, N. Sheppard and J 6. Turner, Spectcochim. Acta 16 (1960) 794.