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Ab initio CI study of CN+: the identity of the ground state
VoIumc
66. number
AB INITlO
CIICMICAL PIiYSICS LETTIlRS
I?
CI STUDY
OF CN+: THE IDENTITY
OF THE GROUND
I October
1979
STATE
Ab inuio confguration rntcr.tctron calcul~tlons tbr some Ion -I>ing electronic sl.ttes (’ X”. tn. 3~ and ‘XI- ) have been cxricd out .md potcurL energ> curxs ae reported for internucku dbrmces ne.tr equthbriurn. The mlculsted result shows th.tt the 311 sfate b the ground state, Icing about 0.41 eV below rhr I\‘* smtt. The 3~-1~ separation 1s predicted to be 0.82 eV. The r;tlsuI.acd resuhs arc compared with both c\pcrimentsl and preiious theoretical studies.
The CN+ ion is of considerable Jstrophysicsl importance [I .2]_ I fowcvcr. there still exists J controversy concerning the identity of the ground state. An 3b initio SCF calcubtion by hloffdt (31 supported the esperimcntA contention f?l that the ground st3te is 3 * ,V+ state. A further SCF study by Wu 14.51 concluded that the ground state ofC:P is 3 XII state. An Lb initio CI LZtlcul&ion by Sbim~kur~ at 31. [6] suggested that the *? st3te is the ground state. but this study N’S not conclusive sixe the average error reported by the 3uthors for the cJlcuIated T, WASabout 1 .I eV_ In this work, 3n 3ttempt is msde to clrtrify the situation and to cAxIatc the ground stttte potential energy curve for internuclear distances near equilibrium by c3rrying out .I Ixge scrtle ab initio SCF Ci caIcuIation_ Furthermore, some of the low-lying electronic states have 31~0 been considered and potential curves for these states sre 31~0 obtained for comparison. The ab initio SCF c3Icuiation which precedes the CI study employs the gsussinn b&s set of Huzinaga’s (9s, 5p) set 171, contrtlcted to .I double zeta (4s, 2p) according to Dunning’s scheme [S] plus a polarization function. (d) of exponents of 0.75 and 0.80 for carbon and nitrogen, respectively- The SCF c3IcuIations have been czlrried out for four states of interest with the folIowing configur3tions: . . . 4a’
17+, ‘z+)
. ..4a2
5als3,
__40” 50’
‘ll and 317,
17$,3x-
)
at five internuclear distances between 20 and 3.0 au. Two further st3tes 14 snd 3x+ which arise from configurations ___40’ 502 1~’ and .__4050 1x4, respectively, are omitted from consideration. since neither of these states should correspond to the ground state as shown by previous results [3-6]_ A configuration interaction calculation has been carried out for each state of interest employing the above-mentioned configuration 3s the reference contigumtion. In each case the CI matrix was formed, which included all single and double excitations of the valence she11 eiectrons from each reference configuration. These were selected by perturbation theory with an energy threshold of 1O-5_ Table 1 summarizes the SCF and CI energies, the dimensions of the CI wavefuncticns and the coefficients of the reference configurations at five different C--N distances_ The 4Er, v3iues refer to portions of energy kept or not kept by the second-order perturbation theory. Since the question to be resolved concerns whether the 12+ or 3II state is the ground state, only these two states are included in table I_ The difference in the dimensions of the wavefunctions is the result of the different spin coupling available for triplet and singlet states, and it is noted that the open-shell reference configuration (311) produced many more terms than the closed-shell one (‘Z-)_ It is also noted that the &cuIated SCF and CI energies in the present work 3re significantly lower than previously reported SCF [5] and CI [6] results. 317
I
co c’
1Ef iqx,
Y1.5Y-s -9 1_65zf~ -YI_bfJ61 - 91 5697 -9 i .-ra9rr
ZDO 1.X Z_-?O 2-60 3.00
-91.6965 -9 I .7-35-Z -91-7397 -91.6589 -91.6371
913735
(785)
-0
-9! Y~?-rf750) -91.912119fk-s? -91.8756ti5OJ -91.7896l701)
KS976 0.909 I 0.9111 0.9062 b.X9/9
fJu-13
-0.004
I 002 I
-0
-0.003S --0.004
1
-91.8501f11S5~
-0.1170
-91_9-t46(1113)
-0.26 1-l -0.311s -0.317,
-0 006-I -0.0057 -0.0055 -0.001-5
-036f9
-0 0018
-91.9558 GlfO) -9 t .9x0 ( 1S-%9) -9l.S687(1757)
1979
October
0.9585 o-9199 0.9391 0.9GlP 0.908 I - --_
s’ .-uumic uniu b, V&k3 inpaxnth~~rs the dimensions of the CI usefunctions. c’ CocffSients of rhtzrefmxcu c-unfguratiorxs.
