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Pseudo-potential evaluation of the ground-state potential curves for the Cl2 and Br2 molecules
Volume
79, number
2
CHEMICAL
PSEUDO-POTENTIAL
EVALUATION
PHYSICS
LETTERS
OF THE GROUND-STATE
15 April 1981
POTENTIAL
CURVES
FOR THE Cl, AND Br, MOLECULES* G. DAS Ci~emrsrry Received
DIYISIO~, Argonne 9 December
Narlorzal
Laboratory.
Argonne.
Rlrnots
60439,
USA
1980
The electronrc wavefunctlons and potential tunes for the ground states of the Cl2 and Brz molecules are calculated usmg pseudo-potent& techmques The agreement with experunent for both molecules IS sattiactory For Cl2 all-electron calcuhtlons are also performed as a study of the accuracy of the pseudo-potentxxl approach to bound states
l_ Introduction Smce the successful apphcatton of the OVC method to the F2 molecule [ 1,2], many dtiferent systems [3] have been studied by this method with satisfactory results However, to the best of the knowledge of the present author, except for a pseudo-potential OVC work [4] on I?, an ODC GVB level effectlvecorepotential study [5], and very recently an SCF and CI study on the one-electron properties of Cl, [6] no etiaustlve, accurate ab mltlo calculations have been reported on the halogen duners While F,, even m the ground state. was once a challenge to quantum chemspectral istry, and r2, with various ill-understood features, IS still a challenge, the other duners, Cl, and Br,, do not have this dlstmctlon, beutg well-understood both theoretically and expenmentally as sunple extensrons of the F2 problem In this report, apart from obtaining theoretical potential curves for these two systems, we also propose to take advantage of their sunphcrty to make the followmg study. Recently we have been pursumg and advocating a pseudo-potential approach which we have named the modified Philips-Klemman (MPK) [4,7] method m contrast to the by-now wellestablished effective-core-potential (ECP) methods A study [S] of the accuracy of the MPK method has recently * Work performed Energy
Sciences
under the auspices of the Office of Basic of the US Department of Energy.
been carried out by the present author on the repulsave states of the double ion Css’. It IS shown there that the agreement between the all-electron and pseudo-potential calculattons gets mcreasmgly worse as the atoms approach each other Smce these calculatlons are on the repulsive states It IS not apparent how weU the MPK approach will descnbe the bound states, particularly with respect to their spectroscoprc charactenstIcs Our motlvatlon m this letter IS two-fold (I) to assess the accuracy of the MPK pseudo-potential techmques and (u) to report theoretrcal ground-state potential curves for Cl, and Br2
2. Allelectron
versus MPK pseudo-potential
methods
In the MPK method (see refs. [4,7,8] for deta&) one treats the ab mrtlo problem very much hke Ihe frozen-core all-electron problem except that the basis set IS truncated to describe only the valence electrons as accurately as in the all-electron treatment The core, m contrast to the ECP methods, IS not completely unrepresented, however In fact, as we shall see below, it IS necessary to choose a pseudo-potential basis set that gives at least a rough representatron of the core shells lying energetically nearest to the valence shells As explamed m previous works [4,7,8], this IS primarily due to the fact that the MPK pseudo-potenteal energy IS correct only to second order m the differentral overlap of the pseudo-valence and core orbit305
CHEhliCAL PHYSICS LETTERS
Volume 79. number 2
