- Email: [email protected]
A modified effective core potential for the copper atom: Low energy electronic states of CuO
Volume 93. number
I
CHChllCAL
PHYSICS LKlTCRS
19 November 1982
A MODIFlEDEFFECTlVECOREPOTENTlALFORTHECOPPERATOM: LOW ENERGY ELECTRONIC STATES OF CuO
Harold BASCH Deparrtnenr of C7ietnrstry. Bar-Ran Uarsersrry, RatnatGarr.
Israel
and RomanOSMAN Department of Pharmacology, Mowrr Smat School o/Medrcrrre, 1 Cusr~~~eL LevyPbce,rVmv York.h'ew York 10029, (IS.4
Reccwd 8 September 1982
To correct for mqor v~lcncc dtomlc corrclallon rncrgy errors a modUied cffcclwc po~nl~al (MCI’) /IX been dcrwd for the copper a1om ~ollowmg Goddardand co-worhcrs, the hlEP II produced by dddmg correction terms lo an db m111oeffcctwc core potenti, fitted to the cxperlmental multlplrt energyscpara~mns for Ihc Cu arom .md IOIIS Compxrson of hlC SW and v&ncc Cl cslculatlons on lhe lotvc~t cncrgy *II, *x+ and *A clcctroruc SIPKS of CuO with c\pcrnucnt.d stants shows thal the alomderwcd MEP dots not cilusc systcmatlc b13s or dlstorrmn of the molwulx bmdmg energy
con-
curves.
I. Introduction
state energies(“D below ‘S) for the copper atom
In the course of valence electron self.consistent field (SCF) studies on models of coppercontmnmg metatloenzymes [I ] using an ab init effective core
potential on the copper atom [2] It was found that cupric complexes with saturated ligands resisted reduction at the metal site; surpnsingly preferring to add the electron to a &and. This anomalous behavior can be traced to the now well-recognizedinabihty of
The importance of intra-atomic correlation energy effects for the proper descnptron of single-hgand
transttron-metalcompounds has been emphastzed [6-S]. The metalloenzyme example cited above demonstrates Its importance m deternunmg the relative stabllltles of drfferent electronic states even in large metal complex systems where the hgand field IS strong and might be consldered
to be dominatmg.
differences
The conventional treatment of such problems with extended basis sets and large multlcontiguratlon (MC)SCF and configuration mteraction (Cl) expm
and ions in favor of those electronic configuratIons with the fewer number ofd electrons. For example, although numerical Hartree-Fock theory predicts the ground state of the copper atom to be 3dt04sl(‘s) with the 3d94s’(‘D) state configuration 036 eV
sions ISclearly impractical with regard even to model systems of metalloenzymes wtuch typically contain over 25 atoms [ 11.An alternative simple and nearly equivalent procedure for handling the mtra-atomic correlation energy problem has been apphed by Goddard and co-workers to compounds of nickel [6,9-l I]. Their procedure consists of constructing a modified effective core potential (MEP) by adding
above it [4], experimentally 1512D lies 1.49 eV above ‘S. It should be noted, however, that basis set expansion III the SCF method typically givesinverted
(ECP) fitted to reproduce correctly the atom (and ion) multiplet energy separattons, while taking care
Hartwe-Fock
theory to correctly
descnbe
energy
between electronic state configuratlons of a given transition-metal atom which differ in the number of d electrons [3]. Thrs differential atonuc correlatron energy error biases the stability of states
0 009-2614/82/0000-0000/S
02.75 0 1982 NorthHolland
terms to the ab initio atom effective core potential
I
Volume 93 number
that the shape of the valence orbitals re.mains essentntlly unchanged. Following Goddard and co-workers (6,10,1 t] and Sollenberger [9] we have constructed a MEP for the copper atom that corrects for the malor HartreeFock errors ln the atom and ion multlplet energy separatmns In order to test whether the lllEP produced by atom-fittmg procedures alone still grves undistorted molecular carried
energy
OUI ab initio
cdculatmns elecrronic
curves
and properties.
vatcnce
for the lowesr
electron energy
MC
2n,
Table 8s.~
1 sets ior
Alom
ular Wparatron (R) (In]. In order to avoid
orbital cu
effects
the correlating to contrrbute
contigurattons essentralty
only
were
1 153
45’ 3d
0.05393 46.7 1 13.43 4 489 1 478
we have
SCF and Cl
2X+
and
2h
to intra-atomic
in the configuration
4s
3d’
a.4505
4P
2.440
4P’
carefully
to chemical
chosen
bond
valence
copper
1 .o
atom
-0.0174637 -0 0943483
Zp’ 3d
gaussian
0577.5220 1.0 0 0157436 0.0985876
0 2864 32 0s 7.780 2 289
and results
and oxygen
O.f7710OD
0 04620
8 810 0 9459 aP
The
-&4401)0
a.1551 37 91
25
0
for-
25’
details
0.8584288 10 0.0350044 0.1695073 0.4032% 1 0.4617022
expansions,
mation.