The SCF and CI potential rnergy -- curves for ri12 ‘Xc_ 3x--- st3tes f-orvdua of the c-x distance - 311 a*d bstwtin Z-0 and 3.0 au ~2 disphyed in fig_ 1. and the interpolated equilibrium distances (r,) Y weI as the arr2sponding ener@ ~2 Iisted in trtbIe 2. Ti12 SCF rest&s show that the 311 state lies only O-16 CV lower than the 3_V- state and thr ciosrd-sheli t ?? stat2 Iies about 34-l 2V above the 311state. The influence of the cunfiiuration mixing is most signifrcant for the cIosed-shell ‘Xc state as shown in fig_ I = axtsing the equiiibrium energy of this stat2 to be Iow2r than the 1II state_ However, the $11 state, which becomes lower than the 3\-- state by 3.66 rV in the Ct dcdation. still iies about l-0, CV !ower than tile *Z+ state_ Ev2n though the energy portions which are not kept by ihe second order perturbation theory (&E(not kept)) and which have energy threshoids of IO-5 are less than 1% for the t? stat and Iess than 3% for the 311state with respect to the AE(kept) vafue, as shown in table l= it is worthwhile to estimate an upper bound for this energ using the zero energy threshold formukl [9] I I ji
_
I
zU$,(kept)
f AEJnot
AEp (kept)
kept)
AE(CI
- SCF) _
Furthermore. the correlation energy due to the quadru-
T(CN) -
I 22 Fig 1. SCF and
CL
1
* 25
t ;Ii
2'&3
potential energy curvesfor CN+
30 (XI).
polar excitation (AEquJd ), which is not considered in this work, may also be estimated by [ 101, AEsd=
(I-
C;) AE(CI
where Co is the coefficient
- SCF) , of the reference configum-
1 October
ci IL.\1ICAL PI f ‘t’SICS LCTTEKS
66. nurnbcr 2
\‘uiun~c
1979
l-.ible 1 Lqtrihbrlun1 dl?at.!nl_eWe) Jlld ti1c cncq) _-__
_
__
___ __
_-._
___
st_tre
--
I_
iv+
--
_ _.
+a’ tmnw
-
311 *II lx-__ wufs. V.&r\
_
._____-
tttint1nun1 ufCN4.t) - - -.. I --.- ---
--
.---
----
--^ 2.00
L;IlldCI~
f 77-g _*__ 2.273 3.189 2.s-t2
-91.61519t3.J.t) -9 1.75 17s (0.00) -9 I .7 1757 (0.9 3)
2.172 1.316 1_34’7
-9 t .7-?556 10.16)
Z.6l-l
-9 I .913GP -9 I-960-%5 -91.907G8 -91 93621 -___.--__-_.
*n parcnrbrsez are dtffcrtnccs
~Kiotds _.-
b’
m ericq
rf
s-q,d
’ 10 __-
-G_ISf7 -0.3957
-O.OS-tl -0.0509
X-t0 2.60 3.00
-0.3Oh7 -0.3ois -0.3027
-0 051-z -0 0547 -0.0609
__ _~___
--- _
a>Atomic
---__--__-
r&II)
__
_
___
-
_
__-
(1 02) (0.00) C1.45) (0.66)
x\Iti1 rcspc~t to the 311 adtc in cV.
