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CALCULATION OF ELECTRON AFFINITIES USING THE NON-CLOSED SHELL MANY-ELECTRON
THEORY OF ATOMIC STRUCTURE
O. Sinanoglu
To cite this version:
O. Sinanoglu. CALCULATION OF ELECTRON AFFINITIES USING THE NON-CLOSED SHELL
MANY-ELECTRON THEORY OF ATOMIC STRUCTURE. Journal de Physique Colloques, 1970,
31 (C4), pp.C4-89-C4-97. �10.1051/jphyscol:1970415�. �jpa-00213870�
JOURNAL DE PHYSIQUE Collog~ic~ C4, s~ipplc!~~~et~t ari 11" 11-17, TOIIIL' 31, h ' o ~ . . - D ~ c . 1970, yugr C4-89
CALCULATION OF ELECTRON AFFINITIES USING THE NON-CLO SED SHELL MANY-ELECTRON THEORY OF
ATOMIC STRUCTURE (*)
by 0 . S I N A N O G ~ U
Yale University New Haven, Conn. 06520, U. S. A.
In another paper in this conference proceedings we outlined some of the aspects of tile theory of electron correlation for ground and excited states and the atomic structure theory it leads to. Here we apply the theory to the calculation of atomic electron affinities (E. A.) at least for the lightereletnents where relativistic effects still d o not require a full relativistic Hartree-Fock starting point.
Electron affinities were obtained this way for C, N, 0, and F in a previous paper, but tlie wave functions (w. f.) used were not reported. Here we give the wave functions of the species involved and discuss some further aspects of the problem. The w. f.'s themselves may be found useful in other contexts, e. g. in e- atom scattering problems.
According t o the theory which we may refer to as NCMET ((( Non-closed Shell Many Electron Theory B) for short, the w. f. and energy of an N-electron state are given by
with ,,@, the restricted Hartree-Fock w. f. and all parts in eq. (I) mutually orthogonal, and
(TO
eq. (2), a relativistic correction (low Z approxi- mation) is also added in the actual calculations.) Equation (1) and (2) contain the threc distinct correlation effects found in tlie theory :(( int >) = Internal correlations
(( F)> = Semi-internal correlations including
orbital polarizations (3)
(( U )> = All-external (closed shell-like)
correlations.
(For further details c. f. references [I], [2].) The part of the w. f. eq. (1) affecting charge distri- butions appreciably is the part
The calculation of this part requires the evaluation of only at most four new radial functions F,(rI, F,(r),
F,(r), and F,(r) for all terms arising out of the 1 s' 2 sn 2 pn' configurations. I n ref. (2) it is shown that each of these F(r)'s are well approximated by a single Slater orbital (STO) with optimized exponents.
Thus
F,(r)
r
3 s*F;,(r) z 3 p*
F,(r)
r
3 d * (5)F,(r) 2 4 f*
where orbitals are only nominally 3 s-like, 3 p-like.
etc
...
They are in reality quite different than the actual orbitals with the same radial quantum numbers.They are maximally-pulled-in-orbitals to the regions of tlie actual 2 s and 2 p's of each species (Thus expan- ded in a complete set, they would contain many nl orbitals).
That only a finite number of new radial f ~ ~ n c t i o n s is required is a consequence of the semi-internal correlation functions' ( j i j ; , 's occuring in X,) spherical harmonic expansion terminating due to the symmetry laws. The X i , , and X, together therefore can be calculated by a finite C. I. This has been done for over 150 states wit11 fully automatic programs deve- loped by 0 k s u z and Sinanoglu and in this labo- ratory. The n ~ e t h o d may be contrasted to conven- tional C. I. where infinitely many configurations are in principle involved and where choice of effective configurations had always been a problem.
I n Table I through VlII we display the w. f.'s
$cD = (pRHF
+
X(i,,t+F, for C, N, 0 , F and their negative ions ground states. Note that these are w. f.'s which are very hearly, but not exactly L2 and S2 eigenfunctions. Where needed we obtain the more exact one too, however, for a gain of usually only about 0.005 eV, this increases the size of the w. f. (and the computation). Depending on the atomic property, this increase may not be warranted. The move complete w. f. of Carbon I (I s2 2 s2 2 p2 3P) with exact LZ, S 2 property is also shown (Table VIII) and may be compared with the simpler one in Table I.These I),, w. f.'s may be used as such in transition probabilities, but for electron affinities (E. A.), one needs also the E,, all-external correlation energies
(*) Work supported by a grant from the U. S. National and X - .
Science Foundation. NCMET gives ways to calculate (say by (( pair-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1970415
0. SINANOGLU
E HF
- . - - -. . - . - -. -. . . - - - - - - - - - - - = - - - -0.37688613E - - - - - - - - - - - - C2 - -. . - 0 . 1 0 2 5 4 9 8 l E - - - - - - - - - - . 0 4 . . _ . ETOTAL = -0.37742957E 0 2 -0.10269768E 5 4
0 1 FFERENCE= -0.54343,700E-01 - 0 . 1 4 7 8 6 7 9 0 E 0 1 SUM OF CONTRIBUTIONS = - 0 . 5 6 3 4 2 4 7 8 E - @ I - C . l 4 7 8 6 4 5 8 E 9 1
EXPONENT = 1 . 7 5 9 9 9 9 9 9
~ - - - - - -- - - - - - - .- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -. . - - -. - -
0 . 9 7 6 9 8 6 8 0 RENflRMAL 1 Z I T I Oh FACTOR =
Table I1 The Wave Function C ~ l t h T*o Kinds Of Correlations (cf. text) f o r C' Oround State, ls'ls'lf 9s
1 COEFFICIENT CONTR sLIC$CY IBUTJONS
A.U. S . Y .
