Theoretical study of the low-lying electronic states of MgH

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39, number 3

‘CHEMICAL

PHYSICSLETTERS

1 May 1976

THEORETICAL STUDY OF THE LOW-LYING ELECTRONK STATES OF MgH M.L. SINK, AD. BANDRAUK * Dgpartement de chimie. Universit.?de Sherbrooke. Sherbrooke. P.Q.,

GnWdQ

W.H. HENNEKER Division of Chemistry, National Research Gwncil, Ottawn. Cnnada

H. LEFEBVRE-BRION Laboratoire de Photophysique Mol&ulaire, Univexiti de Paris-&d. 91405. Orsay, France

and G. RASEEV Chiuersid de Louvain, Louvain, Belgium Received 19 December 1975

Ab initio CI calculations have been performed for the X * Z’, A *R, and B’ *Z* states of MgH, correlating ordy the three valence electrons. This procedure is found to give good agreement with experimental data. In particular, we fmd that the B’ state is w&ly bound with re = 4.9 au and exhibits strong mixing with the ground state at this distance.

1. Introduction In a recent article in this journal, Balfour and Cartwright [ 11 have presented direct experimental evidence for a new 2Zi state of MgH. They fmd that this state, which they designate B’ *Z* , has a shallow potential energy curve (me = 832 cm-l) and a large equilibrium internuclear distance (r, = 4.838 au). The presence of this state explains many problems in the spectrum of MgH, one of them being the rotational perturbations @Ithe A *n-X ‘C+ system [2] . Previous theoretical studies on MgH include the HartreeFock (HF) calculations of Cade and Huo [3] for tlie X * Z” state, and the natural orbital configuration interaction (CI) work of Chan and Davidson [4]. The results of the latter workers indicate that the second root of their 22+ CI corresponds to the new B’ state. However, while their second 2ZZf root does show the general features of the 9’ state, a minimum at large * 1974 Summer visitor at C.E.C.A.M., supported by La Coopiration France-Qu&ec.

R and a shallow potential curve, quantitative agreement is lacking. This lack of accuracy is probably due in part to their basis set (an extended, but not optimal, set of 17a,9n, 46, and 14 Slater orbitals (STW)), and also because the largest R value in their calculation is 5.25 au. Using their CI energies at 4.25, 4.75, and 5.25 au, we have calculated re = 4.967 au, w, = 1547 cm-l, and& = 2.523 cm-l foi their B’ state. This shows that additional computations are needed to improve the theoretical results for &is state_ In this letter, we present the results of accurate ab initio calculations for the potential energycurves of the X 2Z!*, A 211, and B’ 2X+ states, performing extensive CI calculations on the three valence electrons of MgH. We have computed the 2ZZ”states at eight internuclear separations over the range of 2.25-6.25 au, and the A*ll state at six values of R from 2.75 to 5.25 au. In the following section we give the procedure and results of our computations, and in the later sections we present & analysis of our wavefunctions and a comparison of our results with experiment. 505

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cited states of MgH. Our final bases both consisted of 200, -lOn, and 26 functions, with the 2Zt and 211 bases differing but by one value of an eiponent. SCF calculations for the 2 r;’ lb22a2 35” l@402 50 and 311 lo2202302 1n44022p configurations were made at 3.27 1 au, giving values of -200.15633 au and -200.06007 au, respectively, for the ene@y. These energies may be compared to Cade and Hue’s SCF value [3] of -200.1566 au for the 2Zt state. SCF calculations for the 2 2” configuration were carried out for eight in&nuclear distances over the range of 225-6.25 au, and six values of R ranging from 2.75 to 5.25 au for the 211 configuration.

_

We have chosen to follow the procedure which Bagus et gl. [5] have used in their study qf the-X 2 J? &d .A2lIstates of BeH, wherein they have.reported results which are in excellent agreement with experi1m&t.-Theii method was to use an extended ST0 basisset, td compute the SCF wavefunctions for the 21Z? !022a23&and 2n 10~20~1, configurations, and then to carry out ftili valence shell CI calculations fh! both states using a lo2 core. Also, they introduced the use of an SCF WC (SCF plus unit vecto!) mol&ular orbital (MO) basis for the CI step. Details of our calculations differ from theirs only in the use of two ST0 bases (one for the 2X+ states and one for the ?iI state); the additional computation of the second CI root for the %‘?I? state, and the use of a much larger core of lo22u23a2 I& orbit&. The application of their fuII valence shell CI method to this larger system should provide additiona evidence for the accuracy_ of this computational approach. All computations were carried out at C.E.C.A.M., Orsay, France, Using the ALCHEMY computer program [6] .

