The difference electron density of CO is studied by comparison of several calculations. It is shown that the Hartree-Fock-Slater and Hartree-Fock methods yield equally good charge-distributions and that the use of minimal basis sets should be avoided

Feil, D.

With, G. de

English

de With, G.

University of Twente Research Information

Volume 30, number 2 CHEMICAL PHYSIC!3 LETTERS I5 January 1975 _- MOLECULAR CHARGE DISTRIBUTION OF CO G.DEWITHandD. FEIL Chernicai Physics Laboratory, Twente UnilTersify of Tcchr~ology, Enschede. The Netherlot& Received 14 August 1974 Revised mansuaipt received 5 September 1974 The difference electron density of CO is studied by comparison of several calculations. It is shown that the Hattree- Fock-Slatcr and Hartree-Fock methods yield equally good chargedistributions and that the use of minimaI basic sets should bz avoided. 1. Introduction In order to get a better understanding of what type of wavefunction is needed for the calculation of scat- tering amplitudes in X-ray diffraction of molecular crystals, we have compared several wavefunctions of CO. The criterion by which an approximate wave- function is judged is not usually the energy but the electroz density associated with the wavefunction. So we have studied the charge distribution difference .. fun&ion introduced by Roux [! j hp@ = P&j - P.&j I where phi(r) is the eIectron density at the point z for Table 1 the molecular charge distribution and pA[r) is the electron density appropriate to the non-interacting atoms at the same internucIear separation. Ai is customary, p*(f) is computed using the spherically aveiaged F orbitals of the atoms in the ground state. According to Smith and Richardson [i] we used the same basis of atomic orbitals for both molecular and atomic calculatiofi for obtaining Q(r). Except for the minimal basis,calculations all wavefunctions were calculated using Clementi’s exponents [3]. 2. Results and discussion The different calculations on CO which we wmt to Specfication of the wavefunctions used to calculate the moleculti charge distribution NO. Ref. R (au) E (au) Basis C) Idcntifiationd) 1 [41 2.132. -112.7891 (22, 12) HF limit 2 [41 2.132 -112.7790 (16.8) DZ+D+F 3 a) 2.12 -112.6754 (12.4) DZ 4 b) 2.12 -112.8086 x12,4) DZ+CI 5 L61 2.i32 -112.3260 (6,2) SZ-BA ” 6.’ t61 2.132 -112.3436 (632) SZ - Slater 1 181. 2.12 - ‘.(12,4) DZ,HFS a) Calculation with the proFam “New Alchkmy”. b) This is a 217-term CI on “New Alchemy” which lowered the iota1 energy 0.0332 au. Notice that the cner& is beneath the Hartrec-Fock hit. .’ - c) (u, b) means u u-type and b rr-type,basis f&&ion& d) HF Xarfree-co&, HFS Hartrec-Fock-SIater,,DZ double zeta, SZ single zeta, Cl ~~nfiiu&on interaction, BA best atom. . . . ‘: ; : ‘.,. 279 : ‘. . ...’ ,. .’ ‘.; ., . Fig. i. Differcnk density.map‘ for HF-limit cdculation. I& 1 -. ,. . ‘. ‘, ., ..’ !‘. ,, Fig. 2. Difference densjty map for HI7 + d + I ‘calcubtiob. ., ,. : ‘_ ” ‘. . . .‘. :’ . ,, ..1 ;.:. ‘. .: .I..’ ;.. : : ;; j-$-DZ” ., ‘:_; ..:‘.._ ‘. .“_.,, ,, : ,;,; -. .., .- >. .’ ‘.; ,, .“_. ‘. ,,‘., ., : ;. .’ ., . ,. : - ‘_ : ,_. ,.:, ,. .‘. ‘. : .., ‘,,. ,. ._,,_ .,.. ,. “,. ‘.,. _: ,:. . .. Volwhe 36, numbq2 ?IiEMICAL PHhCS LETTERS IS Ian&w 1975 ‘. 1 : . ., ., t-&~z-cj .., ,’ ., ,: I .’ : ’ .’ :’ I . . ,- . . Fig. 4. Difference density map for HFS - DZ - CI calculation. : .‘. )-f-SZ-&$ : .; 1, .’ \ :. ; i . . I r -..- -..,, -i Fig. 5. Differdrice density map for HF‘- SZ &xlation. ; HFS.-DZ’.. t ‘, . , ‘I I / : .;’ !, I 1 .’ ,‘_ .’ . . . f I I II .- .’ .’ . . ,, ‘, Fi,o. 6. Difference den&y map for HFS -: DZ alculatioti. ” ,’ ‘.. _ : l:A, very sophi&‘ated calculation k the he v&y ,’ : @jm&&J data on t,4e cha$ti, d&&y’of C@ we-use negr to the Hartree~FockJimit dtie to$fclean~and 1 this G.!culation as a’ reference. . . Yosi&tine [4] (fig’s: 1’ and ‘7). Xn‘the absence of ext :. : :’ 2. One St&, back@rds in ti&reticril ac’&racy is a (. ‘. ;_ (, .’ ..‘. _.,. ‘. -. ,. .- : _._:: .-’ .:; .-, 28I : “: “.. :. .. .; _. _: : ,, ;.’ ‘. ,.‘, . . :. _..’ . . :: : .. .’ : _ ‘_ ,’ Volume 30;number 2 ” ‘. CHEMICAL PHYSICS LE-ITERS ‘!5 January 1975 t \I :. 1; :. .._c a I. ,,, c 0 : FQ. 7..Dsference density ilong the rnoleculrr axis of CO. l%e r,epresentations at: HF-limit (-%, HF - DZ (: - -1, HFS - Dg (-.y)_ ‘. .’ near H&tree.-Fdck limit calculation (double zeta in agreement with the results of others [2,7]. basis plus a d and an f type function on each atom. [4]) 6. A slight improvement is obtained by the use of -(fig. 2). There is a small difference in electron density exponents calculated according to Slater’s rules in the as comparecj with the reference (on the molecular ax.? ’ bond density =O.Ol.e/a~ lower, lone-pair density minimal bar,iS calculation [6] (difference map not &.C)I_.efa~ higher) suggesting the relative unimpor- shown). In the nitrogen molecule the wavefunction .with best-atom exponents described the bonding tance of the extra s and p basis functions of the reference in comparison with this calculation. regionsomewhat better [2]. 7. List but not least we compared the charge distri- ..’ 3,The next wavefunction considered is taken from .. bution as ca$ulated with the Hartree-Fock-Slater a, double zera basis calculation (with ,the program I. “‘Ne~v’Alchemy”). The difference in charge distribu- model [S] (Yigs. 6 and.7). This is a double zeta basis calculation. ‘The electron density differ&e map is tidn is considerable (figs. 3 and 7) as compared with the reference. On the molecular axis: bond density very much the same as obtained from no. 3. &OS e/u: iower, lone pair density =O.bS ~/Lz$ Ihigher. This,is strong evidence for.the statement that the. Hartree-Fock-Slater’method (as used in.ref. [8 1) : II+ shows that polarization functions are indispens- .ahle for an accurate description of,the charge distribu- canyield waq/efunctlons as good as the normal H&tree-Fock method. (This is probably due to the .tjon. .‘. . . 