PHYSICAL REVIE%' A VOLUME 46, NUMBER 7 1 OCTOBER 1992

Many-body-perturbation-theory calculations of the microwave and vibrational constants of CaC

Marcos A. Castro and Sylvio CanutoDepartamento de Fisica, Uniuersidade Federal de Pernambuco, 50739 Recife, Pernambuco, Brazil

Florian Muller-PlatheLaboratorium fii r Physikalische Ch-ernie, Eidgenossische Technische Hochschule Zentrum, CH 809-2 Zii rich, Switzerland

(Received 19 November 1991;revised manuscript received 2 March 1992)

%e use fourth-order many-body perturbation theory to calculate the rotational and vibrational con-stants of CaC. These spectroscopic constants should be useful in the possible laboratory or astronomicalobservation of this metal carbide.

PACS number(s): 31.20.Di, 33.20.Bx, 95.85.Bh

Microwave spectroscopy is an important tool in theidentification of new molecular species in both laboratoryand space. The search for unknown species usually re-quires some knowledge of the spectroscopic constants asproper identification from measured frequency alone isvery diScult. Accurate theoretical calculations of molec-ular spectroscopic constants is then of considerable in-terest to aid in the search and identification of newmolecular species. HCN [1] is a well-known examplewhere theory has greatly aided in the identification of in-terstellar molecules. Recently SiC, the first metal car-bide, was detected [2] both in laboratory and in space,this observation relied on a preceding calculation [3].Asdiatomic metal carbides have been diScult to detect inthe laboratory, a few have been sought in space. Afterthe recent discovery of SiC it is now worthwhile to con-sider some other diatomic carbides. Because of its ele-mental cosmic abundance and large dipole moment, oneof the most promising metal carbides is CaC. The pur-pose of this Brief Report is then to communicate the re-sults of a many-body-perturbation-theory (MBPT) calcu-lation of the spectroscopic constants of CaC. Other dia-tomic molecules such as MgC [4] and A1C [5] have re-cently been the subject of theoretical studies. In particu-lar A1C, trapped in an inert matrix, was afterwardrecorded by electron spin resonance (ESR) [6].

For the ground state of CaC [4] we consider four possi-ble candidates. Three are derived from the vr and 0 openshells: 7o 3sr 8cr ( X ), 7o 3n.go 9cr( II), and7cr 3m. 8o ( II), and the fourth is the less probableclosed-shell 'X+ state. From the ground state of theseparate atoms it is inferred that the ground state of CaCshould be a triplet state. To distinguish between the twoII states we shall term the first as II(1) and the latterII(2). For the triplet states the calculations are based on

a spin-unrestricted Hartree-Fock (UHF) reference wavefunction. Correlation effects are obtained via MBPT withinclusion of all single, double, triple, and quadruple sub-stitutions that contribute up to fourth order [MBPT(4)]

The basis sets are derived from the suggestion of Dun-ning [8] and Wachters [9] with the addition of diffuse sand p and optimized five-component d-type polarization

-714.50

-714.52—

II+ -71454—

C

714.56

-714.58—

-714.601.90 2.40 2.90

Distance {A}

FIG. 1. Calculated potential-energy curves of CaC.

functions [10]. The final set is C: (10s6p21 ~6s4p2d ) andCa: (14s 1 lp2d ~8s6p2d). All calculations have beenmade with the GAUSSIAN-86 program [11].

The self-consistent field (SCF) calculations give dipolemoments of 5.6, 3.7, 3.8, and 8.8 for the states 'X+, XII(l), and II(2), respectively. The spectroscopic con-

stants and the internuclear distances for the four statesconsidered were obtained by numerical fit of the calculat-ed potential-energy curves. The resulting curves obtainedat the MBPT(4) level is shown in Fig. 1. The groundstate is identified with the X state. This X state dis-sociates into the ground-state products Ca('S)+C( P).The corresponding singlet state cannot be formed fromthe ground-state atoms. Interestingly, the II(1) crosseswith the 'X+ state near its equilibrium position. Also,electronic transition from the X state, in the Franck-Condon region, to the II(1) state populates vibrationallevels very close to the dissociation limit of II(1}.Theseaspects point to interesting photophysical effects in this

46 4415 1992 The American Physical Society

4416 BRIEF REPORTS 46

TABLE I. Spectroscopic constants of CaC calculated from many-body perturbation theory.