DET I = A I 1 I A 1 5 8 2SA 2 5 8 2P-A 2POA 2 P t A I 1 . 0 0 0 0 0 0 0 0 -0.37708642E 0 2 -0.10260431E 0 4
7sA I I t A ICR 7P-8 1 P + A 7P-A 7 P O I 7P+A I O.OP536824 -CC 566Ql306E-04 -0.15422847E-02
OET 3=A 1 1 S A 1SR 2PGR 3POA 2P-A ZPOA 2P+A I 0 . 0 0 5 3 6 8 5 9 - 0 . 5 6 6 8 4 9 5 9 E - 0 4 -0.15423841E-02 DET $ = A I 1 5 4 LSR 2P+k 3P-A 1P-A ZPOA 2 P + 4 J - 0 1 0 0 5 3 6 6 5 8 - C V 5 6 6 8 4 8 2 4 E - 0 4 -0.15423805E-02 OET 5.6 I I I A 15R 75A 2P-R 3SA 2PCA 2 P t A I 0 . 0 0 7 7 5 4 8 0 - 0 . 7 5 0 0 3 2 7 0 E - 0 4 -0.20408210E-02
OET 6 5 4 1 IF4 I S 8 7SA 2P-R 3ROA ZPOA ZP*A I 9 . 0 3 0 5 4 6 3 2 -0.12387057E-02 - 0 . 3 3 7 0 4 8 8 5 E - 0 1
OFT 7 1 6 I I C A 1 % 7 5 4 2POR 30-A 2POA 2P+A 1 - 0 . 0 5 2 9 0 7 7 2 -0.37161132E-02 - 0 . 1 0 1 1 1 4 5 5 E 0 0 R E T 8 - 4 l r A I 5 R 7CA 2P+R 3 0 -- b- 7 P n 4 2P+4 1 0 . 0 7 4 8 7 7 9 0 0 . 7 4 1 W 4 9 E - 0 2 0 . 2 0 2 2 2 9 3 3 E O Q OET 9 1 1 1 1 S A 1 5 8 2SP 2P-R 2P-A 3 0 + 4 2 P t b I 0 . 0 5 2 9 0 7 7 6 -0.37161163E-02 -0.10111463E 0 0
DET 1O.P I l C A 1 S Y 7SP 2POR ZP-A 3SA 2P+A I 0 . 0 0 7 7 5 4 8 0 -0.75003210E-04 -0.20408193E-02
OFT l l = A I I I A 1SH 7SP 2POR 2P-A 3DCA 2 P t A I - 0 . 0 6 1 0 9 2 6 6 - n . 4 9 5 4 8 2 4 9 ~ - 0 2 - 0 . 1 3 4 8 1 9 6 0 ~ 0 0 DET 1 2 = A I 15A L F R 7S4 7P+H 2P-A 30-A Z P t A I C.C5290778 - 0 . 3 7 1 6 1 1 7 5 E - 0 2 -0.10111466E OC
OFT 13-A I ISA ISR 2SA 2P-H 2P-A 2POA 30++A I 0 . 0 7 4 8 2 2 8 8 -0.74322331E-02 -0.2022292BE 0 0
QLI 14=A 1 1SA 1 x 8 2SA 2POR 2P-A ZPCA 3 0 * 4 1 - 0 . 0 5 2 9 0 7 7 6 - 0 . 3 7 1 6 1 1 6 5 E - 0 2 -3.10111464E 0 0
OET 15.A I 1 5 1 1 % 2SA 2P+R 2P-A 2PCA 3SA I 0 . 0 0 7 7 5 4 8 0 -0.75003250E-04 -0.20408204E-02
D E T 1h.A I 1FA 1 5 R 2.54 ZP+B ZP-A ZPCP 3Q0A ) 0 . 0 3 0 5 4 6 3 4 -0.1238706$E-92 - 0 . 3 3 7 0 4 9 1 5 E - 0 1
OFT 17=A I l I d 1 5 8 300A 2SB 2P-A 2POA 2P+A I 0.0000000C -0.86861281E-17 - 0 . 2 3 6 3 4 7 4 6 E - 1 5
D E T 1 8 - A I 1SA 1 5 8 ZSP 3DQR 2P-A 2POP 2P+A I 0 ~ 0 0 0 0 0 0 0 0 O~OOOOOQ90E CO 0 + 0 0 0 0 0 0 0 0 E 0 0
OFT 19=A I 1CA 1 5 8 7SA 2 5 8 4F-A 2PPA 2P+b I -G.00000000 - C . l 1 4 9 9 3 2 5 E - 1 8 -0.31289388E-17
n F T 7 n = A 1 l C A ICR 756 75H 7P-A 4FnA 7P+P 1 0 .D000(1MO 0.19469982E-18 0.52977353E-17
OET 71.1 I 1SA 1SR 2 5 6 2SR 2P-A 2POA *F+A 1 - 0 . 0 0 0 0 0 0 0 0 - 0 . 6 5 8 9 4 4 9 8 E - 1 9 -0.17929735E-17
A.U. E.V.