2.2. CI calc7hrions CI wavefumtions were then constructed by using a 10~2~~30~1,~ core, and adding all single, double, and trip!e excitations to the reference configurations (core)411~50 for the * I3+ state, and (core) 4a22sr for the 2 n. Wavefunctions containing 1542 and 1776 configurations were generated by this process for the 22+ and 2Kl states, respectively. The Cl MO’s used for these calculations were formed by adding unit vectors from the ST0 basis to the SCF orbitals for each state. These unit vectors were chosen so that STO’s which appeared to be more important for the core were omitted. This procedure gave a (17u, 7n, 26) SCF WC basis for both symmetries. The first

The near HF ST0 basis of Cade and Huo [3] was taken as the starting point for our basis sets. Several exponents for the more diffuse orbitals of this basis were changed slightly, and additional diffuse functions added so as to provide a more flexible basis for ‘use in representing both the ground state and the ex-

and secocd rootsofthe full22+ Cirnatrixwere

found at the computed SCF points, and likewise for the lowest 211 root.

Tablei SW and CI energies (au) R

SCF X2x+

2.250

-200.05924

2.750 3.271 3.750 4.430 4.840 5.250 6.250

-200.13953

506

-200.15633 -200.14790 --200.12314 -200.10679 -200.11097 -200.11242

CI Ah

x2-++

B’=x+

A%

-200.04921 -200.06007 Y200.04677 -200.01603 -199.99656 -199.978iS

-200.09872 -200.17797 -200.19537 -200.18909 -200.17071 -200.16075-200.15375 -2(jO.14755

-199.94536 -200.02311 -200.05;66 -200.07549 -200.09114 -200.0943s -200.09325 -200.0795i

-200.09315 -2OO.lO626 -200.09743 -200.07791 -2C!O.O6808 -200.06097

Voltime

39, number 3

CHEhIICAL

3. Results

The SCF together

energies for’the X ?Z+ and A 211 states,

with the results obtained

from the CI calcu-

lations

for these states and the B 2Zi state are given in table 1. Using the computed energies, we have constructed potential curves for these states, which are shown in fig. l_ It can be seen from this figure that CI has important effects for both the X and A states. For the X state, the SCF curve has a small maximum at about 4.8 au, which disappears in our CI result. This feature is identical to ihat found by Bagus et al. [5] in their calculations on the X 2Ec+ state of BeH. To test the similarity further, we carried out Cl calculations on the X 2C+ state using the deletc-bythreshold technique, where configurations are deleted from the CI list if they contribute less than a given theshold td the energy. The results of these threshold calculations are given in table 2. The value of the threshold to the ener,v. The results of these threshold 200-250 configurations. The dotted portion of the X2x+ CI curve in fig. 1 shows the major difference between the full Cf and threshold CI results. Clearly, as in Be!& the maximum vanishes only when the full CI matrix is used. WC also note that tfis maximum is related to the abrupt change in structure of the 40 and So orbit& in this region of R. Turning to the A 211 state, we see that at large R, the valence shell correlation becomes increasingly important. This is

I ---Cl

E(au

)

SCF

PHYSICS

LETTERS

1 May 1976

due partly figuration, tion to the Finally,

to the incorrect behavior of the SCF conwhich does not allow for proper dissociaatomic limit Mg (3P) t Hi2S). we see that our computed B’ 2 Zf potential curve shows the characteristics described in ref. [l] of being broad with a minimum near 4.9 au. It also appears to dissociate to the same atomic limit as the A 211 state, indicating that the arguments of Balfour and Cartwright [l] for this state are correct. An analysis of our 2 xi CI wavefunctions shows some interesting features regarding the R dependence of the configurations for the X and B’ states. Table 3 gives a list of fifteen configurations found to be important for both states. The CI coefficients of these configurations are given near re for the X and B’ states, and also at 6.25 au. The SCF configuration 4a250 is dominant for the X state, and the main contributor for the B’ state corresponds to the 4050~ configuration. It should be noted, however, that the B’ state has several other important configurations, which change in importance with R. This can be seen more clearly in table 4, where we have displayed the relative distribution of these fifteen configurations over the eight calculated points. Three things can be learned from this display. First, the X state is well represented by the fiist configuration until 4.30 au, then other configurations begin to become important. Secondly, the B’ state is not well represented by a single configuration description at any value of R. Finally, and most importantly, the X and B’ states have several important

configurations

4.430,4X40,

in common

at the points

a:ld 5.250 au, but not at other values

of R. Table 2 CI energies for X * TZ+using threshold (au) R

E

Threshold

2.250

-200.0985

222

2x

2.750

-200.17749

175

5x10”