.I’
C(Clle,t,d)
~- -- ----_--.^ -___I__~ 311st‘ltc ~---___--L ---‘!-‘qud I) -l&o& b)
-91.9305 -91.9706
-0.IS88 -0 7037
-91.96-Z3 -9 1.9322 -9 I .85X
-G 2130 -0.73s 1 -0 23-w
’ x+ s-ate . _ _ __- ___ .__- - _---.-_
-
t;ttt,fSa3
T.tbIc 3 E~11nuttd correI.ttion cncrg*e> .md tor.11 rflcrgtC5 0f tile I \* .md 311 Stdfc\ 0fCW ---.__ _..___ - _., _ -- ----- -
rtcw J)
---------.---
~,cxI-~
EfCIfc\trd)
-0.OI49
-9i_9002
-0.0195 -0.0258
-919629 -91.9885
-0 -0
-9 l-9709 -91.9123
0139 O-IO6
units.
bJ C>tmutcd torrcf&tiofl mcrgics due to .dI doubie e\cit&ions_ c) Cstitn.tted curr&tion cncrges due 10 qtudrupok r\citatron_ d) Cxtrdpolatcd totA energies.
tion tistcd in table I_ Table 3 sutnmxizcs the extrapoktcd corr&tion cncrgics due to rhc double cxcitation (fE&,“$,) and the estimated contributions from the quadrupotar excitation (ilEqWd) as wcii as the estimated t0t.d CI energies (E(U),,,) for the IT+ and jII stJtcs of CKf. The estimated contribution from the quadrupok excitation for the I Z+ stdtc is signific;lntl~ lager than for the ZKI state. The cstrapolatcd energies are -91.9737 .IU Q-c = 2207 au) for the t Z* state and -9 19SS7 a.~ (Y, = 1.102 au) for the 3fI state. rcspectivcly. The difference in energy between these two states decrc.xses to O-41 eV_ with the 3ll stztc still lying below the 1 x+ state, Based upon the estimated energy difference between the 3 fl and f R states of 1.36 rf-:03 eV and the experimental excitation energy of 1.03 eV for the 1 St -+ III excitation [2], Wu [S] concluded that the ground state is the JfI state, lying about 03 eV below the t2? state. His conclusion was based upon the SCF rcsuIt and the corrcfation energy difference between the two states
t 3 II and 1Fl) VJS taken to bc zero. with the argument that the 2p-3p corrckrion energy of the united-atom Mg was expected to be smalI irrespective to the spin muItipIrcity of the two electrons. As shown in table 4. the corrcIation energies calculated by the extrapollltion schemes including the “EQUd vtlluc as mentioned above, arc afmosr idcntica1 in the region of the equilibrium r(CN) both for the 3II .md I II states. This justifies the previous assumption that the difference in the correfation energies between these two stares is &lost ncgIiTable 5 Estimated correlation energi2s
of the 3yt .md 1 tt statesa)
r(CCN) 3)
3-I
‘lx
2.0
-0.2037 -0.2232 -0.24SS -02870 -0.2752
-0.1771 -0.3213 -0.2406 -02805 -0.3375
2.2 2.4 Z-6 3.0 a) Atomic
units.