E HF = -0.37708642E 0 2 - 0 . 1 0 2 6 0 4 3 1 E 0 4 kTOTAL = -0.37746198E 0 2 - 0 . l Q 2 7 0 6 5 i I E 0 4 DIFFERENCE= - 0 . 3 7 5 5 6 6 4 8 E - 0 1 -0.10219074E 0 1 SUN. OF CONT.O.lBUT.ID#S..= - 0 , 3 7 5 5 6 2 . 2 P E ~ 0 1 . . . ~ ~ ~ . 1 . 0 2 ~ 8 9 6 0 ~ . . Q i
,E)(PONENT = 1 . 6 5 0 0 0 0 0 1
CALCULATION O F ELECTRON AFFINITIES USING T H E NON-CLOSED SHELL MANY-I-.Ll:CTItON C4-01
---- - . . Table TI1 'IRc Have Function X b ( c c . t e x t ) fop N i t ~ o g e n
*J
nFT l = A I 1 5 4 I 2SA 7SU ?P-A 7 P r 4 2P+A I - - - - - - -- .- -. --4AJS
I . o o o o n o o o - 0 . 5 4 4 0 0 8 5 4 ~ 0 2 DU_-L=4-l-ll?---l~~--~!:~--3!3A--2O=3--2!2!--2P?A_n_n-J - -- Q ~ 3 Q 2 4 5 Q 1 3 . zP333_7J3$8_l_EIQ_4__
0ET ? = A I 15A %PC4 ?P-4 7 P f d 2 9 t h 1
9ET 4 - 4 I 1Cd I C q 7P+R 7 P - 4 7 0 - 6 2PC4 Z P t 4 I -0.902'85053 - 0 . 3 0 7 1 7 9 0 l F - 0 4
0.00- @ . 3 0 7 L 7 8 0 ) F - 0 4
OFT 4=b I 1SJ 1"' 1SA 2p-R 154 Z P l A ?P+A I 5 . 0 1 3 9 6 8 7 6 - 0 . 3 6 5 4 0 4 8 2 6 - 0 3
O E L - ~ ? L ~ - ~ S ~ - - - ~ ~ . I - - -15A-- 1!z3-..3923- .-2_P-C4--2!?4.-- I-- ----. - - . . Q ~ 5 2 1 5 _ 7 _ 3 0 -_021/25_8_020Ez_02~
n E T 7=A I I S & 1 ' ' 5 4 .'Or3 3 9 - 3 ?PnA 2P+A I - 7 . 3 4 7 7 5 3 1 3 - 0 . 4 5 7 7 4 0 2 7 6 - 0 2
A - ~ ~ -~- ~ L L - Z P ~ I - - ~ J Z Z ~ - Z P ~ _ ~ ~ ~ f i ZP_*A---J - - - . . h ~ 6 1 ~ 3 1 7 . . = L u s * _ ~ . ~ Q ~ _ E ~ -
nFT 4 = A I l 5 4 q U ' 5 4 7P-t3 ?P-A ??+A 7P+b I
D E T ~ ) = P I 1 5 ' 1 , $ A 23n" 2 0 - A 7 p + ~ 1 " - 0 4 7 7 5 3 1 5 0 . n w - 0 . 4 5 7 7 4 0 4 2 E - 0 2 0- I F - 0 3
OFT I 1 =A I I \ 4 'et1 7 5 4 ? I " d 7*-A 30.36 ZP+A I - i . S 5 1 4 0 5 9 -0.6103Z06LE-02
Df!-J2:Ll-l52- -35'- 254- -311f4 .3_0:4 > 9 A _ Z ! _ b _ _ 1 _ . O E T i i = ~ I I \ & I c r ? ( A > ? - H ?,?-o Z P J L qn++b I
~ . - - 0.047 - - - - - 75 - . 318.. zO2_4_577441_7_E:_02_ .
0.36751320 -0.91548153E-02
C E 1 L 1 4 z A - l - I S b - ~ S B . - - ~ S A - - ~ P C B - - ~ P Z A - - ~ ~ ~ ~ 1QrQ4111111- --:Qr45114Q45S:P2..-_ -Q112455Q11E_gQ
1ET 15=0 I ICA I 7CA ? P + q ??-A ?PCA 3Sb 1
3FT 1 4 = b I 15A ' ' '<A ? P + H 7P-4 ? p i i d 7n:b I
0 . 0 1 3 9 6 8 7 9 - 0 . 3 6 5 4 6 5 6 7 E - 0 3 -0.99442331E-02 0 . 0 7 7 5 7 0 1 3 n 1 ~ 3 7 ~ - n > n-t.-
~ E T 17-1 I 1 5 4 ' n " ~ 2 5 0 2 2 - 4 2 ~ 3Z P + A 1 O.CC000000 - 0 . 3 2 4 7 7 1 6 5 E - 1 7 -0.88369585E-16
0 E l 3 z A l l A l _3SA--3DL9._2E=A--2PI:!aa2Pf444411-I- ---_---_- ~ Q ~ Q Q Q Q Q Q Q Q - ~ ~ ~ ~ ~ Q A ~ Q ~ ~ Z ~ I ~ E I ~ Z ~ ~ ~ . . ~ Q P I ~ Z ~ I ~ ~ S E : ~ ~
DFT I ? = & I 1 5 0 1 ( 9 A 2SH 4F-4 2PGb 2 0 t b I -0.10000000 - 0 - 5 2 2 2 5 9 9 7 E - 1 9 -0.14210568E-11
M I - Z ~ I A - I - ~ S S - - - ~ S ~ - - ~ ~ S A - - - Z ~ ~ - - ~ ~ ~ A - 4 E D A - - Z E ~ A - - - 1 - - - P i - - - ~ P i - P i ~ ~ P i ~ - Q ~ 1 O Q Q 2 Q Q Q ~ - ~ - - z Q r ~ ~ ~ ~ ~ ~ ~ 1 E - l 9 -Q.l817312ZE:J~
7FT 71=A I I S 4 1 5 0 ZSA ?SR 7P-A ? P O I 4F+b I - 0 ~ 0 0 0 0 0 0 0 0 - 0 . 4 8 2 9 1 2 1 7 E - 1 9 -0.13139925E-11
_ _ _
4 . U . E.V.
F Y T = - 0 . 5 4 4 0 0 8 5 4 E '02
-".
1 4 5 ? 2 7 4 2 F 3 4 .. .r n ~ 4 1 - - - n . 5 4 4 ~ 7 ~ 0 7 - L ) . I ~ H I ~ I ~ ~ ~ 0 4 IlIFFE?FNCE= - 0 . 4 6 9 6 3 2 1 5 E - 0 1 -0.12778578E 0 1
. ~ ~ ~ ~ ~ - - ~ ~ - - - 5 Y ' I ~ I ' ~ - ~ ~ Y I 4 1 B Y 1 1 D ~ 5 5 ~ ~ I ~ D ~ 4 ~ S 6 2 ~ I I 2 E ~ Q 1 1 ~ ~ 4 ~ 1 Z I 2 ! ! ~ 1 l E ~ O 1 1 1 ~ 1 . . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 1 1 1 ~ ~ . ~ ~ ~ ~ ~ ~ . . ~ ~ . ~ ~ ~ ~ . ~ ~ . ~
bXPflYrNT = 7.C4947995
. . . . - . .- . . - - - -
-
- - .RrN'II;HPI 1 7 9 T l l l V F4CT11R = 0 . 9 8 8 4 9 4 0 9
. - - --. . - - . - - - - -
Table SV The Have Function
t,
l c r t e x t ) forug
, G P v.p
. .