2. Calculational
-0.2006930
0.1402
3s n
contributions
Cu and 0 a) Atomic
function ofintemrolecfor comparison with experiments
strites 0CCuO
correlatron
19 Novcmbcr I982
CHEMICALt’IlYSlCSLCTIIXS
0 7194
0 3089032 0 4197049
0 2146 0.8500
10 1.0
basis sets used UIthese calcutatlons are shown in table 1.The 3d and 4s bases of Cu were obtamed by exponent and coefficrent optimizatron for the Cu’,
a) Not normabed.
3d94st(3D) state configuration using the ab trnho Cu atom ECP ofTopro1 et al. (‘21 to replace the 18 electron [Ar] core of electrons. The 4p basis is taken dnectly from Topiol et al. [2]. The 2s and 7p basrs for ox,*gen was r&o atom.optnnized for the ?s’?-p4 (3P) praund state using the oxygen atom ECP ofTop101et al. [13]. The hlEP was derived as descrrbed by Goddard and co-workers [6,10,1 I] and Sollenberger 191. In short, a two-component correction term (V,) of the same analytic form as the ECP ISadded to the ab initio ECP (21 wrth the constratnts that the changesin poten-
As suggested by Sollenberger 191, VP w_as set equal to Vs. The final parameter values for the V, are shown in table 2 and the resultant copper atom and ion multrplet energy separations are in table 3. The derived MEP for copper together with the ab mitio ECP for oxygen (131 and the basis sets of table I (with the Cu 4s uncontracted to form three separate basrs functions) were used to obtain the lowest energy “II, ‘E” and 2A electronic state energy curves of CuO. The MC SCF/CL calculations were carried out using the ALlS 1141 system of programs rnodtfted (IS] to incorporate an extended version of Kahn’s
tial be localized and that
to the immediate
v, have a mmimum
vicinity
of the atom
where the corresponrhng
(trl) valence orbltal has its maxunum amplitude. These conditions are sufficient to determine 3
out of
4 p=u-neter~ in tit. The fourth parameter for Va was varied
ro reproduce
best the experimental
energy
52
VIc~rvxt~~n terms to gwc hrEP
for the copper
aI
81
0.1
0 04125
0.165
1.2X
-0.8085
2
0.5625
2.25
0 835
-7.515
a) i$ = CI~-~exp(-at&
cl
atom 8)
1
sep-
between the lowest energy Cu. Cut+ and state configurationsdiffering rn the number of d electrons. The fourth parameter for vs was used to optimize the various 3d”-‘4s’ states of Cu and Cut+. arations
Cd*
Table 2
+ Dlexp (-@I?); the ab mitio copper atom ECP in ref. [?I.
DI
to be added to
Volume 93, number
I
CtlCbllCAL PIIYSIU
Table 4
Table3 Slalc conligonllon
Exper,mcnfaI b,
CCr c)
hwd)
3d’O4s’ 6) 3dg4sZ $D) 3d’O4p’ (2P)
0 1.49 3.8 I
0 -0 48 4.40
0 1.58 5.41
Cu’ + 3d’O 3d94s’
C’S) (3D)
7.72 10.53
5.34 6.12
112 9 91
Cuz+ 3d9
&I)
28OL
Cu
19 Novcnlbcr 1982
LLI’ILRS
258
28.36
=ri
CSIC c?.p 3)
1.768 1.724
653 640
I91 2I
22,
talc cup.b)
I 70 -
700 661
2 1.? -
IS200 I3000
ca1c.
1.71
747
0.69
elp. kc) e~p. a)
1.76 1.72
733
-
24000 15300 21100
*A
Q)rromtcf.~12). b~lromd (171. ‘) rrom ref. [ 18J: R, cdcula~rd promgwn
ECPgaussian integral evaluation program [ 161. The confiyrat~on
expansion hst was obtained
by the ite-
0 0
WIUC of 8.
the expenmentally observed z11,,2 and ?Aslz states are taken for comparison purposa.
mtivenaturalorbitalanalysis/valence Cl featureof the ALIS [ 141 system. The calculations were camed out in C2v symmelry makmg the 2n and ?-Aelectronic states thus obtained space polarned. The resultant energy curves are displayed m fig. I and a comparison of calculated and experunental spectroscopic constants for the lowest energy ?fl, IX* and “A electronic states of CuO are shown in table 4. In table 4
3. Discussion As shown m table 3,generally the calculated Cu atom and ran mulflplet state energy separations are greatly improved using the MEP. Of course, tn the lunited (double-zeta quality) size basslssets used here (table 1) il is clear that the optimization procedure that produces the hlEP also, to J certain extent, corrects for both relativistic and basis set errors. It is therefore,
npproprtare
to keep the baas set that was
usedto genemtethe MEP in~iloleculsr calculatmns. rather than reopttmize the basrs set for the MEPatom as is usually done. The electronrc structure descnption of the ground ?l’l state of CuO has been given by den Boer and Kaleveld [ 191. A CuO u bond is fomled from copper and oxygen atoms in their respective ground 3dt”4s1 (%) and 2~?!p~(~P) states to form the loa2a2302 [a43n3 IS4 2il
(1)
state canfiguration. The binding energy curve is a smooth function of internuclear bond dlstnnce and the set of fourconliguntions,3a22n3,
40’Za3
and
to describe accurately the complere range of bond distances shown in fig. 1; 3a and 4a are the corresponding 3014u)2~?