3.271

-200.295 12 -200.18856 -200.17015 -200.15075 -200.15346

234 2% 198 247 241

2x 10-G 1 x 10-h 5x104 3x loa 2 x 10-e

-200.14722

218

1x10”

3.750 4-430 4.840

Fig. 1. Calculated potential curves for MgH. The full lxlrves refer to the CI results; the dashed curves refer to the SCF resuits, and the dotted curve refers to results obtained by the threshold CI method.

N 3)

5.250 6.250

1

10-e

a) N is the number of confiiurations resulting from the use

of the threshold.

507

Volume 3?, number 3

.I

PHYSICS

LEl$ZRS

I May 1976

‘_

: _-

:

Table 3 Ci cmfficients

OF important Configuration

1

CHEhkAL -_

:

cotigqrations

for both the Xix+ R=

3.271

0.976787

4&q

0.110661

mid B’*Z+

states at three values of R
R = 4.840 0.899700

0.954763

-0.351984

0.119453

2

40502

0.059244 -0.677042

3

4a2 6c

-fJ.O11548 0268246

-0.039264 -0.113737

0.003602 -0.000588

4

-0.027536 0.352843

-0.072299 -0.264153

0.005309 -0.031970

5

0.001110 -0.004327

-0.013209 -0.038179

-0.144532

0.246443 0.756151

0.015509

405a60

(1) b)

-0.0237 19 0.129634

-0.057529 -0.113005

-0.00899 1 -0.C124305

7

4u507u

(1)

-0.036739 0.193515

-0.122328 -0.169461

0.025 097 .-0.144814

-0.003783 -0.013649

0.050166 -0.4ogoo4

8

4u5080

(1)

0.007028 -0.030273

9

4~506~

(2)

0.036264 -0.163443

0.093916 0.108873

-0.021047 0.011614

10

4a5o7o (2)

0.046442 -0.274388

0.162411 0.310501

0.033185 0.104665

11

4oSfJ8a (2)

-0.009549 0.005877

0.015546 0.034961

-0.074342 0.571792

12

507u*

-0.064615 -0.018936

-0.103452 0.057990

-0.003064 0.004908

13

5a8u2

-0.010440

-0.007

287

4u2G

-0.043581 0.161295

-0.07747 -0.094729

15

502n”

-0.021400 0.028955

-0.040090 -0.030515

-0.132831 -0.002727

0.005650

I4

X=x* _B’ 2 x+

0.075262 -0.62829 0

6

-0.001942

a)

1

0.018629 0.012302 -0.119575 -0.038644

a) Upper value X ‘C* stare, lower value B’ ‘z+ stare. b) These configurations have two spin functions.

4. Discussion

calculation, and for the X state, are similar to the SCF results.of Cade and Huo [3] . Comparing our Ci

The accuracy of our CI results can be tested further by calculating spectroscopic constants fro-m our potential curves. Dunham a&lyses were therefore caked out for the X afid B’2Z’, and A 2ri theoreti&l potentials. The. results of these analyses are given in tibk 5 along with‘observed values: We note briefly &t&e SCF rtisults are tj&a.l for this type-of -. .g)g : : _----

spectroscopic constants with the observed values shows very good agreement for the X, A, and B’ states. The experimental spectroscopic constants in

I; .

:,

table 5 for the B’ state and Cartwright fined their data of ref. puted potential curves Balfkr

are the unpublished values of [lo] , who have recently re[l] for the B’ state. Our comfor these states appear to rep;

Volume 39, number 3

CH&lI&L

PHYSICS LEITERS

lhfayl976

..

,-

Table 4 Distribution of important ~onfiiuration:, as a function of R (ati) for the X * Zc and .B’ z Z+ states :

R

ia)

2.250

2.750

3.27 1

3.7.5(?