4. The inclusion of configuration interaction * use of the LC’AO expansion instead of the use of the (fig. 4) makes a difference of Iess than 0.01 e/a; as muffinetin approximation, the first approximation be- ing better in rnolecujes, the latter in solids, [9] .) This compared.with no, 3 (as expected [5]). statement is already supported by atomic calculations -51 A mi+nal~basis set calculation using best-atom made &th a doubieieta basis, e.g. for the’C, N and 0 elltponents [6] does not resemble,at all no. 3. The’ ‘; atoms, the greatest difference being less than 0.01 e/a; greater part of the bond density is ioiver tharithe sum [IO]. '. ., : of the atomic densities in that region (iig. 5). This is _’ _’ .:. ;’ .._. . . . ,“‘Thiz Js a’217:-term CI dn “New Alchemy” w+ch lowered 3: Conclusion ._ :_ the total energy 0.0332 au. Notice that The energy is.beneath : -. the I&tree-F&k Limi&’ ‘. ( ,. We.hiight saj~ that in an el.&tron density aria&is .: . . . -. ., .- -. : .’ 2#2,- -- :,, .‘1, ‘. ,;, .‘. .: ,‘. :’ .._.. : ...,. .,: I, . ._ .. ..I. .‘_ ,. .;‘ .,, -- :. : ,!‘, :.’ .,., ,. : ‘. ‘a,. ., .’ .: :.. : : . . . _ ::. Volume 30,n&bes 2 ._ CHGilCAt.PIfYSICS LETTERS ‘, ,lS JWU~~‘I975 _.,, : :, .- ,. : .. . ‘cme s&&d use ar least a double zeta ~as~s.caicul~~jo~~ . “preferably e&e&d with some polarization functions. ,’ d&&&d. $e &re‘v&y ritqch obliged f& Dr: S. Eiar’ce~mna f$r heI$uidiscu$dns. _ ., ~Inclusion of conf&ratiofi interaction seems not Eo .compensate for pol&zition. T_he use’of minimal basis . . ,. :,; ‘, ,, _, :: -- ;‘, set ~~I~~~ation~ should be avoided.’ 1 ‘Referen& ._. .:,I,‘.. ._ : :: ., ,‘_. 1 However, there seems to be no ~~jec~i~~ in uSing a ‘: ‘: .’ ‘. ‘. ~rt~ee-Fock’-~~ater ~~a~~~un.ct~o~ (tviih the same, .’ ., quality af basis set) instead of a narmat Hart@e--Fc& [I] if. &uk, S. &wuia& iid R* ~~u~~I~J.C~i~_ P&s. 54, (1956)218. : :. ‘. calctilatioi This give,S rise to an enormbus saving of [2j P.R. Smith‘zn+i J.W. Richard&n, J. Phys. k+rn; ?I ” .‘, computer time: ,!lPB?) 924, ,, 131 E. C$menti, N&i !. Res. Develop. 4 (1965)‘ supple, .: . tab& 45 -0 I. . “ ~. ‘. 141 AD_ Mchan and K’Yoshimine, IBM 5. Res, D&efo& 1 I (19571 suppi. would like to thank Mr. EJ; Baerends, Prufessar P. Ros: Mr. M.C. van Hem& and-Dr. 5 J.C. iMuIder for their genkrous supply of sijme of the wavefunctions’ ^ ‘, R. McWceny and B.T. Sutcliffe, hfetksds of mokculir quantum mechanics (Academic Press, Nw.York, 1969) .’ p* 138. B-J. Rans%, Rev; Mod: Phys. 32 fI960f 239. A.F. VsnXatIedge, J. Phys. Chem. 78’(1974) 763. E.J. Bacrends, D. Elfis and P. ROS, C&em. Phys:.2 (m973) : I. _’ J.?d. Ziman, DrincipIes of thd thc& of s&i& (Cambridge ’ Univ. Press, London, 1972) ch. 3. G. de With and D. Foil, unpubljs~cd r&Its. _’ ,:. .’ . . ,T . . 1: .’ ‘,_ .. :. ; .“,~ ,” . . . . ‘. ‘. ‘, (, ~’ _. .:.,. ._ . . : s’ ‘. .’ ~ .: .. ..” ; . _, ,/’ ., .: . ,’ . . : : .’ _ ‘. ‘:‘ ‘., _. ‘: . . . .~ ‘1 ,:, ‘, .‘. .I li ; . . ,, ,’ ‘. _ : ,- : _” ‘, (, . _/’ ,. (,, z .: ..,I., _’ .) “1,. . . .~ ., ,” .,( ,.(’ “. .’ : ‘.,, .‘_ ., ).” : ‘, ‘, _: : : ,,I ,. ,. : ‘_.,. . 1: .,) ((. (~ .’ ,, ‘, “, “, .( * : .;. ,,, ‘. ‘. . .:_, :, ),. ‘., ,’ _‘/ .’ .:,, “. ., ‘_ ,.: : ‘.- ” .: .“.‘ ‘. ;: ‘1 ‘- ( .  .‘.,_ 

Molecular charge distribution of CO

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