(two spin couplngs) IS adequate
53
Volume 93. number
I
CHCLIICAL
PHYSICS LCTTCRS
bonding/antibondmg o molecular orbitals (MOs) involvlng 0 7-p and Cu 4s and 3-n is essentially the 0 3-p orbital In describmg the configurations III the previous sentence the orbltals common to the four configuralIons were dehberately omitted but were, of course, tncludrd in the MC SCF/Cl calculations. Table 4 shows the good agreement obtauted for the ground (X ?ll) state of CuO between theory and expermlent for the equilibrium bond distance (Rc withm 0.0448), the harmonic stretch frequency (wc wtthin 13 cm-l) and the dissociation energy (7G% of D,). A quick comparison of these results with den
Boer and Kaleveld [ 191, whose allelectron extended basis set calculations did not m&de atomrc correlation effects, provides convmcing evidence of the efficacy of the MEP for the copper atom. These authors
typically obtain only ~30% of the bmdmg energy and R, vduss that differ by =O.l?, A from expenment, depending on the basis set used. However, more pomtedly, their ‘n state bindmg energy curve has a hump et mtermediate bond distances whch can be attnbuted to an avoided crossing of the inverted ‘.S and ID (?D below ‘S) atormc copper Icvels. Fig. 1 sl~owsno such ma_\mum on the energy curve for Ill which must then be artificially due to atormc correlation effects. tluber and Herrbeg’s tabulation of rhc spectrosof CuO [ 121 lists a 2x+ (Krontg symmetry uncertain) as the fist excited state of CuO.
19 Novrmbcr 1982
10’20”30’ ln”27r4164 ‘r, ,
(2)
where the orbital character of the 30 molecular orbital changes from primarily 0 7-p, to Cu 4s in going from R = R, to R = -. The calculated oxygen atom JP-ID multiplet energy separation from the 211-1Z
separationat largeR ISthen 222 eV comparedto 1.96 eV experimentally [5] _ Table 4 shows the good agreement obtamed here
between calculated and experimental values of w, (w~tlun 39 cm-‘) and the adiabatic excitatron energy (T, within 2200 cm-l) for the ICf state. From these compansons for both the ?fl and ZZt states it is clear that the MEP 1snot systematically distortmg the molecular curves, forexample, in the form of exaggerated butding energies or shortened equtlibrium bond distances. Thislatter type behavior in molecular cakulatlons might be expected from the adrhtlon of attmctive terms to the original atom ECP, as was done here
to generate the MEP. Although the exact vahre of the rotational constant (Be) is not given, it IS stated [IS] that B, for the 6 “Z state is smaller than that for the X ?n state. Since Ri IS proportional to B,’ it must be that R,(6 ‘2) > RJX ‘iI). The calculated values m table 4, however, show R,(‘Z) < R,(‘Il). Thus the fact that the calculatedR, for “fl IS too short and for IS LStoo long m comparison
to expenment
However, two lower energy ‘C states have smce been observed [ 17,20] in enusslon and the comparison III table 4 ISwith the lowest of them, labelled 6 2B [ 171. We have also MC SCF/CI calculated the lowest energy ?C- state and fiild it to be essentially repulsive, dissoc~ating to the ground state Cu(?S) f 0(3P) atoms.
found are due to orbital basis set and inter-atomic correlation effects rather than systematic bias or distortion in the electromc structure description due to the MEP. The calculated lowest energy ?A state dissociates to Cu 3d94s2(?D) + 0 ~s??P~(~P) which is only 1.75 eV above the IS + 3P combined ground states dissociation limit due to the Cu ?G2D multiplet energy
Therefore,
separation
copic constants
the observed bound S ZZ state should be
would seem to indicate that the differences
in tius basis set (1.58 eV III table 3 wtb
of Zt symmetry. The calculated ?I? state (table 4) correlates with the Cu 3dlo4~l(~S) + 0 2$2pJ(tD)
morecontractedtable 1 Cu 4s basis).The domenant electromcconfigurationat 1111 Cu-0 dwances
atom states to which it dtssoclates monotontcally (without a barrier) due to the incipiently attrachve mteraction of the Cu 4s orbital with the 2pz Me on the oxygen atom at large R. However, eight configurotIons arc reqtured to descnbe properly the 2x+ state at all internuclear separations, smce at smaller distances (<4.8 au) the donunant configuration ISof the charge-transfer type descnbingilchargedlstribu-
has the form
tion
of the form Cu+ 3dIO(lS)
The major configuration 54
+ O-
?sl?p5(2P).