als, requlrlng that the fatter be kept as small as possible For carrying out the comparison between the nllelectron and MPK methods we adopt the followmg procedure which IS slmllar to our previous work [S] on the repulsive states Choose a basis set to span both core and valence. (I) freeze the core orb&& m rhelr atomic Hartree-Fock forms except for sma!f orthogonahty effects, (u) consider a set of configurarlons representmg all the “molecular” correlation wlthm the lmlltatlons of the basis set, and (111) obtain the all-electron OVC wa\efunctlons and the potential curve Now carry out the MPK cnlculatlons as follows (I) select the full valence subset out of the all-elzctron basks set as well as some representative “outer“ core funcrIons. (II) construct the core-porent& mntrtz eiements
usulg the same core orbltals as those used m the allelectron calculatrons Also form the core-valence overlap matrLv {.SiG }
15 Aprd 1981
latlons on Cl, cons&s at each center of a truncated “nommal” set [9] for Cl augmented with sultable polarlzntlon s and d functions In choosmg the latter It IS assumed that only the 3p shells undergo appreclable polarlzatlon effects This IS found to be true over the range of Internuclear separatxons m wtuch we are interested Our polar!zatlon functrons are, however, far from ekhaustlveFor ~proved accuracy. tt IS essentzal that one adds and optumzes more polartzatton functions The basts set IS shown m table i _The correspondmgallelectron SCF energy for the chiorme atom IS 457.4597 With the full nornIna set [9] the energq IS -457 48 16. Although much of the difference IS due to a difference III the descrlptlon of the core caused by the truncation of the basis set, the corresponding orthogonaltty effects on the valence orbttais may have sigmficant effect on the molecular mteractlon The types of configuratrons used are shown m table 2 The first IS the molecular Hartree-Fock configuration followed by 13 molecular correlation terms descrlbmg the 3p electrons The last two correspond to 3s + 3~0 excltatlons The magmtude of mLvmg coefficients of these confrgurdtlons as they occur m the wavefunctlon of the Cl2 ground state at R = 3 76 are also shown m table 7. in table 3 we hst m the second column the all-elecTable 1
and (m) employ the same configurations as above, and obtam the MPK wavefunctions and potential curve In contrast to our earher work, we shall also study the dependence of the pseudo-potential curve on the choice of the basrs for the “outer-core” representatlon
3 _Calculations
and results
We shall carry out the pseudo-potential and a& electron comparison only for the Cl, molecule The Br2 curve WLUthen be obtamed usu?g the pseudopotential OVC framework.
The alletectron 306
basis functions
used for the C&U-
Ems sets used for the c&ulatlons of Cl2 and Br2 wavefunctlons Oniy the starred functions are consldered for the find pseudo-potentnl calculations
Series
Chlorme n
Broome 1
r
I1
1
1
0
2
2
0
18 416 16 316
3
3
0
4
2
5 6 7
8 9 10 11 12 13 14
1
3-
3
0
5.206
0 0
3 296
2873*
4 4
0
5 839*
3
1
1998 5 461
3 4
0 0
i 809s 1809’
4
I
2 914
2 2 2 3 3 3 3 4
1 1 1 1 1 2 2 2
14 458 8 45.5 5 298** 2 609* 1.4.56* 1456* 2 609*
4 5 3 4 4
1 1 2 2 2
1615 1998 3 188 2914 1.165
1.456*
Volume
79, number
2
CHEhIICAL
PHYSICS
1
,~s+r&lp~npa4,,lp~ npo;
3
npagnpsru-
-c tzpo2,
0 1199
4
npognprrg
5
rzpo; -c (n+ l)s$
6
npugz -
(12 + I ,su;
0 0018
7
npo;
-
,ldo;
0 0333
8
npoi
- ndo$
0 0134
9
npo;
-
rlpau(n +npou(n+
+ 1)png
0 0495
1)prru
0 1165 0 0044
(n+ l)pni
00011
10
rrpo; -L (n + l)prri
0 0016
11
npa’
- ndrri
0 0418
12
npag --* tidrri
0 0131
13
npn2
- npo;
0 0204
14
npxg
+ npaz
0 0388
15
nsu$ - npai
0 0161
16
nsouz - npa:,
0 02.51
g
@3P
R
-0 0073 2p(r
= 14.458)
of Cl2 and Br? based
on all-electron
and pseudo-potential
2p(<=8
models
baw
(u)
basis (m) 0 0796 0482
0 1403 -0 047 1 -0 0806
0 2406 -0 0234 -0 0854
0 2205 -0 0365 -0 0886
3.5 40 4.5
-0
-0 -0
-0 -0
-0 -0
-0 -0
50 55 60 80
-0 0612 -0 04 10 -0 0139 -0 0025
0646 0371
Encrgles
Br2
0 2349 -0 026 -0 0818 0720 0479
455)
pseudo-potent&
pseudo-potential (I)
- 0.0813