4.430

4.840

5.250

6.250

x

X

XB

XBB B B

XE XB

X B

B B B

XB XB

XBa) B

B B

B B

B B B B

B B B B

2 3 4 ; 7 8 9 10 11 12 13 14

B

XB B B

B B

B

B

XB

XB XB

B B

B B

B

B

B B

B B

B

B

.B

B

XB

XB

B B

XB X B

B

B

B

B

B

X B

B

15

X

X

X

X

a) Index correspondsto the configurationsgiven in table 3. b) The letters X and B denote the confiiurations which have CI coefficients greater in magnitude than 0.1 for the X *Z’ and B’ *Z+ states, respectively.

Table 5 Spectroscopic constants for MgH (in cm-‘)

=e X*C+ SCF CI

0.0 0.0

expt . a)

A*& SCF CI expt. a) B’*Z+ CI expt. b) a) Ref. 171.

0.0

20817 19375 19278

21968 22410

Be

weXe

3.2675 3.2872 3.2693

1612.5 1484.6 1497.0

5.8261 5.7564 5.818

24.690

3.1613 3.2199 3.1729

1735.2 1571.8 1598

6.2240 5.9992 6.178

22.101 33.930 31.9

0.08644 0.14058 0.1883

829.83 828.4

25544 2.585

7.1568 11.8

0.02454

4.9340

4.885

29.930 32

0.10186 0.18107

0.1668

b, Ref. [IO].

resent the experimental curves quite well. We also find that the new B’ state crosses the A “II state at about 4.1 au, which would explain the rotational perturbations observed in the A-X system [2] ; and that the B’ and A states appear to dissociate to

the same Mg(3P) f H(%) atomic limit, in agreement with the conclusions of ref. [I ] . From an analysis of our CI wavefunctions, we find that the X and B’ states have important configurations in common only near the minimum of the B’ state, indicating that

: -Vol”nie-39, nu;nbkr 3 ,I CHEMiCALPHYSIdS LETTERS -_ ..:. .. ~o.transition moment caIc&tion might be pe&ed in Prance-&@bec for a grant to-undertake this region of RI This behavior has be&r observed in culations at CE.C_AM, the calculations on the A J2;+-X lx* transitions in

.L,ii 183 and NaH,[9j,

piainthe large discrepancy between-the number of B’-_X bands observed, and the number predicted by the Franck-Condon factors derived from the exper- imental RKR curves [IO]. We plan to return to this

point in further work on this molecule. As a final remark, we add that treating MgH as 2 three valence electron problem‘has produced good agreement with available.experimkntaI data.

Acknowledgement We wish to thank Professor CM Moser for the use facilities

at the Centre

Europeen de We also thank Dr. P.S. Bagus for suggesting the use of his method for MgH, and to Dr. W J. Balfour for communicating his B’ state data prior to publication. Finally, A.D.B. would like to thank ia Cooperation

Calcul Atomique et Moleculaire, Orsay, France.

510

these c&

which were treated as two va-

lence electron problems-by Hinze and co-workers. A transition moment variation such as this may ex-

of the computing

1 May.1976

References [l] WJ. Balfour and ti.M. Cartwright, Chem. Phys. Letters 32 (1975) 82. [Z] WJ. Balfour, Astrophys. J. 162 (1970) 1031. [3] P.E. Cade and W.hI, Huo, J. Chem. Phys. 47 (1967) 649. [4] A.C.H. &an and E.R_ Dsvidson?S. Chem. Phys. 52 (1970) 4108. [S] P.S. Bagus, C.M. Moser, P. Goethais and G. Verhaegen, J. Chem. Phys. 58 (1973) 1886. [6] A.D. McLean, Proceedings of the Conference on Potential Energy Surfaces in Chemistry, RA18, Librarian, IBM Research Laboratory, San Jose, California; P.S. Bagus. Proceedings of the Seminar on Selected Topics in hfolecuiar Physics, IBhl Germany, Luhwigsburg, Germany. j7 J B. Rosen, Spectroscopic data related to diatomic molecules (Pergamon, Oxford, 1970). [8] K.K. Docken and J. Hinze, J. Chem. Phys. 57 (1972) 4922,4936.

[9] ES. Sachs, J. Hinze and N-H. Sabelli, J. Chem. Phys. 62 (1975) 3367,3384. [ 101 WJ. Balfour and H.M. Cartwrignt,

to be published.