at all distances is
the
loa20230240~ l~~%r~16~ ‘A ,
(3)
where the (30,40) hlOs change orbital character from (Cu 4s, 02pz) to (0 2pz, Cu 4s) as the mtemuclear distance decreases, leading to a charge distnbution that looks hke Cu+3d?4s(3D) + O-@Zp5(2P) at R,. As can be seen in fig. I an avotded crossing in the IA energy curve between the neutral and chargetransfer configurations leads to a maximum or barrier
Volume 93, number I
CIICXIICAL
PHYSICS LtXl-I
III the 3.6
adlabam
3fl-2A
evcltatlon
atom MEP is mtended for use m model studies of mctalloenzymes mvolvmg copper-okygcn bondmg Results already obtamed using the Cu ME1 m such model studies show the correct redov properties of the metalloenzyme, m contrast to the mcorrect brhrvlor obtamed usmg (he unmodllicd ab mwo Cu atom ECP. as mentloncd III sectlon I _
References [I ]
Colorado
Q 8700 cm-I
1&,~3,~llr4~7r4
IS3 ,
1sexpected to have a bmdmg energy curve similar to that shown III fig. 1 for ?A smcc the 30 h10 wtll be clinging III character from pure 4s 3t large R, where lt will gee rise to an mclpiently repulsivemleractron, to muted Cu 4s-0 3pz bonding m the neighborhood of R,. In general, given the relotwcly hlghenergy nature of the charge-transfer configuratIon on Cu (Cu’, 3d94sI) near R,, it ISsomewhat surprising that the lowest energy $A state should be found experunentally near the /3“C state where the Cu atom contiguration at 11sR, (Cu’, 3d’O) is of much lower energy m the free atom. It thus appears that the ‘A state requires further investigation.
R 0~m.m .md II Uaxh, Ou.m~um Chcmrc.d Studrcc ut tliu %_~IJ~IS~I al Acl10n ot Superowdc DI*niul.irs. ,\mcrlL.m Conlursncu on Thcoretic~l Chrmirtry.
energy IS
loo high. Interestingly enough, the spectroscopic constants for the next assigned‘A state (E “4) [I? J, also shown in table 4, are very close to the calculated lA state. Appelblad et al. [ 171, however, asign the p ?A state as arising from configuration (3) It should be noted that an alternate possible major configuration for the r~ stale,
( I98
13) B II Uokh.T
Rouldcr.
I)
II. Dunnms Jr and J I
Il~rrwon J.Chcm
I’hys 75 (1981) 3566. [JJ C W. Bauschllchor Jr , S P.Welch [j)
.md II I’drlrldgc. J Chcm Phys 76 ( 1982) 1033 C I: Iloorc, Atomic encrfly Icvcls. NUS Clrculu 467
(Ndil llur Sld , W~sl~mg~on, 19-l9) 161 S P \VJlLh .md \V A Godd.mt 111.J Am Chcm Sue 100 (1978) 1338 A B Rwes dnd R I I cnshe, J Chum Phys 75 ( I98 I) I293 [S] S P Walch dnd C \I’ Uduxhhchcr Jr , Clluni Phyc Lcllcrs
[ 71
86 (1982) 66 191 hl.J. Sollcnbcrgr, hldslcrs rhae, Calilornid lnsl~rl~ru 01 Tvclinology (1975) [ IO] S I’.
\\'JILIlJnd
WA GodddrdIII. J
AIII
UIUIII
SOL 98
(197637908. I I I ] T II Uplon .md W A. Godd.ud 111.J. Ani Chcm SW 100(1978)5659 [ 17) K I’. llubur and G. Hcnbsrg. Conskmls uf dl.ItonnL molcculcs (Van Nostwld, Prmccton, 1979) pp. 208, 209,700 [I,] S TOplOi, J \V ~lOShO\I I!2 and Cf biSbUS,J cilClll I’hys 70 (1979) 3008. [ 141 K Rucdcnberg. L hl. Chcung .md ST. Clbcrt, lntcrn Quantum
Chcn:
I6 (1979)
J.
1069
1151 D C&n. prlvJtc connnumLJ(lon [ I61 L R. K.dln. P. Uaybulr .md DC TruhlJr, J Cl~cm. I%),.
4. Conclusions The MEP denved here for the copper atom does not introduce any systematic bias or distortion mto molecular bindmg energy curves while correctmg for the maJor intra-atomic correlation energy errors that give rise to incorrect atomic multlplet energy sepxa-
tions. These latter errors can have serious consequences for molecular
19 Novcmbcr 1982
RS
electronic
energy levels.
The Cu
[ I71
65 (1976) 3826 D Appclblad, A Lagcrqvlst. I Rcnhorn dnd R W TicId,
[ ISJ
Phywa ScrrptJ 2, (1980) 603 B Pmchcmcl, 1 Lckbvre and J. Schamps, J Ploys UIO
(1977) 3215. D II.\!‘. den Boer and C W E.~lcveld. Chum. Pliys Lcltcr$ 69 (1980) 389 (2Oj Y Lefcbvrc, B Pmchtmcl and J Sclumps. J WA
I I91
Specu!.68(1977)81.