These coefficients are the same as those occurring with their respective basis functions m the asymptotic 3p orbital from the all-electron calculation Thus will ensure that the core-vaience overlap is real&x and small The correspondmg pseudo-potential potential curves using the same core as used for the allelectron calculations are shown m columns 4-6 of table 3 In fig 1 these curves are compared with the all-electron curve We observe that even though the weU uepth IS surprtstngly sun&r for the first two curves, they differ markedly m other details Also, the third curve, whxh IS comparable to the previous calculations reported m ref [S] , 1s not mxkedly different from the second
R
baus 2 76 3 26 3 76 426 4.76
=
Cl2 all-electron
caicuiatzom
-020352p(~=529S)+O57533p(S_=2609)
tron mteractlon energies, E(R) - E(m), for various internuclear separattons As we menttoned before, these energies are calculated with a frozen atomic core obtained from the asymptotic calculattons with the truncated basis set Sample calculations indicate that no slgmficant improvement results If instead we Table 3 lnteractlon energies E(R) - E(m) for theground states m hartree and I?, mternuclear separstlon. UI bohr
1981
We shall consider three types of basis sets for these calculations AU of them will contam the full valence basrs subset However, the first contams no 2p functlons (I e , all the functrons marked wrth smgle asterrsks III table 1) and the second contams all the functions marked with single or double asterisks, whtie the thud conststs of aU the functions of the first set with the more compact 3p at each center replaced by the hnear combmatlon
0 9847
2
C7, _ pseudo-potential
3.2
hlagmtude of mL\mg coefficients for Cl, at R = 3 76
Configuration
I5 April
had selected the futl nominal set plus the polarlzatlon functions already considered For example, the value ofE(R) -E(m) for the latter calculations at R = 4 26 IS -0 0732 versus -0 0720 for the truncated set.
Table 2 Confiiuratlon types used for the ground states of Cl;! and Br2 The occupancy of only the valence shells 1s shown; for Cl, n = 3 and for Br, n = 4 Evcitatlon description IS used for all but the first confiiuratlon Series
LETTERS
0784 0525
0768 0512
-0
0731
307
Volume
79, number -002
CHEhflCAL
2
-
ALL-ELECTRON
-----
PSEUDO WITH
---
PSEUDO WlTH
I
I
I
I ’1
POTENTIAL
CURVE
(II)
POTENTIAL
LETTERS
15 AprrlI5’31
(in) 1s comparable to an ECP approach since in the latter. too, one constrains the pseudo-valence orbital to have the same kmd of mlxmg with the core over the whole molecular range. Unless one IS Interested III tughly accurate potential curves, however, pseudo-potential calculations with either basis set (u) or (111) IS satisfactory. In table 4 the calculated spectroscopic constants based on both the all-electron curve as well as the pseudo-potential ones with basis sets of (11) and (in) are compared with experunent
I
CURVE
BASIS
PHYSlCS
CURVE
BASIS tt,11
3 3 Br2
pseudo-poremlal
cclmlatiorw
4
-0 IO. 3 25
I 3 50
I 3 75
I 400
I 425
I 4 50
-175
R IBohrsl i-4 1 Comptirlson of the potential curbes for Cl, obmmed theoretIcally by tiilectron nnd pseudo-potentml methods
As we have noted before, the purpose of mtroducmg outer-core basis functions IS to ensure that by evphclt orthogonahty to a crude representation of the outer core. the core-valence overlap remams small. This IS reahstlcally achieved with both kmds (u) and (111) of pseudo-potential basis. Each basis has Its advantages and disadvantages Willie basis (11) affords more flexlblhty than basis (M) It 1s also more expensive Apparently basis (11) results are closer to the all-electron curve than either of the other two The MPK pseudo-potential with a restrlcced basis