319
criiploysd
It is ~vvorrhrrhitc to rnsutiui~ that thr gnmud 5t;lW of the isuckctcouic CL n~uIcct~ie is calcuI.ttcd tu be ;L ‘Xi state I> ittg Jbout 033 CV bsluw I %, >t.itc‘ [I I I_ The diffkrcmx in corr&tion energy bctwccn the ’ Xz ad 311, st;lte was~~tirn~tsd as 0.063 JU (1.71 8%) f 121. l~ltrle it is nut possible to strictly sumpsre the X&-F vzduc bstwvceu tht.xe two stata of-Cl since the opru-she11 SCF vsluc fix the jIi, state was uut repurtcd_ the cffeet of electron correbtiun seems to be brge ettou$ to rcvcrsc ths reintivc ordering of these two states f-or C2 (i’s_ cztIcuhtiott3 (I) and (II) of ref_ II I I)_ IIowvcr. the 311 .ud i X* states for the x-*cr-_ value bemwn CS* of X4-l cV is ruucii larger thm the estiuisted differencz in correlation energy between these two statesFrom this drtaikd analysis brrsed upon the correlatiou energy estimation procedrvt by SCF and Iarge scale Cl r~lcttiation, it may be concluded that the ground state of the CL’+ ion should be ;I 311 state of the [__4035a 1x3] reference configuration.
in this study.
111 EL. Lutr..\stropl~r. J. 163 (1971) 151. [3[ J.IJ. .\fotfJt. J. No!. Struut. 6 (1970) 1%. [-tj A_A_N’u_Chem_ Ph\k_ 11 (1977) 17X [S 1 AA_ Wu. Chum. Ph> s. Letters 59 ( 1978) X7[6i X. ShimAura. iI_ Inou~e. X. IIonjou_ M- SJg-lrz and I;_ Ohno. Cheru_ Phk L Lez:Icr%55 ( 1975) 11 I 171 S_ tlurirqyx. J_ Chcm. Ph\% 47 (1965) 1293. [St T_fl_ Dunn~. J- Chern. P&-s_ 53 ( 1970) X23191 E.R. Daxidson. private communicxrion. [ 101 S-R_ Lan$off and L-R_ Dd%idsun. Intern. J. Qrun:um Chem
[ 11:
7 t 1973
999_
J. BarsuBn. Z_ Naturtorsrf~ 77:,(1971) 1031, and referakxs therein. G. Verh.g:cn. W.G. Richards .md CA!. Moser. J. Chem. Phyr -t6 (1967) 160_
66. number
AB INITlO
CIICMICAL PIiYSICS LETTIlRS
I?
CI STUDY
OF CN+: THE IDENTITY
OF THE GROUND
I October
1979
STATE
Ab inuio confguration rntcr.tctron calcul~tlons tbr some Ion -I>ing electronic sl.ttes (’ X”. tn. 3~ and ‘XI- ) have been cxricd out .md potcurL energ> curxs ae reported for internucku dbrmces ne.tr equthbriurn. The mlculsted result shows th.tt the 311 sfate b the ground state, Icing about 0.41 eV below rhr I\‘* smtt. The 3~-1~ separation 1s predicted to be 0.82 eV. The r;tlsuI.acd resuhs arc compared with both c\pcrimentsl and preiious theoretical studies.