I
CHChllCAL
PHYSICS LKlTCRS
19 November 1982
A MODIFlEDEFFECTlVECOREPOTENTlALFORTHECOPPERATOM: LOW ENERGY ELECTRONIC STATES OF CuO
Harold BASCH Deparrtnenr of C7ietnrstry. Bar-Ran Uarsersrry, RatnatGarr.
Israel
and RomanOSMAN Department of Pharmacology, Mowrr Smat School o/Medrcrrre, 1 Cusr~~~eL LevyPbce,rVmv York.h'ew York 10029, (IS.4
Reccwd 8 September 1982
To correct for mqor v~lcncc dtomlc corrclallon rncrgy errors a modUied cffcclwc po~nl~al (MCI’) /IX been dcrwd for the copper a1om ~ollowmg Goddardand co-worhcrs, the hlEP II produced by dddmg correction terms lo an db m111oeffcctwc core potenti, fitted to the cxperlmental multlplrt energyscpara~mns for Ihc Cu arom .md IOIIS Compxrson of hlC SW and v&ncc Cl cslculatlons on lhe lotvc~t cncrgy *II, *x+ and *A clcctroruc SIPKS of CuO with c\pcrnucnt.d stants shows thal the alomderwcd MEP dots not cilusc systcmatlc b13s or dlstorrmn of the molwulx bmdmg energy
con-
curves.
I. Introduction
state energies(“D below ‘S) for the copper atom
In the course of valence electron self.consistent field (SCF) studies on models of coppercontmnmg metatloenzymes [I ] using an ab init effective core
potential on the copper atom [2] It was found that cupric complexes with saturated ligands resisted reduction at the metal site; surpnsingly preferring to add the electron to a &and. This anomalous behavior can be traced to the now well-recognizedinabihty of
The importance of intra-atomic correlation energy effects for the proper descnptron of single-hgand
transttron-metalcompounds has been emphastzed [6-S]. The metalloenzyme example cited above demonstrates Its importance m deternunmg the relative stabllltles of drfferent electronic states even in large metal complex systems where the hgand field IS strong and might be consldered
to be dominatmg.
differences
The conventional treatment of such problems with extended basis sets and large multlcontiguratlon (MC)SCF and configuration mteraction (Cl) expm
and ions in favor of those electronic configuratIons with the fewer number ofd electrons. For example, although numerical Hartree-Fock theory predicts the ground state of the copper atom to be 3dt04sl(‘s) with the 3d94s’(‘D) state configuration 036 eV
sions ISclearly impractical with regard even to model systems of metalloenzymes wtuch typically contain over 25 atoms [ 11.An alternative simple and nearly equivalent procedure for handling the mtra-atomic correlation energy problem has been apphed by Goddard and co-workers to compounds of nickel [6,9-l I]. Their procedure consists of constructing a modified effective core potential (MEP) by adding
above it [4], experimentally 1512D lies 1.49 eV above ‘S. It should be noted, however, that basis set expansion III the SCF method typically givesinverted
(ECP) fitted to reproduce correctly the atom (and ion) multiplet energy separattons, while taking care
Hartwe-Fock
theory to correctly
descnbe
energy
between electronic state configuratlons of a given transition-metal atom which differ in the number of d electrons [3]. Thrs differential atonuc correlatron energy error biases the stability of states
0 009-2614/82/0000-0000/S
02.75 0 1982 NorthHolland
terms to the ab initio atom effective core potential
I
Volume 93 number
that the shape of the valence orbitals re.mains essentntlly unchanged. Following Goddard and co-workers (6,10,1 t] and Sollenberger [9] we have constructed a MEP for the copper atom that corrects for the malor HartreeFock errors ln the atom and ion multlplet energy separatmns In order to test whether the lllEP produced by atom-fittmg procedures alone still grves undistorted molecular carried
energy
OUI ab initio
cdculatmns elecrronic
curves
and properties.
vatcnce
for the lowesr
electron energy
MC
2n,
Table 8s.~
1 sets ior
Alom
ular Wparatron (R) (In]. In order to avoid
orbital cu
effects
the correlating to contrrbute
contigurattons essentralty
only
were
1 153
45’ 3d
0.05393 46.7 1 13.43 4 489 1 478
we have
SCF and Cl
2X+
and
2h
to intra-atomic
in the configuration
4s
3d’
a.4505
4P
2.440
4P’
carefully
to chemical
chosen
bond
valence
copper
1 .o
atom
-0.0174637 -0 0943483
Zp’ 3d
gaussian
0577.5220 1.0 0 0157436 0.0985876
0 2864 32 0s 7.780 2 289
and results
and oxygen
O.f7710OD
0 04620
8 810 0 9459 aP
The
-&4401)0
a.1551 37 91
25
0
for-
25’
details
0.8584288 10 0.0350044 0.1695073 0.4032% 1 0.4617022
expansions,
mation.