---~---_-~---.---_---A*u*---ExYr---
nFT 1=b I 1Sb I S 8 7 5 1 2x6 7P-A 2P-8 7POB Z P t B I 1 . 0 0 0 0 0 0 0 0 - 0 . 5 4 3 2 1 6 9 3 E 0 2 -0.14780802E 04
0E1--~A-1~15A---15B--2EOA--3EQB-12EzA~-2E=B--2~DB--ZE~B---111----11--1--_zQ~QO916991-_~--=Q~Z~SlrQ11lEzQ3---~Qx1Q~81682E~
DET 3=A I I S d I S 3 7 P t A 3P-R 2P-A 2P-8 ZPOB 2 P t 8 I 0 . 0 0 9 0 8 1 1 6 - 0 . 2 5 7 0 0 5 4 5 E - 0 3 -0.69930567E-02
w 4 - A ( 1 5 4 1 c f 1 7 p m 7~ 7 n A
-
7 p - 7 ~ 0) P + R ~ I ~ . ~ ~ O ~ Q Q I I o . l - ~ - n s n.779-OET 5=A ( 1Sn 1 5 9 ZPcA ?SR 3D--P 2P-P 2POR 2 P t R 1 0 . 0 2 9 6 9 7 2 9 -0.20520847E-02 -0.55836733E-01
DE1--brk1~1~~--1~Y--IPfikB~25Y-~2~zAB-3D=B--2E1)B--2E?B---111--~~11-1~1--zQ~Q39B6DBB---B-zD~H3919913EzQ22----zD~9~Q1424~E=4~
nET 7 - 4 I 1 S d 1 5 A ZSR 7P-4 3 0 - - 8 ZPOR ?P*B I 0.0563391C - 0 . 6 9 7 9 9 3 1 1 E - 0 2 -0.18992225E 00
D L I ~ ~ B ~ 8 1 ~ 1 5 4 ~ ~ ~ 1 5 9 ~ ~ 2 E 9 ~ ~ ~ 2 S Y ~ B 2 E ~ A ~ ~ 2 ~ z B ~ ~ 3 S Y ~ ~ B Z P ~ B ~ ~ ~ 1 1 ~ 1 ~ ~ ~ ~ 1 ~ ~ ~ 1 ~ ~ ~ Q ~ D D ~ I 3 B Q I ~ ~ ~ ~ ~ ~ 4 ~ 5 B 2 D 1 9 1 I £ ~ D 3 ~ ~ ~ ~ ~ ~ Q r 1 5 B 3 6 6 Q 2 E : B 2
O F T 9 = b r ~ c n I < R Z P Q A 7 s s 2 ~ - A Z P - n ?DOH 7 ~ + 8 I -0.04681975 - 0 . 4 7 3 6 1 4 1 3 ~ - 0 2 - 0 . 1 2 8 8 6 9 2 7 ~ 00 P E T I O E ~ I 1 5 4 I C R > P + A ? S B 9 0 - 4 ?P-8 m - ~ 7 ~ t n I n . n 4 1 ~ n 7 4 0.36707574F-09 0.s851-
OFT l l = b 1 1 5 8 1 ( b 7POA 2 5 8 2P-A ZP-il 2P,JH 3 0 + 8 1 - 0 . 0 4 1 3 9 8 0 5 -0.36266535E-02 - 0 . 9 8 6 8 0 3 7 0 E - C l
P E 1 ~ 1 2 z h ~ l ~ l S B ~ ~ ~ l 5 3 9 9 Z ~ ~ 4 ~ _ n ~ 2 S B ~ B 2 ! z A ~ e 2 ! ~ ~ . ~ Z E 3 8 ~ ~ 3 5 B ~ ~ ~ ~ 1 . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ f i ~ ~ C 3 4 4 B 4 3 3 3 3 3 3 ~ D r 9 l 3 4 k ~ 3 9 ~ z D k ~ k ~ ~ ~ Q ~ 1 ~ 6 ~ 3 8 ~ ~ k ~ Q 2 OET 13.n ( l c n 1 5 n ~ P + A ~ S R 2 ~ - A Z P - H 2 0 0 9 3 0 0 8 I 0 . 0 2 4 8 4 2 8 9 - 0 . 1 2 5 6 5 1 5 2 E - 0 2 -0.34189477E-01
O E 1 ~ J ~ z h ~ l ~ l S A ~ ~ ~ 1 5 9 9 ~ 9 2 5 4 ~ 4 2 ~ ~ A ~ B 3 3 ~ Y B B 2 _ P z ~ ~ ~ 2 P D 8 a a 2 P _ + i ) i ) i ) i ) 1 I I . ~ ~ ~ ~ ~ D ~ D 1 1 2 1 1 6 2 ~ ~ ~ I I ~ ~ D ~ 6 4 B 1 I 1 9 Q £ z D 3 ~ 3 3 ~ ~ ~ Q x 1 B 1 B Q ~ ~ 1 E ~ 4 l QET 15=A I 1 5 4 l S N 1 5 4 7 P t A 3'1--H ?P-P 7 0 7 8 ?P+R I - 0 . 0 2 4 3 8 9 1 1 - 0 . 1 3 3 6 3 1 2 4 E - 0 2 - 0 . 3 6 3 6 0 7 4 l E - 0 1
ILU 14=e I 1 s n ICB ' ( A ? F R LPOA s~ -- 9 7POP 7~ + R I n . n a ~ ~ m n n.norrnonaaF o n n.nn-
nET 17.A I ISA 1 5 4 ' 5 4 25R 2P+A 4F---82PCR 2D+R I - 0 . 0 0 0 0 0 0 0 0 -5.000000DOE 0 0 -0.0000000OE 00
I I E I _ l 3 e P _ l _ 1 S _ d _ ~ ~ l c 3 ?54_n_n-2i~BB2PC4_4.?Pz9_.3_Prh.. Z_P?_R.--I . _ _ - - - _ 1 4 ~ D C 2 2 ? 0 8 2 . .--. zQ~11Dl_R_954£1Q3 --- zQ~2_998232QE:42 O E T I ~ = A I 1 5 c i s m - 5 4 759 IDIJA 7 ~ - P 4 ~ - a z ~ t ~ 3 ) - ~ . 0 0 0 0 0 0 0 0 - O . O O O D O O O O E 0 0 -O.OOOOOOOOE 00 D E T - Z O E O _ ~ - ~ S A _ - _ ~ S ~ ~ - - L S ~ ~ ~ ~ L S B - ~ L ~ _ ~ A ~ lP=Y..~5E==3_2P_+_R_--J__ _ - z D . ODDDDOOO -0 .CDD9OOD3E-M --- z4~DDQQQODQE-4Q