The basis set, which IS again a valence nommal set [9] augmented by polanzatlon functions, IS shown m table 1 The basis contams the 3p functions required to represent the %zV - 1” outer core The core Itself, however. 1s now obtained from a numerical HartreeFock calculation of the bromine 2P3,? state The correspondmg potential curve IS shown in table 3 and the spectroscopic constants m table 4. The qualhty of the Br7 results 1s clearly superior to those of Cl,. Since the main difference hes In the choice of the core, we contend that It IS necessary, among other thmgs, to improve the core for chlorme, if one IS interested m more reahstlc spectroscopic constants. Thts IS true both m pseudo-potentlsl as well as all-electron calcu:atlons
Acknowledgement The author
gratefully
acknowledges
useful
dlscus-
Table 4
Spectroscopic constants of Cl2 and Brz BT2
Cl2 hlPK bnsls (u)
XlPK basis (u0
cup
hlPK basis (u)
ev
theory 3 85 491 34 0 23 0 002 2 18
3 89 484 31 0 12 0 002 7 28
381 510 34 0 23 0 002 2 36
3 76 560 2.7 0 24 0.0014 2 48a)
4 42 302 13
4 31 325 11 0 082 0 00032 i97a)
di-elect.ron
‘e @oh) We (cm-‘) WeXe
(Cm-‘)
Be (cm-‘) ae (cm-l) De W)
0
077
0 00037 192
Volume 79. number 2
sions with Dr L.R above calculatmns
CHEMICAL PHYSICS LETTERS
Kahn on various
aspects
of the
15 Apnl1981
[4] G Das and A C Wahl. J Chem. Phys. 69 (1978) 53 [5] L.R. Kahn, P Baybutt and D G Truhlar, J Chem. Phys 65 (1976)
3826.
[6] J H Williams and R D Amos. Chem. Phys Letters 70 (1980) 162 G Das and AC
References
[7]
[ 1 ] G Das and A C Wahl, Phys Rev Letters 25 (1970)
[SI G Das, Chem. Phys Letters 71 (1980) 202 [9] AC Wahi, P J Bertoncuu, K Kaiser and R H. Land,
J. Chem. Phys. 56 (1972) 3532 [2] M A hiorrlson and P S Hay, J Chem
Phys
991,
70 (1979)
4034. [3] A C. Wahl and G Das, tn Methods of electrontc structure theory, ed H F Schaefer III (Plenum Press, New York, 1977)
WahI. J Chem
Phys
64 (1976)
4672
BISON. A Fortran Computmg System for SelfCorwstentField Calculations of Dutomlc Molecde~, AI~OIIIE National Laboratory Tech Report No. 7271
309
79, number
2
CHEMICAL
PSEUDO-POTENTIAL
EVALUATION
PHYSICS
LETTERS
OF THE GROUND-STATE
15 April 1981
POTENTIAL
CURVES
FOR THE Cl, AND Br, MOLECULES* G. DAS Ci~emrsrry Received
DIYISIO~, Argonne 9 December
Narlorzal
Laboratory.
Argonne.
Rlrnots
60439,
USA
1980
The electronrc wavefunctlons and potential tunes for the ground states of the Cl2 and Brz molecules are calculated usmg pseudo-potent& techmques The agreement with experunent for both molecules IS sattiactory For Cl2 all-electron calcuhtlons are also performed as a study of the accuracy of the pseudo-potentxxl approach to bound states
l_ Introduction Smce the successful apphcatton of the OVC method to the F2 molecule [ 1,2], many dtiferent systems [3] have been studied by this method with satisfactory results However, to the best of the knowledge of the present author, except for a pseudo-potential OVC work [4] on I?, an ODC GVB level effectlvecorepotential study [5], and very recently an SCF and CI study on the one-electron properties of Cl, [6] no etiaustlve, accurate ab mltlo calculations have been reported on the halogen duners While F,, even m the ground state. was once a challenge to quantum chemspectral istry, and r2, with various ill-understood features, IS still a challenge, the other duners, Cl, and Br,, do not have this dlstmctlon, beutg well-understood both theoretically and expenmentally as sunple extensrons of the F2 problem In this report, apart from obtaining theoretical potential curves for these two systems, we also propose to take advantage of their sunphcrty to make the followmg study. Recently we have been pursumg and advocating a pseudo-potential approach which we have named the modified Philips-Klemman (MPK) [4,7] method m contrast to the by-now wellestablished effective-core-potential (ECP) methods A study [S] of the accuracy of the MPK method has recently * Work performed Energy
Sciences
under the auspices of the Office of Basic of the US Department of Energy.
