Analytic SCF wave functions for transition-metal atoms

Volume 6, number 5

ANALYTIC

1 September

CHEPiiICAL PEYSXCS LETTERS

SCF WAVE

FUNCTIONS

Depnrtment03 Chemistry,

University

FOR

TRANSITION-METAL

of Alberta,

Edmonton. ALbe&,

t970

ATOMS

Gmuda

Received 12 June 1970

Anfklytic self-consistentfield wave functionshavebeen obhined for the t~it~o~-me~ stcuns in tbeir ground-state configurstions. The atomic orbit& &we bean expanded in terms of linear combinations of orbit.& from basis sets of 10 and IS Hater-type functions.

For the transition-metal atoms we take the electronic configuration to be ls2 2s2 2p6 3s2 3~6 3dn 4~2 with ti running from I for scandium to 8 for nickel. In order to describe the outer electrons reasonably, we have assigned a second ST0 to the 3p,3d and 4s shells in the lo-ST0 sets and then added one more 3d ST0 to form the 11-ST0 sets. Orthonormal analytic SCF orbitals (1)

are constructed from the norm&zed basis STO’s, &, which contain arbi’al exponent parameters Ta. (cia) are the expansion coefficients. The computer program is based on the mathematical formulation by Roothaan and Bagus IL]. The restits of the calculations are presented in tables 1 and 2. The number of significant figures given does not indicate optimization to that accuracy but these are figures used io the catculations. The data for the expansion coefficients and

Tabfe 1 Optimized exponents & for the basis functions &.

SC

3.8

20.5013

2s

3.35351.

Ti 21.4886

V

22.4754

Cr

23.4620

Mn-

24.4559

3.49878

3.67266

3.85926

3.957a9

Fe

25.4437

CO

26.4271

4.01798

4.11711

Ni

27.417 6 4*15309

33

4.96476

5.21024

5.47021

5.73694

5.88717

6.14115

6.40541

6.60145

4s

1.17268

1.22886

1.28075

1.32962

1.37252

1.42321

L.46818

1.5L1oa

43

3.88007

4.06509

4.26660

4.47576

4.64800

C74085

4.32631

s.03411

14.1484

14.4493

zp

11.1432

11.7093

12.2128

12.6066

13.0652

13.52I.7

3p

3.13091

3.36384

3.59021

3.81120

&02759

4.24904

4.46382

3P

8.43400

8.93812

9.40026

9.78342

10.20591

10.62065

lt.z.670

3d

4.68005 ll.4487

1.70898

1.96303

L1553.9

2.32568

2.50136

2.6LfOS

2.73611

2.86757

3d

4.18168

4.64848

5.03808

5.40069

5.76765

6.07007

6-38500

6.70655

3d

6.20131

6.74823

7.16160

7.63974

8.06634-

a.50918

8.87268

9.21388

3d

2.92937

3.26158

3.52287

3.80466

406477

4.32157

4254254

4.75082

8d

1.36069

1.56405

1.70656

1.84514

1.98206

2.07073

2.16126

2.25016

293

Volunx 6, number 5

..’

CBEMICAL PHYSICS -LETTERS

t

_.:

1 .September 1976

Table 2 Comparison Number of ST0 basis functiona

SC

z

of total energies -(in atomic units) for trsnsition-metal

atoms

Ti

v

Cr

Mn

Fe

co

.Ni

3d4( 5D)

Zd5(%)

3d6( 5D)

3d7(4F)

3d8f3F)

33

.W D)

M ( F)

Sd3(*i?)

7a)

-75946415

-846.81560

-940.97195

;1041.0062

-1I47.1067

-1259.0855

-1377.3744

1Oh)

-759.27455

-847.86971

-942.26517

-1042_6001

-1149.0599

-1261.5303

-1380.3907

-1505.7267

llb), 22c,

-759.28174

-847.88465

-942.28964

-1042.6361

-114S.lOS5

-1261.5979

-1380.4793

-1505.8389

-759.73553

-848.40526

-942.98266

-1043.3061

-1149.8651

~1262.4424

-1381.4134

-1506.8696

-1502.0487

a) Ref. 141.

b) Present -work. C)Ref.

orbital

[5].

energies

are available

upon request.

We

have made a constderable effort in optimizing the non-linear parameters ($.J but it is not claimed that these parameters are fully optimized. In terms of total energies the lo-ST0 basis sets achieved about 4 eV of improvement over the values given by the Xl-ST0 basis sets of Karo et al. [Z]. The present H-ST0 basis sets yield values about 0.5 eV better than those of the II-ST0 sets of Claydon and Carlson [3]. These comparisons demonstrate that it is important optimize the variational parameters carefully. In the present work the optimization of the

to

IO-STO-sets was carried out first, and then for the II-ST0 sets no attempt has been made to reoptimiza the 5s-type and 3p-tylje basis functions.

Generous support given to the present work by the National Research Council of Canada is gratefully acknowledged. The author wishes to record his appreciation of the meticulous preparation of input data cards by K. Huzinaga. REFERENCES [l] C. C. J. Roothaan and P. S. Bagus, Methods in computational physics. Vol. 2 (Academic Press, New York. 1963) p.-47. . [2] - _A. M. Karo, F. McMurphy and R; K. Nesbet, Phys. Rev. 165 (1968) 123. [3] C. R. Claydon and K. D. Carlson, J. Chem. Phys. 49

(1968) 1331. [4] E. Clementi and D. L. Raimondi,

J. Chem. Phys. 38 (1963) 2686. [S] E. Clementi, J. Chem. Phys. 41 (1964) 295.

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