State Method R (A) co, (cm ') B, (cm ') cox, (cm ') a, (10 ' cm ') D6 (10 ' cm ')

MBPT(2) 2.305MBPT(3) 2.342

DQ-MBPT{4) 2.359MBPT(4) 2.373

599.6565.6540.5534.2

0.34380.33300.32840.3243

5.95.25.72.7

2.62.52.71.9

4.54.64.84.8

3g MBPT(2) 2.324MBPT(3) 2.337

DQ-MBPT{4) 2.353MBPT(4) 2.346

476.1

476.6454.6504.7

0.33840.33450.32980.3318

5.1

7.26.26.4

4.54.44.53.3

6.86.66.95.7

H(1) MBPT(2) 2.590MBPT(3) 2.613

DQ-MBPT(4) 2.629MBPT(4) 2.635

437.0430.2409.3425.7

0.27240.26770.26420.2631

—47.1—33.6—24.3—14.6

—5.1—7.4—8.2

8.9

4.24.1

4.44.0

H(2) MBPT(2) 2.124MBPT(3) 2.145

DQ-MBPT(4) 2.155MBPT(4) 2.166

737.4671.2634.6626.5

0.40510.39720.39350.3895

10.16.55.87.6

2.22.52.93.4

4.95.66.1

6.0

region. At the MBPT(4) level the 'X+, II(1), and II(2)states are calculated to lie about 10000, 10600, and12 400 cm ', respectively.

The calculated spectroscopic constants are shown inTable I. Results obtained from intermediate theoreticallevels such as MBPT(2), MBPT(3), doublequadruple —many-body-perturbation-theory DQ-MBPT(4), and MBPT(4) are displayed to show the convergenceof the MBPT results. DQ-MBPT(4) signifies that thecontributions of single and triple substitutions, that firstappear in fourth order, are not included. DQ-MBPT(4)corresponds to a truncated coupled-cluster iteration [12]and for that reason it is included. As Table I shows theMBPT series converges rapidly, particularly for the cal-culated ground state X . The spin contamination at theSCF level is very mild for this state ((S )UH„=2.04) andbecomes negligible after correlation corrections. It is infact known that electron correlation decreases the spincontamination of UHF reference states [13]. Also it israther well demonstrated [14] that large spin contamina-tion undermines the rate of convergence of the MBPTseries, a problem not found in this present study.

The best calculated value for the interatomic distanceof CaC is 2.35 A. The metallic carbides have large bond

distance compared to ordinary diatomic molecules. Stillthe CaC radical has the largest among the calculated dia-tomic metal carbides. For comparison, the calculatedground-state interatomic distances are 2.09 A for MgC[4], 1.98 A for A1C [5], and 1.72 A for SiC [2,3]. Thuscompared to MgC, CaC has a smaller rotational constantbut a larger dipole moment.

Summarizing, the ground state of CaC is calculated tobe the X state. To aid in the possible identification ofthis elusive metal carbide its spectroscopic constants havebeen calculated at the MBPT(4) level. The MBPT seriesis rapidly convergent and presents no serious problemsdue to the UHF nature of the reference state and predictsa rotational constant of B,=0.332 cm '. Rotationalconstants are given by the equilibrium internuclear dis-tance and this calculated value should be particularly ac-curate as in this region a single reference configuration isusually a good starting approximation for MBPT, as op-posed to describing bond stretching and bond breaking.The knowledge of this rotational constant increases thelikelihood that the millimeter-wave spectrum of free CaCwill be measured in the laboratory making possible a sen-sitive search is astronomical sources.

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[10]For C the basis is the original (9s5p ~5s3p ) Dunning's sug-

gestion augmented with one s-, one p-, and two d-typefunctions with exponents 0.05, 0.035, 0.164, and 0.671, re-spectively. For Ca the substrate is the (14s9p ~gs4p ) basisof Wachters augmented with two p-type and two d-typefunctions with exponents of 0.12, 0.05, 0.319, and 1.645,respectively.

BRIEF REPORTS

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