been carried out by the present author on the repulsave states of the double ion Css’. It IS shown there that the agreement between the all-electron and pseudo-potential calculattons gets mcreasmgly worse as the atoms approach each other Smce these calculatlons are on the repulsive states It IS not apparent how weU the MPK approach will descnbe the bound states, particularly with respect to their spectroscoprc charactenstIcs Our motlvatlon m this letter IS two-fold (I) to assess the accuracy of the MPK pseudo-potential techmques and (u) to report theoretrcal ground-state potential curves for Cl, and Br2
2. Allelectron
versus MPK pseudo-potential
methods
In the MPK method (see refs. [4,7,8] for deta&) one treats the ab mrtlo problem very much hke Ihe frozen-core all-electron problem except that the basis set IS truncated to describe only the valence electrons as accurately as in the all-electron treatment The core, m contrast to the ECP methods, IS not completely unrepresented, however In fact, as we shall see below, it IS necessary to choose a pseudo-potential basis set that gives at least a rough representatron of the core shells lying energetically nearest to the valence shells As explamed m previous works [4,7,8], this IS primarily due to the fact that the MPK pseudo-potenteal energy IS correct only to second order m the differentral overlap of the pseudo-valence and core orbit305
CHEhliCAL PHYSICS LETTERS
Volume 79. number 2
als, requlrlng that the fatter be kept as small as possible For carrying out the comparison between the nllelectron and MPK methods we adopt the followmg procedure which IS slmllar to our previous work [S] on the repulsive states Choose a basis set to span both core and valence. (I) freeze the core orb&& m rhelr atomic Hartree-Fock forms except for sma!f orthogonahty effects, (u) consider a set of configurarlons representmg all the “molecular” correlation wlthm the lmlltatlons of the basis set, and (111) obtain the all-electron OVC wa\efunctlons and the potential curve Now carry out the MPK cnlculatlons as follows (I) select the full valence subset out of the all-elzctron basks set as well as some representative “outer“ core funcrIons. (II) construct the core-porent& mntrtz eiements
usulg the same core orbltals as those used m the allelectron calculatrons Also form the core-valence overlap matrLv {.SiG }
15 Aprd 1981
latlons on Cl, cons&s at each center of a truncated “nommal” set [9] for Cl augmented with sultable polarlzntlon s and d functions In choosmg the latter It IS assumed that only the 3p shells undergo appreclable polarlzatlon effects This IS found to be true over the range of Internuclear separatxons m wtuch we are interested Our polar!zatlon functrons are, however, far from ekhaustlveFor ~proved accuracy. tt IS essentzal that one adds and optumzes more polartzatton functions The basts set IS shown m table i _The correspondmgallelectron SCF energy for the chiorme atom IS 457.4597 With the full nornIna set [9] the energq IS -457 48 16. Although much of the difference IS due to a difference III the descrlptlon of the core caused by the truncation of the basis set, the corresponding orthogonaltty effects on the valence orbttais may have sigmficant effect on the molecular mteractlon The types of configuratrons used are shown m table 2 The first IS the molecular Hartree-Fock configuration followed by 13 molecular correlation terms descrlbmg the 3p electrons The last two correspond to 3s + 3~0 excltatlons The magmtude of mLvmg coefficients of these confrgurdtlons as they occur m the wavefunctlon of the Cl2 ground state at R = 3 76 are also shown m table 7. in table 3 we hst m the second column the all-elecTable 1
and (m) employ the same configurations as above, and obtam the MPK wavefunctions and potential curve In contrast to our earher work, we shall also study the dependence of the pseudo-potential curve on the choice of the basrs for the “outer-core” representatlon
3 _Calculations
and results
We shall carry out the pseudo-potential and a& electron comparison only for the Cl, molecule The Br2 curve WLUthen be obtamed usu?g the pseudopotential OVC framework.