~ E 71=h ( T l q c ' 5 4 7 5 ~ Z P P A ?D-r, ? P P H ? P O ? I 0 . 0 0 2 6 8 n 9 1 - 0 . 1 3 2 4 2 1 ~ 9 ~ - 0 4 - 0 . 3 6 0 3 ~ 4 6 1 ~ - 0 3 E T 77.6 I 1 7 4 1 2 2 4 75d 'PnA ?P-11 :PC9 4 F 0 9 1 c ~ n n n n n . a m m m n ~ n n -o
?ET 73-A I l s n I ? t A 7SR 2P+A 2 P - P 7PCR 7 0 - 8 I -C.00491303 - 0 . 4 8 5 3 4 9 5 1 E - 0 4 -0.13206244E-02
O ~ ~ ~ ~ ~ ~ ~ ~ ~ S ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ L ~ ~ ~ ~ B ~ ~ L ~ ~ B ~ ~ ~ P ~ D ~ ~ ~ ~ ~ B ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . ~ ~ ~ ~ ~ ~ D ~ D D C Q Q Q Q Q ~ . . ~ ~ ~ ~ D ~ Q Q ~ D ~ Q ~ D ~ ~ D D ~ ~ ~ ~ ~ ~ D ~ ~ ~ D ~ ~ ~ ~ ~ E ~ ~ ~
DFT 75.A r 1 5 4 151t W n 4 ZSr) 2 0 - f l 2P-h 7P33 ZP+9 I -0.OL211041 -0.34163433E-03 -0.92957881E-02
D U _ ~ = ~ ~ l ~ 1 ~ 1 ~ ~ 1 ~ _ n ~ ~ ~ ~ ~ 4 ~ ~ 3 ~ ~ ~ ~ ~ 2 ~ ~ 4 ~ ~ ~ 0 ~ 9 ~ ~ 2 ~ 1 ) 1 ) ~ ~ 2 e _ * ~ ~ ~ ~ 1 ~ ~ ~ _ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Q ~ Q Q 9 ~ S _ s 4 Q ~ ~ ~ ~ ~ : Q ~ 2 2 2 ~ 4 I 4 3 E z Q 3 ~ ~ ~ ~ ~ z Q ~ ~ Q I 9 9 5 I 8 k : J 2
DET 27-A ( i 5 l 1 5 9 7 5 b 258 4F-A ZP-R 7PrIH Z P + H I O.COOC0000 0 . 0 0 0 0 0 0 0 9 6 0 0 0.00000000E 00
ET Z ~ = A I 1 5 4 I 7 7 4 7 % ~ 7 0 - A i r - H ?P?R ?P+~I I n.onoocnnn 0.0-F o n n-n-
nFT 29.A I 1 5 L 1 '5A ' r n 2P-4 7P-0 r F j 0 2P+R I -0.0000C000 -0.00000000E 0 0 -0.000000OOE 00
7£1-3~~Ll~lS~~~~15~_q~_q253333LfiY_BL~zABB2_Dz~~~21J~_r_r3f?fid~~J111111111~11111Q9QQQ4_0QQQ9~999._0_oQQ040_0~QffQ4~~9-99Q~4Q~Q~~~~~-~~
- - - - - -
4.0. F.V.
0. SLNANOGLU
'
1 7 3Table V The Wave F u n c t i o n f o r O x y e n O r o u n d S t a t e I I l O 1 )
P
-
kr LnLr
COEFFlClENT CONTRIBUTIONS
A.U. F . V .
DET I = A L l 5 A l a b 2SA 2 % OFT ?=A 1 I S A I C d ?PCP 3P0H OFT 3=A I 1 S k 1SH 2 P t A 3P-8 OET 4=A 1 l 5 A IS11 2PCA 2SB OFT h=A I ICA 1 \ H 2PCA 2CH DET 7.A 1 l S A 1Sa 2 P j A 1 . 5 8 nFT R=A I 1CA 1CH ZPPA 2CH DET 9=A I l S A 1SB 2 P l A ZSD DFT 10-A I ICA I 5 H ZP+A 2SH
DET 1 1 - 4 I 7513
DET 1 2 - 4 1 l C A 1 5 t l 2 P t A 2Sd OET
OFT OET n t T DFr IIET OET llFT n t r UFT n E L DFT OFT nF T OFT nFT QEL nFT
1SA I S A 1 SA 1 FA
u
I CA I S A I r n 1 S A 1 Cb _LIB
I CA I S A 1 CA 1 s n 1 CA _118
LSA
1SH L S A
~ s n z 3 4 l S H ZSA I St4 ?CA
-
ICH 1% 3UC.A 7CAICH 2 2 4 ZSH 2POA 2P+A 2CH
a
7SR L S d 2 \ n 2.511 ) \ I 3
_11h
LCH 2.50 311r)n 2 s n 256
a
7CH
2P-A ZP-B LPD8 - 2 P 3 8 2P-A 2P-8 ZPOB 2P+R ZP-A ZP-d LPOB ZP+B 30-A 2P-H 2POB 2 P t d
O R 7P+R 2P-A 3 0 - 8 ZPOB 2P+B 2P-A 3 0 - - a ZPQB L P + B ZP-A 2P-8 3 5 8 2 P + 8 LP-A LP:B 3 U D l 2P+B ZP-A 2P-8 3 0 - 8 2 P + 8
ZP-4 Z P - i ZPDB 3 3 0 H 3U-H 2P-8 2POb 2P+R 30--8 2P-H ZPOR L P t R 2POA 4F--H 2PO8 Z P t B LP+P 4 f - - - 8 2 p 0 8 2 p + 0 L P U A Z P - H 3 ~ - a Z P + B 2PCP ZP-H 4 F - 8 1 P + B 2P+A L P - 8 4F--H 2V+d ZPOA 2P-tJ Z P O R 3P0B 2POA 2P-8 2POH 4FCH
>P+A ?P-H 7PGR 3P-R ZP-A Z P - n Z P O B LP+H 2P-A 2P-H 2POB 2 P t B 4F-P 2P-d 2POB 2P+6 2P-A 4 F - 6 2POB 2 P + 8 7P-A 7P-H 4FOR 7 P I R 2P-A ZP-H 2POB 4F+H
A.U. E.V.