2. Calculational
-0.2006930
0.1402
3s n
contributions
Cu and 0 a) Atomic
function ofintemrolecfor comparison with experiments
strites 0CCuO
correlatron
19 Novcmbcr I982
CHEMICALt’IlYSlCSLCTIIXS
0 7194
0 3089032 0 4197049
0 2146 0.8500
10 1.0
basis sets used UIthese calcutatlons are shown in table 1.The 3d and 4s bases of Cu were obtamed by exponent and coefficrent optimizatron for the Cu’,
a) Not normabed.
3d94st(3D) state configuration using the ab trnho Cu atom ECP ofTopro1 et al. (‘21 to replace the 18 electron [Ar] core of electrons. The 4p basis is taken dnectly from Topiol et al. [2]. The 2s and 7p basrs for ox,*gen was r&o atom.optnnized for the ?s’?-p4 (3P) praund state using the oxygen atom ECP ofTop101et al. [13]. The hlEP was derived as descrrbed by Goddard and co-workers [6,10,1 I] and Sollenberger 191. In short, a two-component correction term (V,) of the same analytic form as the ECP ISadded to the ab initio ECP (21 wrth the constratnts that the changesin poten-
As suggested by Sollenberger 191, VP w_as set equal to Vs. The final parameter values for the V, are shown in table 2 and the resultant copper atom and ion multrplet energy separations are in table 3. The derived MEP for copper together with the ab mitio ECP for oxygen (131 and the basis sets of table I (with the Cu 4s uncontracted to form three separate basrs functions) were used to obtain the lowest energy “II, ‘E” and 2A electronic state energy curves of CuO. The MC SCF/CL calculations were carried out using the ALlS 1141 system of programs rnodtfted (IS] to incorporate an extended version of Kahn’s
tial be localized and that
to the immediate
v, have a mmimum
vicinity
of the atom
where the corresponrhng
(trl) valence orbltal has its maxunum amplitude. These conditions are sufficient to determine 3
out of
4 p=u-neter~ in tit. The fourth parameter for Va was varied
ro reproduce
best the experimental
energy
52
VIc~rvxt~~n terms to gwc hrEP
for the copper
aI
81
0.1
0 04125
0.165
1.2X
-0.8085
2
0.5625
2.25
0 835
-7.515
a) i$ = CI~-~exp(-at&
cl
atom 8)
1
sep-
between the lowest energy Cu. Cut+ and state configurationsdiffering rn the number of d electrons. The fourth parameter for vs was used to optimize the various 3d”-‘4s’ states of Cu and Cut+. arations
Cd*
Table 2
+ Dlexp (-@I?); the ab mitio copper atom ECP in ref. [?I.
DI
to be added to
Volume 93, number
I
CtlCbllCAL PIIYSIU
Table 4
Table3 Slalc conligonllon
Exper,mcnfaI b,
CCr c)
hwd)
3d’O4s’ 6) 3dg4sZ $D) 3d’O4p’ (2P)
0 1.49 3.8 I
0 -0 48 4.40
0 1.58 5.41
Cu’ + 3d’O 3d94s’
C’S) (3D)
7.72 10.53
5.34 6.12
112 9 91
Cuz+ 3d9
&I)
28OL
Cu
19 Novcnlbcr 1982
LLI’ILRS
258
28.36
=ri
CSIC c?.p 3)
1.768 1.724
653 640
I91 2I
22,
talc cup.b)
I 70 -
700 661
2 1.? -
IS200 I3000
ca1c.
1.71
747
0.69
elp. kc) e~p. a)
1.76 1.72
733
-
24000 15300 21100
*A
Q)rromtcf.~12). b~lromd (171. ‘) rrom ref. [ 18J: R, cdcula~rd promgwn
ECPgaussian integral evaluation program [ 161. The confiyrat~on
expansion hst was obtained
by the ite-
0 0
WIUC of 8.
the expenmentally observed z11,,2 and ?Aslz states are taken for comparison purposa.
mtivenaturalorbitalanalysis/valence Cl featureof the ALIS [ 141 system. The calculations were camed out in C2v symmelry makmg the 2n and ?-Aelectronic states thus obtained space polarned. The resultant energy curves are displayed m fig. I and a comparison of calculated and experunental spectroscopic constants for the lowest energy ?fl, IX* and “A electronic states of CuO are shown in table 4. In table 4
3. Discussion As shown m table 3,generally the calculated Cu atom and ran mulflplet state energy separations are greatly improved using the MEP. Of course, tn the lunited (double-zeta quality) size basslssets used here (table 1) il is clear that the optimization procedure that produces the hlEP also, to J certain extent, corrects for both relativistic and basis set errors. It is therefore,
npproprtare
to keep the baas set that was
usedto genemtethe MEP in~iloleculsr calculatmns. rather than reopttmize the basrs set for the MEPatom as is usually done. The electronrc structure descnption of the ground ?l’l state of CuO has been given by den Boer and Kaleveld [ 191. A CuO u bond is fomled from copper and oxygen atoms in their respective ground 3dt”4s1 (%) and 2~?!p~(~P) states to form the loa2a2302 [a43n3 IS4 2il
(1)
state canfiguration. The binding energy curve is a smooth function of internuclear bond dlstnnce and the set of fourconliguntions,3a22n3,
40’Za3
and
to describe accurately the complere range of bond distances shown in fig. 1; 3a and 4a are the corresponding 3014u)2~?