The alletectron 306
basis functions
used for the C&U-
Ems sets used for the c&ulatlons of Cl2 and Br2 wavefunctlons Oniy the starred functions are consldered for the find pseudo-potentnl calculations
Series
Chlorme n
Broome 1
r
I1
1
1
0
2
2
0
18 416 16 316
3
3
0
4
2
5 6 7
8 9 10 11 12 13 14
1
3-
3
0
5.206
0 0
3 296
2873*
4 4
0
5 839*
3
1
1998 5 461
3 4
0 0
i 809s 1809’
4
I
2 914
2 2 2 3 3 3 3 4
1 1 1 1 1 2 2 2
14 458 8 45.5 5 298** 2 609* 1.4.56* 1456* 2 609*
4 5 3 4 4
1 1 2 2 2
1615 1998 3 188 2914 1.165
1.456*
Volume
79, number
2
CHEhIICAL
PHYSICS
1
,~s+r&lp~npa4,,lp~ npo;
3
npagnpsru-
-c tzpo2,
0 1199
4
npognprrg
5
rzpo; -c (n+ l)s$
6
npugz -
(12 + I ,su;
0 0018
7
npo;
-
,ldo;
0 0333
8
npoi
- ndo$
0 0134
9
npo;
-
rlpau(n +npou(n+
+ 1)png
0 0495
1)prru
0 1165 0 0044
(n+ l)pni
00011
10
rrpo; -L (n + l)prri
0 0016
11
npa’
- ndrri
0 0418
12
npag --* tidrri
0 0131
13
npn2
- npo;
0 0204
14
npxg
+ npaz
0 0388
15
nsu$ - npai
0 0161
16
nsouz - npa:,
0 02.51
g
@3P
R
-0 0073 2p(r
= 14.458)
of Cl2 and Br? based
on all-electron
and pseudo-potential
2p(<=8
models
baw
(u)
basis (m) 0 0796 0482
0 1403 -0 047 1 -0 0806
0 2406 -0 0234 -0 0854
0 2205 -0 0365 -0 0886
3.5 40 4.5
-0
-0 -0
-0 -0
-0 -0
-0 -0
50 55 60 80
-0 0612 -0 04 10 -0 0139 -0 0025
0646 0371
Encrgles
Br2
0 2349 -0 026 -0 0818 0720 0479
455)
pseudo-potent&
pseudo-potential (I)
- 0.0813
These coefficients are the same as those occurring with their respective basis functions m the asymptotic 3p orbital from the all-electron calculation Thus will ensure that the core-vaience overlap is real&x and small The correspondmg pseudo-potential potential curves using the same core as used for the allelectron calculations are shown m columns 4-6 of table 3 In fig 1 these curves are compared with the all-electron curve We observe that even though the weU uepth IS surprtstngly sun&r for the first two curves, they differ markedly m other details Also, the third curve, whxh IS comparable to the previous calculations reported m ref [S] , 1s not mxkedly different from the second
R
baus 2 76 3 26 3 76 426 4.76
=
Cl2 all-electron
caicuiatzom
-020352p(~=529S)+O57533p(S_=2609)
tron mteractlon energies, E(R) - E(m), for various internuclear separattons As we menttoned before, these energies are calculated with a frozen atomic core obtained from the asymptotic calculattons with the truncated basis set Sample calculations indicate that no slgmficant improvement results If instead we Table 3 lnteractlon energies E(R) - E(m) for theground states m hartree and I?, mternuclear separstlon. UI bohr
1981
We shall consider three types of basis sets for these calculations AU of them will contam the full valence basrs subset However, the first contams no 2p functlons (I e , all the functrons marked wrth smgle asterrsks III table 1) and the second contams all the functions marked with single or double asterisks, whtie the thud conststs of aU the functions of the first set with the more compact 3p at each center replaced by the hnear combmatlon
0 9847
2
C7, _ pseudo-potential
3.2
hlagmtude of mL\mg coefficients for Cl, at R = 3 76
Configuration
I5 April
had selected the futl nominal set plus the polarlzatlon functions already considered For example, the value ofE(R) -E(m) for the latter calculations at R = 4 26 IS -0 0732 versus -0 0720 for the truncated set.