KENUTMALI ZATJCN FACTUH = 0 . 9 9 3 6 0 7 6 6
****IHER~ IS h o I N T W P A R T FUR T n l s C A S E * * * *
Table VI The Wave F u n c t i o n
Y
( c 2 . t e x t ) f o r 0- lb!&:S{-
G bl Y l l G Y
COEFFICIENT CONTRIBUTIONS
. . . . . . . . . . . .
A.U. E.V.
0,E.I 21=A 1 ICA I S 8 3OflA 2CR 2P-A 2P-R 2POA ZPOR 2P+A I ( I ~ O p B z 7 ( l b Z 0 . 2 3 6 3 3 9 7 3 E - 0 3 -0,64307473E-02
OFT 72=A 1 ICA ICR 7SA 3 0 0 8 2P-A 2P-8 2POd 2POB 2 P t A I 0 . 0 0 8 7 1 4 9 8 - 0 . 3 0 5 5 6 7 6 2 E - 0 3 -0.83171425E-02 OFT 23.A ( 1CA 1SR 2SA 2S8 4 F - A ZP-8 2POA ZPOB 2P+4 J - 0 . 0 9 6 8 6 4 0 5 - 9 ~ 6 6 3 4 1 1 b 6 E - 0 4 -0.18051258E-02 OFT 7 4 1 6 I 1CA ICR 7 5 4 2 5 8 2P-A 4F-8 2POA 2POB 2P+A I -0.00001242 - 0 . 5 7 8 2 8 0 5 3 E - 1 4 -0.15734874E-12
OET Z S . 4 1 15A 1 S B 7 5 4 25-8 2P-A Z P - 8 4 F 0 4 2POB ZP+A I -0,00840923 -0.99541433E-04 -0.27084985E-02
OFT 76=A 1 ICA I t R 756. 2 5 8 2P-A 2 P - 8 2POA 4 F 0 8 2P+A I - 0 . 0 0 0 0 1 5 2 4 0 . 1 7 7 4 5 2 4 l E - 1 4 0.68284375E-13
4.U q . . . E.V.. ... ...
F HF 6 4 l E 0 2 -0- 0 +
ETOTAL = -0.74809635E 0 2 -0.20355522E 0 4
... 0J.F.F.EREHC.E. . ~ R r . 1 . ? 9 9 . 1 7 . ~ Z E ~ O ~ . . . ~ P t . 5 ? 4 0 . Z . 6 ~ l . E . . 9 0 ...
SUM OF CONTRIBUTIONS = -0.19990322E-01 -0.55393186E 0 0
. . . IXPONCNT. =... ... ? ~ ~ O . Q Q P Q ~ O ...
RENORMALIZATION FACTOR r 0 . 9 9 6 8 1 8 6 8
CALCULATION O F ELECTRON AFFlNLTlES USING T H E NON CLOSED SHELL hlANY-ELECTRON C-1-93
t t I T a b l e VII The Wave F u n c t i o n ( Y b ( c f t e x t ) f o r F l u o r i n e I I * S v
E ~ ~ Q G Y
C O N T R I B U T I O N S
DET l = A 1 l S h 1 x 8 7SA 7SL% Z P - A Z P - I \ 2 P ' I B 2 P t A ? P + O I I .OI?C~L'CT
"ET 2 - A - 1 1 S A . 1 8 3 I P - A 3 E ~ l 3 L P - A 2 P - 3 2P:n L P t A Z P t B I - G r C 0 3 5 6 3 Y 4 nET ?=A I l S A 15H 7'CA Z S i l 3 0 - 4 2 P - d Z " " t l P + A Z P + Y I - 5 . l l 6 6 4 1 7 1 n E r & = A - l - l S A I S 8 2 P L A Z S B 2 P - A 3 0 - 3 ZPCa 2 P t A 2 P t B 1 - C . 0 3 1 6 7 4 7 5 nET 5.6 1 1 s t - I c H ?PCA 2 S H 7 P - A ? P - H 3SR 2 P t A 2 P t H 1 i . ~ r ) 5 2 0 r 1 3 1 O F T 6.A I l < A I 5 9 ? P C & 7<R 7 P - A > P - R 3n"R 7 P t A 7 P t H 1 ~ . r > h 5 7 ? 4 6 O E T 7 - 4 1 1 5 1 I C H ~ P T A z s u Z P - A 7 ~ - H Z P ~ R 3 0 + b Z P + R I - C 1 0 1 h 6 4 L b 7 0ET 8 = A 1 - l S A 1SB Z P L A 2 S d 2 P - A 2 P - 8 ZP.CB 2 P t A 3 0 t h 1 - C . C 3 1 b 7 4 7 3 nFT 9=A 1 I S A I S R 7SA 2 P j A 3 0 - H 2P-R 2POR ZPIA 2 P t H I C . C l 5 C 3 3 h 2 OET 1C;A 1 L S A 1 S 8 2SA Z P L A 21'-A 2 P - B ZPCB 3 0 t h Z P + B I C . C l 5 C 3 3 6 3 n E T l l = A I I Z A I < R 2SA 7Sl! 7 P S A 4 F - - 8 2 P p R 2 P t A 7 P + U I - C . C 1 1 9 C b 7 5
b . l l . F . Y .