(two spin couplngs) IS adequate
53
Volume 93. number
I
CHCLIICAL
PHYSICS LCTTCRS
bonding/antibondmg o molecular orbitals (MOs) involvlng 0 7-p and Cu 4s and 3-n is essentially the 0 3-p orbital In describmg the configurations III the previous sentence the orbltals common to the four configuralIons were dehberately omitted but were, of course, tncludrd in the MC SCF/Cl calculations. Table 4 shows the good agreement obtauted for the ground (X ?ll) state of CuO between theory and expermlent for the equilibrium bond distance (Rc withm 0.0448), the harmonic stretch frequency (wc wtthin 13 cm-l) and the dissociation energy (7G% of D,). A quick comparison of these results with den
Boer and Kaleveld [ 191, whose allelectron extended basis set calculations did not m&de atomrc correlation effects, provides convmcing evidence of the efficacy of the MEP for the copper atom. These authors
typically obtain only ~30% of the bmdmg energy and R, vduss that differ by =O.l?, A from expenment, depending on the basis set used. However, more pomtedly, their ‘n state bindmg energy curve has a hump et mtermediate bond distances whch can be attnbuted to an avoided crossing of the inverted ‘.S and ID (?D below ‘S) atormc copper Icvels. Fig. 1 sl~owsno such ma_\mum on the energy curve for Ill which must then be artificially due to atormc correlation effects. tluber and Herrbeg’s tabulation of rhc spectrosof CuO [ 121 lists a 2x+ (Krontg symmetry uncertain) as the fist excited state of CuO.
19 Novrmbcr 1982
10’20”30’ ln”27r4164 ‘r, ,
(2)
where the orbital character of the 30 molecular orbital changes from primarily 0 7-p, to Cu 4s in going from R = R, to R = -. The calculated oxygen atom JP-ID multiplet energy separation from the 211-1Z
separationat largeR ISthen 222 eV comparedto 1.96 eV experimentally [5] _ Table 4 shows the good agreement obtamed here
between calculated and experimental values of w, (w~tlun 39 cm-‘) and the adiabatic excitatron energy (T, within 2200 cm-l) for the ICf state. From these compansons for both the ?fl and ZZt states it is clear that the MEP 1snot systematically distortmg the molecular curves, forexample, in the form of exaggerated butding energies or shortened equtlibrium bond distances. Thislatter type behavior in molecular cakulatlons might be expected from the adrhtlon of attmctive terms to the original atom ECP, as was done here
to generate the MEP. Although the exact vahre of the rotational constant (Be) is not given, it IS stated [IS] that B, for the 6 “Z state is smaller than that for the X ?n state. Since Ri IS proportional to B,’ it must be that R,(6 ‘2) > RJX ‘iI). The calculated values m table 4, however, show R,(‘Z) < R,(‘Il). Thus the fact that the calculatedR, for “fl IS too short and for IS LStoo long m comparison
to expenment
However, two lower energy ‘C states have smce been observed [ 17,20] in enusslon and the comparison III table 4 ISwith the lowest of them, labelled 6 2B [ 171. We have also MC SCF/CI calculated the lowest energy ?C- state and fiild it to be essentially repulsive, dissoc~ating to the ground state Cu(?S) f 0(3P) atoms.
found are due to orbital basis set and inter-atomic correlation effects rather than systematic bias or distortion in the electromc structure description due to the MEP. The calculated lowest energy ?A state dissociates to Cu 3d94s2(?D) + 0 ~s??P~(~P) which is only 1.75 eV above the IS + 3P combined ground states dissociation limit due to the Cu ?G2D multiplet energy
Therefore,
separation
copic constants
the observed bound S ZZ state should be
would seem to indicate that the differences
in tius basis set (1.58 eV III table 3 wtb
of Zt symmetry. The calculated ?I? state (table 4) correlates with the Cu 3dlo4~l(~S) + 0 2$2pJ(tD)
morecontractedtable 1 Cu 4s basis).The domenant electromcconfigurationat 1111 Cu-0 dwances
atom states to which it dtssoclates monotontcally (without a barrier) due to the incipiently attrachve mteraction of the Cu 4s orbital with the 2pz Me on the oxygen atom at large R. However, eight configurotIons arc reqtured to descnbe properly the 2x+ state at all internuclear separations, smce at smaller distances (<4.8 au) the donunant configuration ISof the charge-transfer type descnbingilchargedlstribu-
has the form
tion
of the form Cu+ 3dIO(lS)
The major configuration 54
+ O-
?sl?p5(2P).