Table 2 Confiiuratlon types used for the ground states of Cl;! and Br2 The occupancy of only the valence shells 1s shown; for Cl, n = 3 and for Br, n = 4 Evcitatlon description IS used for all but the first confiiuratlon Series
LETTERS
0784 0525
0768 0512
-0
0731
307
Volume
79, number -002
CHEhflCAL
2
-
ALL-ELECTRON
-----
PSEUDO WITH
---
PSEUDO WlTH
I
I
I
I ’1
POTENTIAL
CURVE
(II)
POTENTIAL
LETTERS
15 AprrlI5’31
(in) 1s comparable to an ECP approach since in the latter. too, one constrains the pseudo-valence orbital to have the same kmd of mlxmg with the core over the whole molecular range. Unless one IS Interested III tughly accurate potential curves, however, pseudo-potential calculations with either basis set (u) or (111) IS satisfactory. In table 4 the calculated spectroscopic constants based on both the all-electron curve as well as the pseudo-potential ones with basis sets of (11) and (in) are compared with experunent
I
CURVE
BASIS
PHYSlCS
CURVE
BASIS tt,11
3 3 Br2
pseudo-poremlal
cclmlatiorw
4
-0 IO. 3 25
I 3 50
I 3 75
I 400
I 425
I 4 50
-175
R IBohrsl i-4 1 Comptirlson of the potential curbes for Cl, obmmed theoretIcally by tiilectron nnd pseudo-potentml methods
As we have noted before, the purpose of mtroducmg outer-core basis functions IS to ensure that by evphclt orthogonahty to a crude representation of the outer core. the core-valence overlap remams small. This IS reahstlcally achieved with both kmds (u) and (111) of pseudo-potential basis. Each basis has Its advantages and disadvantages Willie basis (11) affords more flexlblhty than basis (M) It 1s also more expensive Apparently basis (11) results are closer to the all-electron curve than either of the other two The MPK pseudo-potential with a restrlcced basis
The basis set, which IS again a valence nommal set [9] augmented by polanzatlon functions, IS shown m table 1 The basis contams the 3p functions required to represent the %zV - 1” outer core The core Itself, however. 1s now obtained from a numerical HartreeFock calculation of the bromine 2P3,? state The correspondmg potential curve IS shown in table 3 and the spectroscopic constants m table 4. The qualhty of the Br7 results 1s clearly superior to those of Cl,. Since the main difference hes In the choice of the core, we contend that It IS necessary, among other thmgs, to improve the core for chlorme, if one IS interested m more reahstlc spectroscopic constants. Thts IS true both m pseudo-potentlsl as well as all-electron calcu:atlons
Acknowledgement The author
gratefully
acknowledges
useful
dlscus-
Table 4
Spectroscopic constants of Cl2 and Brz BT2
Cl2 hlPK bnsls (u)
XlPK basis (u0
cup
hlPK basis (u)
ev
theory 3 85 491 34 0 23 0 002 2 18
3 89 484 31 0 12 0 002 7 28
381 510 34 0 23 0 002 2 36
3 76 560 2.7 0 24 0.0014 2 48a)
4 42 302 13
4 31 325 11 0 082 0 00032 i97a)
di-elect.ron
‘e @oh) We (cm-‘) WeXe
(Cm-‘)
Be (cm-‘) ae (cm-l) De W)
0
077
0 00037 192
Volume 79. number 2
sions with Dr L.R above calculatmns
CHEMICAL PHYSICS LETTERS
Kahn on various
aspects
of the
15 Apnl1981
[4] G Das and A C Wahl. J Chem. Phys. 69 (1978) 53 [5] L.R. Kahn, P Baybutt and D G Truhlar, J Chem. Phys 65 (1976)
3826.
[6] J H Williams and R D Amos. Chem. Phys Letters 70 (1980) 162 G Das and AC
References
[7]
[ 1 ] G Das and A C Wahl, Phys Rev Letters 25 (1970)
[SI G Das, Chem. Phys Letters 71 (1980) 202 [9] AC Wahi, P J Bertoncuu, K Kaiser and R H. Land,
J. Chem. Phys. 56 (1972) 3532 [2] M A hiorrlson and P S Hay, J Chem
Phys
991,
70 (1979)
4034. [3] A C. Wahl and G Das, tn Methods of electrontc structure theory, ed H F Schaefer III (Plenum Press, New York, 1977)
WahI. J Chem
Phys
64 (1976)
4672
BISON. A Fortran Computmg System for SelfCorwstentField Calculations of Dutomlc Molecde~, AI~OIIIE National Laboratory Tech Report No. 7271
309