- 0 . 9 9 4 C 9 2 9 C E Cl2 - 0 . 2 7 C 4 9 0 2 9 E 5 4 - i . U U 6 7 3 6 3 5 E - 0 4 - 0 . 2 + 1 2 7 8 8 3 € - 0 2 -?.12258066E-02 - 0 . 3 3 3 5 3 9 0 3 E - C 1
-
, . . . . . - - -D ~ r 1 7 = & 1 I C A ~ q n ? c & 7 0 - a > ~ - n 20-x ) P + A ? P + H I OLOCMI~II r.407 7 1 ~ 1 7 3 ~ - n 7 1-n.
DET 17.A I 1SA 1843 2SA 7 5 6 2PCA 2 P - d 4 F - 8 2 P t A 2 P t R I - P . 0 1 0 6 4 8 8 1 - 0 . 1 8 4 6 6 3 2 0 E - 0 3 - 0 . 5 0 2 4 6 4 1 3 E - 0 2 D E I - I ~ A l l S A 1 5 3 2 S A Z S B 2 e C A 2 P - B 2eU0. 3 P C A - - Z E + B I -C.CCOCCOOC -C.CCOCQQQCE~CQ :Q.O.2QO~QQBQE_QQ OET 1 5 = A I 1 5 A 1 5 8 2SA 2SR 2POA 2P-R 2 P l 8 4FCA 2 P + R I C. CCC00'3CC C.CO00000OE C I 0 . 0 0 0 0 0 0 0 0 E 0 0 0 6 1 l 6 : b .l - 1 S A 1 S B - 2 S A .-ZI&--ZP2A.-ZP=B.-2PCB. . Z P f A - - 3 e C B I C.OOC3QbCL -C.l69ZbQ46ErQb. -Qr46Q515CQE:P5 DET 1 7 = 4 1 1SA 1SR 2 5 A 2 S H 2 P P A 2P-8 2PCB 2 P + A 4 F O 8 I -;.00652159 - 0 . h 9 2 5 4 6 1 3 E - 0 4 - @ . 1 8 8 4 4 0 1 4 E - 0 2 OFT I n = A 1 I < n ? < A z r R 7 p - A ' P n b iPnR 3 P r H 7 P * R I fl-aQnmfAl n. 1 h 9 7 m A F - O h n.-
DET 19.b 1 I S A 1 5 H 7SA 7 5 8 2 P - A 2 P C b 2PO8 4FOR 2 P + B I - 0 . 0 0 6 5 2 1 5 9 - 0 . 6 9 2 5 4 6 2 4 E - 0 4 - 0 . 1 8 8 4 4 0 1 7 E - 0 2 o E I . ~ C I A - I . ~ S A 1 S B ~ .-2SA Z S B - - L e = A - _ L P = B .BZP@A. . 9 i ' f h B B Z e f R 1 -0.OQQQZ2Zl. .-_~C14Q2ZQQ119E:QZ---~&eLQ%4_3ZZZE:Q9
nET 21.6 I l S A I S R 2 5 A 2SH 2 P - A ZP-R 2PCA 4 F + H 2 P t O I 0 . 0 1 0 6 4 8 8 3 - C . l 8 4 6 6 3 6 1 E - 0 3 - 0 . 5 C . 2 4 6 5 2 4 E - 0 2 O E I - 2 2 - A - l . 1 S A 1 5 8 - - - 2 S A --- 2 S B -- 2 P e A d d Z P ~ B Z P C 2 _ _ 2PCA _ _ 4 E + f B :a~QLL¶ObZ9..~~~~C.2iORk46LE~Ql-~~BB:Q~6LQL~QZIE:Q2 OFT 7 3 = A I I S A 1SR 3 D F A 2 5 8 2 P - A 2 P - 0 2 P 0 8 2 P + b 2 P + B 1 - 0 . 0 1 9 2 1 5 4 1 - 0 . 1 6 3 4 3 4 1 8 E - 0 2 - 0 . + 4 4 7 0 0 4 7 € - 0 1 DFT 7 4 ; 4 I I C A 1 % > < A 3 n Q H 7 P - A >P-R 7PnR 7 P t 4 7 P I R I n . 0 1 7 3 5 7 7 5 0.11 Q n 4 7 4 3 F - 0 7 n.37391797F-01 OFT ? % A 1 l S A I S 8 ZSA 2 8 8 4 F - A 2 P - 8 2 P O 8 2 P i A 2 P + O I 0 . 0 0 0 0 0 0 8 2 0 . 5 7 1 0 9 1 5 4 E - 1 5 0 . 1 5 5 3 9 2 6 3 E - 1 3
.~ -
O E I - 2 ~ A - l ~ 1 S A - - 1 S B - - - 2 S A - - - 2 S h - - Z P ~ A - . 4 E ~ B 2 P 0 O ~ ~ Z ~ ~ A ~ ~ 2 ~ i 8 ~ ~ ~ l ~ ~ ~ Q r ( l l Q h ~ 9 6 6 ~ . . ~ ~ ~ Q ~ L R I 6 Z B C ~ E ~ Q ~ 1 ~ ~ ~ ~ ~ Q Q I Q Z ~ ~ 4 5 I E ~ Q 2 JET 2 7 = A 1 1 S A I S 8 2SA 2 5 8 2 P - A 2 P - 8 4 F 0 8 Z P I A 2 P I 8 I 0 . 0 1 3 0 4 2 0 2 - 0 . 2 7 6 9 9 3 7 3 E - 0 3 - 0 . 1 5 3 6 9 3 2 8 E - 0 2
3 E f 2 8 ~ A - l - 1 S A 1 S B - . . - 2 S A - - - Z S B - - 2 P ~ A I I Z P ~ B B B 2 P 0 ~ - n 4 E ~ A d d 2 P f h n ~ ~ i I I I . QrQQ(faQQRZ__--_-OrIZCP5ZPPE~LII-IIIIQa1~~i%6ZZE:13
7ET 2 9 = A I 1 S b LSR 2 5 4 2 5 8 2 P - b 2 F - 8 2POB 2 P t A 4 F + B I 0 . 0 1 0 6 4 9 6 7 - 0 . 1 8 4 6 7 8 1 8 E - 0 3 - 0 . 5 0 2 5 0 4 9 0 E - 0 2
A.U. E.V.