The CN+ ion is of considerable Jstrophysicsl importance [I .2]_ I fowcvcr. there still exists J controversy concerning the identity of the ground state. An 3b initio SCF calcubtion by hloffdt (31 supported the esperimcntA contention f?l that the ground st3te is 3 * ,V+ state. A further SCF study by Wu 14.51 concluded that the ground state ofC:P is 3 XII state. An Lb initio CI LZtlcul&ion by Sbim~kur~ at 31. [6] suggested that the *? st3te is the ground state. but this study N’S not conclusive sixe the average error reported by the 3uthors for the cJlcuIated T, WASabout 1 .I eV_ In this work, 3n 3ttempt is msde to clrtrify the situation and to cAxIatc the ground stttte potential energy curve for internuclear distances near equilibrium by c3rrying out .I Ixge scrtle ab initio SCF Ci caIcuIation_ Furthermore, some of the low-lying electronic states have 31~0 been considered and potential curves for these states sre 31~0 obtained for comparison. The ab initio SCF c3Icuiation which precedes the CI study employs the gsussinn b&s set of Huzinaga’s (9s, 5p) set 171, contrtlcted to .I double zeta (4s, 2p) according to Dunning’s scheme [S] plus a polarization function. (d) of exponents of 0.75 and 0.80 for carbon and nitrogen, respectively- The SCF c3IcuIations have been czlrried out for four states of interest with the folIowing configur3tions: . . . 4a’
17+, ‘z+)
. ..4a2
5als3,
__40” 50’
‘ll and 317,
17$,3x-
)
at five internuclear distances between 20 and 3.0 au. Two further st3tes 14 snd 3x+ which arise from configurations ___40’ 502 1~’ and .__4050 1x4, respectively, are omitted from consideration. since neither of these states should correspond to the ground state as shown by previous results [3-6]_ A configuration interaction calculation has been carried out for each state of interest employing the above-mentioned configuration 3s the reference contigumtion. In each case the CI matrix was formed, which included all single and double excitations of the valence she11 eiectrons from each reference configuration. These were selected by perturbation theory with an energy threshold of 1O-5_ Table 1 summarizes the SCF and CI energies, the dimensions of the CI wavefuncticns and the coefficients of the reference configurations at five different C--N distances_ The 4Er, v3iues refer to portions of energy kept or not kept by the second-order perturbation theory. Since the question to be resolved concerns whether the 12+ or 3II state is the ground state, only these two states are included in table I_ The difference in the dimensions of the wavefunctions is the result of the different spin coupling available for triplet and singlet states, and it is noted that the open-shell reference configuration (311) produced many more terms than the closed-shell one (‘Z-)_ It is also noted that the &cuIated SCF and CI energies in the present work 3re significantly lower than previously reported SCF [5] and CI [6] results. 317
I
co c’
1Ef iqx,
Y1.5Y-s -9 1_65zf~ -YI_bfJ61 - 91 5697 -9 i .-ra9rr
ZDO 1.X Z_-?O 2-60 3.00
-91.6965 -9 I .7-35-Z -91-7397 -91.6589 -91.6371
913735
(785)
-0
-9! Y~?-rf750) -91.912119fk-s? -91.8756ti5OJ -91.7896l701)
KS976 0.909 I 0.9111 0.9062 b.X9/9
fJu-13
-0.004
I 002 I
-0
-0.003S --0.004
1
-91.8501f11S5~
-0.1170
-91_9-t46(1113)
-0.26 1-l -0.311s -0.317,
-0 006-I -0.0057 -0.0055 -0.001-5
-036f9
-0 0018
-91.9558 GlfO) -9 t .9x0 ( 1S-%9) -9l.S687(1757)
1979
October
0.9585 o-9199 0.9391 0.9GlP 0.908 I - --_
s’ .-uumic uniu b, V&k3 inpaxnth~~rs the dimensions of the CI usefunctions. c’ CocffSients of rhtzrefmxcu c-unfguratiorxs.
The SCF and CI potential rnergy -- curves for ri12 ‘Xc_ 3x--- st3tes f-orvdua of the c-x distance - 311 a*d bstwtin Z-0 and 3.0 au ~2 disphyed in fig_ 1. and the interpolated equilibrium distances (r,) Y weI as the arr2sponding ener@ ~2 Iisted in trtbIe 2. Ti12 SCF rest&s show that the 311 state lies only O-16 CV lower than the 3_V- state and thr ciosrd-sheli t ?? stat2 Iies about 34-l 2V above the 311state. The influence of the cunfiiuration mixing is most signifrcant for the cIosed-shell ‘Xc state as shown in fig_ I = axtsing the equiiibrium energy of this stat2 to be Iow2r than the 1II state_ However, the $11 state, which becomes lower than the 3\-- state by 3.66 rV in the Ct dcdation. still iies about l-0, CV !ower than tile *Z+ state_ Ev2n though the energy portions which are not kept by ihe second order perturbation theory (&E(not kept)) and which have energy threshoids of IO-5 are less than 1% for the t? stat and Iess than 3% for the 311state with respect to the AE(kept) vafue, as shown in table l= it is worthwhile to estimate an upper bound for this energ using the zero energy threshold formukl [9] I I ji
_
I
zU$,(kept)
f AEJnot
AEp (kept)
kept)
AE(CI
- SCF) _
Furthermore. the correlation energy due to the quadru-
T(CN) -
I 22 Fig 1. SCF and
CL
1
* 25
t ;Ii
2'&3
potential energy curvesfor CN+
30 (XI).