at all distances is
the
loa20230240~ l~~%r~16~ ‘A ,
(3)
where the (30,40) hlOs change orbital character from (Cu 4s, 02pz) to (0 2pz, Cu 4s) as the mtemuclear distance decreases, leading to a charge distnbution that looks hke Cu+3d?4s(3D) + O-@Zp5(2P) at R,. As can be seen in fig. I an avotded crossing in the IA energy curve between the neutral and chargetransfer configurations leads to a maximum or barrier
Volume 93, number I
CIICXIICAL
PHYSICS LtXl-I
III the 3.6
adlabam
3fl-2A
evcltatlon
atom MEP is mtended for use m model studies of mctalloenzymes mvolvmg copper-okygcn bondmg Results already obtamed using the Cu ME1 m such model studies show the correct redov properties of the metalloenzyme, m contrast to the mcorrect brhrvlor obtamed usmg (he unmodllicd ab mwo Cu atom ECP. as mentloncd III sectlon I _
References [I ]
Colorado
Q 8700 cm-I
1&,~3,~llr4~7r4
IS3 ,
1sexpected to have a bmdmg energy curve similar to that shown III fig. 1 for ?A smcc the 30 h10 wtll be clinging III character from pure 4s 3t large R, where lt will gee rise to an mclpiently repulsivemleractron, to muted Cu 4s-0 3pz bonding m the neighborhood of R,. In general, given the relotwcly hlghenergy nature of the charge-transfer configuratIon on Cu (Cu’, 3d94sI) near R,, it ISsomewhat surprising that the lowest energy $A state should be found experunentally near the /3“C state where the Cu atom contiguration at 11sR, (Cu’, 3d’O) is of much lower energy m the free atom. It thus appears that the ‘A state requires further investigation.
R 0~m.m .md II Uaxh, Ou.m~um Chcmrc.d Studrcc ut tliu %_~IJ~IS~I al Acl10n ot Superowdc DI*niul.irs. ,\mcrlL.m Conlursncu on Thcoretic~l Chrmirtry.
energy IS
loo high. Interestingly enough, the spectroscopic constants for the next assigned‘A state (E “4) [I? J, also shown in table 4, are very close to the calculated lA state. Appelblad et al. [ 171, however, asign the p ?A state as arising from configuration (3) It should be noted that an alternate possible major configuration for the r~ stale,
( I98
13) B II Uokh.T
Rouldcr.
I)
II. Dunnms Jr and J I
Il~rrwon J.Chcm
I’hys 75 (1981) 3566. [JJ C W. Bauschllchor Jr , S P.Welch [j)
.md II I’drlrldgc. J Chcm Phys 76 ( 1982) 1033 C I: Iloorc, Atomic encrfly Icvcls. NUS Clrculu 467
(Ndil llur Sld , W~sl~mg~on, 19-l9) 161 S P \VJlLh .md \V A Godd.mt 111.J Am Chcm Sue 100 (1978) 1338 A B Rwes dnd R I I cnshe, J Chum Phys 75 ( I98 I) I293 [S] S P Walch dnd C \I’ Uduxhhchcr Jr , Clluni Phyc Lcllcrs
[ 71
86 (1982) 66 191 hl.J. Sollcnbcrgr, hldslcrs rhae, Calilornid lnsl~rl~ru 01 Tvclinology (1975) [ IO] S I’.
\\'JILIlJnd
WA GodddrdIII. J
AIII
UIUIII
SOL 98
(197637908. I I I ] T II Uplon .md W A. Godd.ud 111.J. Ani Chcm SW 100(1978)5659 [ 17) K I’. llubur and G. Hcnbsrg. Conskmls uf dl.ItonnL molcculcs (Van Nostwld, Prmccton, 1979) pp. 208, 209,700 [I,] S TOplOi, J \V ~lOShO\I I!2 and Cf biSbUS,J cilClll I’hys 70 (1979) 3008. [ 141 K Rucdcnberg. L hl. Chcung .md ST. Clbcrt, lntcrn Quantum
Chcn:
I6 (1979)
J.
1069
1151 D C&n. prlvJtc connnumLJ(lon [ I61 L R. K.dln. P. Uaybulr .md DC TruhlJr, J Cl~cm. I%),.
4. Conclusions The MEP denved here for the copper atom does not introduce any systematic bias or distortion mto molecular bindmg energy curves while correctmg for the maJor intra-atomic correlation energy errors that give rise to incorrect atomic multlplet energy sepxa-
tions. These latter errors can have serious consequences for molecular
19 Novcmbcr 1982
RS
electronic
energy levels.
The Cu
[ I71
65 (1976) 3826 D Appclblad, A Lagcrqvlst. I Rcnhorn dnd R W TicId,
[ ISJ
Phywa ScrrptJ 2, (1980) 603 B Pmchcmcl, 1 Lckbvre and J. Schamps, J Ploys UIO
(1977) 3215. D II.\!‘. den Boer and C W E.~lcveld. Chum. Pliys Lcltcr$ 69 (1980) 389 (2Oj Y Lefcbvrc, B Pmchtmcl and J Sclumps. J WA
I I91
Specu!.68(1977)81.