E HF = - 0 . 9 9 4 0 9 2 9 0 E 0 2 - 0 . 2 7 0 4 9 0 2 9 E 0 4 TAt = - 0 . 9 9 4 W S 4 F 0 7 - 0 - L Z D 5 5 7 7 7 F 0 4 DIFFERENCE. - 0 . 2 2 9 6 3 5 2 4 E - 0 1 - 0 . 6 2 4 8 3 1 9 7 E 0 0
. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ S U ~ D E ~ C O b l I R l B U I 1 O ~ ~ ~ ~ ~ ~ O L 1 Z Z 9 b 3 4 3 ~ ~ Q 1 1 1 ~ O L 1 6 2 4 B 9 1 2 6 E ~ O ~ P ~ ~ P P ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ EXPONENT = 3 . 0 3 9 9 9 9 9 9
T a b l e V I I I F u l l Symmetry Wave F u n c t i o n of Carbon I. l a 2 2 a 2 2p2 3~
[The wave f u n c t i o n c o n t a i n s t h e non-cloaed s h e l l r e s t r i c t e d H a r t r e e - ~ o c k p l u s t h e
"non-dynamical" c o r r e l a t i o n wave f u n c t i o n ( i n t e r n a l + e e m i - i n t e r n a l + polarization c o r r e l a $ i o n s ) a s i n d i c a t e d b y t h e E l e c t r o n C o r r e l a t i o n t h e o r y Ccf. t e x t ] . I t h a s e x a c t L , s2 symmetry).
D E T b F = b I 1 S A 1 5 8 Z S A 2 5 0 2PCA 2 P + A I
C O E F F I C I E N T 1 . 0 0 0 0 0 0 0 0 C O E F F I C I E N T
A.U. E.V.
- 0 . l C 2 9 8 8 2 e E - C 4 - C . Z 0 0 2 2 R 6 4 E - 0 3 - 0 . 1 5 6 5 5 2 O ? E - C 4 - 0 . 4 2 5 9 7 4 3 2 E - 0 3 - 0 . 1 9 P 5 0 2 E 3 E - C 4 - C . 5 4 0 1 2 1 4 4 E - 0 3 - 0 . Z Z R S L 4 4 5 k - C s - 0 . a 2 2 8 9 7 S s t - 0 3 - 0 . 8 5 8 5 9 2 9 5 E - 0 3 - 0 . 2 3 3 6 2 1 0 R E - 0 1 - 0 . 1 7 1 7 1 9 0 3 E - C i - 0 . 4 6 7 2 4 3 3 6 6 - 0 1 - 0 . 1 2 9 9 4 6 7 3 E - C 2 - 0 . 3 5 3 5 8 1 9 2 E - 0 1 - 0 . 4 4 3 9 7 7 t R E - C 2 - 0 . 1 2 0 1 0 5 2 b t 00 - 0 . 2 3 5 1 2 2 9 0 E - C ? - C . 6 3 9 7 6 3 7 7 E - 0 2 - 0 . 5 6 9 3 3 7 0 4 t . - C 2 - 0 . 1 6 0 3 5 7 1 9 E 0 0 - 0 . 4 4 C 0 2 7 t 4 E - C 2 - C . l 1 9 7 3 0 4 6 E 0 9 DET 2 = b I I S A 1 8 8 2P-A 3 P + B ZPOA 2 P t A 1
OET 3 = A 1 1 S A I S M 2P-8 3P*A ZPOA 2 P t A I OET 4 = A I I S A l S B 2POB 3 P O b 2POA 2 P + A ) OET 5 = b ( 1 S A 1 S B Z P t 8 ?P-b 2PCA Z P t A ) DET 6 = b 1 I S A 1 5 8 2P-A 2 S B 3 0 t A 2 P I A I DET 7 - 6 1 1 S A 1SB 2 P - b 2 S 8 2POA 3 O * r A I DET 8.A I I S A 1 5 0 2 S A 2P-A 3 U t B 2P+A I OET 9 = A I 1 S A 1SO 2SA 2 P - 8 3 U t A 2 P + A I OET l O = b I 1 S A 1 5 8 2 S A 2POE 3 5 6 2P+A I OET i l = ~ I ~ S A is; ~ S A 2 ~ 0 % ~ O O A Z P + A I OET 1 2 = b I 1 S A 1SH 2 S A 2 P t S 3 0 - A 2 P t A 1 OET 1 3 1 6 1 I S A 1SB 2 S A 2P-A 2 P O b 3 U + + 8 I DET 14.A 1 1 S b 1SP 2 S b 2P-8 ZPOA 3 D + + A I DET 1 5 = A ( 1 S A 18.3 2 S A 2POB ZPOA 3 0 + A 1 OET 16.A I 1 S A 1SB 2 S A 2 P t O 2POA 3 S A I DET 1 7 = b 1 1 S A 1 5 2 S A 2 P t 8 2POA 3 0 O A I UET l 8 = b I 1 S A I S R 2 S A 2SH 2P-A 4 F + + A I
UE T UE T OE T UE T OE T OET DE T DET OET OET OET UET
2 bB JUOll 2 S C Z S B Z P t A 3 P t A JPOA 2 S b 2 SA
2POA 2 P + A I 2POA 2 P I A I 4FOA 2 P + A I 2POA 4 F t A I 2 P 0 8 2 P + A I
7PCA 2P+O I
L P - A 2 P t A I 3U.A 2 P + h 1 2POS 3 U t t A I 2 P O b
ZPOA 2P+R
A.U. E.V.
E HF = - 0 . 3 7 6 8 8 6 5 C E 0 2 - 0 . 1 0 2 5 4 9 9 1 E 6 4 E l O T A L = - 0 . 3 7 7 4 3 3 5 1 E 0 2 - 0 . 1 0 2 6 9 8 8 8 E 0 4 OLFFERENCE- - 0 . 5 4 7 4 7 1 C 5 F - 0 1 - 0 . 1 4 8 9 6 5 5 6 E 0 1 SUM CF C U N T R l B L T l O N S = - 0 . 5 4 7 4 6 5 9 0 E - 0 1 - 0 . 1 4 B 9 6 4 1 6 E 0 1
EXPONENT = 1 . 7 4 9 9 9 9 3 7