polar excitation (AEquJd ), which is not considered in this work, may also be estimated by [ 101, AEsd=
(I-
C;) AE(CI
where Co is the coefficient
- SCF) , of the reference configum-
1 October
ci IL.\1ICAL PI f ‘t’SICS LCTTEKS
66. nurnbcr 2
\‘uiun~c
1979
l-.ible 1 Lqtrihbrlun1 dl?at.!nl_eWe) Jlld ti1c cncq) _-__
_
__
___ __
_-._
___
st_tre
--
I_
iv+
--
_ _.
+a’ tmnw
-
311 *II lx-__ wufs. V.&r\
_
._____-
tttint1nun1 ufCN4.t) - - -.. I --.- ---
--
.---
----
--^ 2.00
L;IlldCI~
f 77-g _*__ 2.273 3.189 2.s-t2
-91.61519t3.J.t) -9 1.75 17s (0.00) -9 I .7 1757 (0.9 3)
2.172 1.316 1_34’7
-9 t .7-?556 10.16)
Z.6l-l
-9 I .913GP -9 I-960-%5 -91.907G8 -91 93621 -___.--__-_.
*n parcnrbrsez are dtffcrtnccs
~Kiotds _.-
b’
m ericq
rf
s-q,d
’ 10 __-
-G_ISf7 -0.3957
-O.OS-tl -0.0509
X-t0 2.60 3.00
-0.3Oh7 -0.3ois -0.3027
-0 051-z -0 0547 -0.0609
__ _~___
--- _
a>Atomic
---__--__-
r&II)
__
_
___
-
_
__-
(1 02) (0.00) C1.45) (0.66)
x\Iti1 rcspc~t to the 311 adtc in cV.
.I’
C(Clle,t,d)
~- -- ----_--.^ -___I__~ 311st‘ltc ~---___--L ---‘!-‘qud I) -l&o& b)
-91.9305 -91.9706
-0.IS88 -0 7037
-91.96-Z3 -9 1.9322 -9 I .85X
-G 2130 -0.73s 1 -0 23-w
’ x+ s-ate . _ _ __- ___ .__- - _---.-_
-
t;ttt,fSa3
T.tbIc 3 E~11nuttd correI.ttion cncrg*e> .md tor.11 rflcrgtC5 0f tile I \* .md 311 Stdfc\ 0fCW ---.__ _..___ - _., _ -- ----- -
rtcw J)
---------.---
~,cxI-~
EfCIfc\trd)
-0.OI49
-9i_9002
-0.0195 -0.0258
-919629 -91.9885
-0 -0
-9 l-9709 -91.9123
0139 O-IO6
units.
bJ C>tmutcd torrcf&tiofl mcrgics due to .dI doubie e\cit&ions_ c) Cstitn.tted curr&tion cncrges due 10 qtudrupok r\citatron_ d) Cxtrdpolatcd totA energies.
tion tistcd in table I_ Table 3 sutnmxizcs the extrapoktcd corr&tion cncrgics due to rhc double cxcitation (fE&,“$,) and the estimated contributions from the quadrupotar excitation (ilEqWd) as wcii as the estimated t0t.d CI energies (E(U),,,) for the IT+ and jII stJtcs of CKf. The estimated contribution from the quadrupok excitation for the I Z+ stdtc is signific;lntl~ lager than for the ZKI state. The cstrapolatcd energies are -91.9737 .IU Q-c = 2207 au) for the t Z* state and -9 19SS7 a.~ (Y, = 1.102 au) for the 3fI state. rcspectivcly. The difference in energy between these two states decrc.xses to O-41 eV_ with the 3ll stztc still lying below the 1 x+ state, Based upon the estimated energy difference between the 3 fl and f R states of 1.36 rf-:03 eV and the experimental excitation energy of 1.03 eV for the 1 St -+ III excitation [2], Wu [S] concluded that the ground state is the JfI state, lying about 03 eV below the t2? state. His conclusion was based upon the SCF rcsuIt and the corrcfation energy difference between the two states
t 3 II and 1Fl) VJS taken to bc zero. with the argument that the 2p-3p corrckrion energy of the united-atom Mg was expected to be smalI irrespective to the spin muItipIrcity of the two electrons. As shown in table 4. the corrcIation energies calculated by the extrapollltion schemes including the “EQUd vtlluc as mentioned above, arc afmosr idcntica1 in the region of the equilibrium r(CN) both for the 3II .md I II states. This justifies the previous assumption that the difference in the correfation energies between these two stares is &lost ncgIiTable 5 Estimated correlation energi2s
of the 3yt .md 1 tt statesa)
r(CCN) 3)
3-I
‘lx
2.0
-0.2037 -0.2232 -0.24SS -02870 -0.2752
-0.1771 -0.3213 -0.2406 -02805 -0.3375
2.2 2.4 Z-6 3.0 a) Atomic
units.
319
criiploysd
It is ~vvorrhrrhitc to rnsutiui~ that thr gnmud 5t;lW of the isuckctcouic CL n~uIcct~ie is calcuI.ttcd tu be ;L ‘Xi state I> ittg Jbout 033 CV bsluw I %, >t.itc‘ [I I I_ The diffkrcmx in corr&tion energy bctwccn the ’ Xz ad 311, st;lte was~~tirn~tsd as 0.063 JU (1.71 8%) f 121. l~ltrle it is nut possible to strictly sumpsre the X&-F vzduc bstwvceu tht.xe two stata of-Cl since the opru-she11 SCF vsluc fix the jIi, state was uut repurtcd_ the cffeet of electron correbtiun seems to be brge ettou$ to rcvcrsc ths reintivc ordering of these two states f-or C2 (i’s_ cztIcuhtiott3 (I) and (II) of ref_ II I I)_ IIowvcr. the 311 .ud i X* states for the x-*cr-_ value bemwn CS* of X4-l cV is ruucii larger thm the estiuisted differencz in correlation energy between these two statesFrom this drtaikd analysis brrsed upon the correlatiou energy estimation procedrvt by SCF and Iarge scale Cl r~lcttiation, it may be concluded that the ground state of the CL’+ ion should be ;I 311 state of the [__4035a 1x3] reference configuration.
in this study.
111 EL. Lutr..\stropl~r. J. 163 (1971) 151. [3[ J.IJ. .\fotfJt. J. No!. Struut. 6 (1970) 1%. [-tj A_A_N’u_Chem_ Ph\k_ 11 (1977) 17X [S 1 AA_ Wu. Chum. Ph> s. Letters 59 ( 1978) X7[6i X. ShimAura. iI_ Inou~e. X. IIonjou_ M- SJg-lrz and I;_ Ohno. Cheru_ Phk L Lez:Icr%55 ( 1975) 11 I 171 S_ tlurirqyx. J_ Chcm. Ph\% 47 (1965) 1293. [St T_fl_ Dunn~. J- Chern. P&-s_ 53 ( 1970) X23191 E.R. Daxidson. private communicxrion. [ 101 S-R_ Lan$off and L-R_ Dd%idsun. Intern. J. Qrun:um Chem
[ 11:
7 t 1973
999_
J. BarsuBn. Z_ Naturtorsrf~ 77:,(1971) 1031, and referakxs therein. G. Verh.g:cn. W.G. Richards .md CA!. Moser. J. Chem. Phyr -t6 (1967) 160_