Spectroscopic constants and potential energy curves of GeF+

5 May 1995

CHEMICAL PHYSICS LETTERS

ELSEVIER

Chemical Physics Letters 237 (1995) 7-13

Spectroscopic constants and potential energy curves of GeF + Hua Xu, K. Balasubramanian Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA

Received 5 December 1994; in final form 20 February 1995

Abstract

Spectroscopic constants and potential energy curves of 27 electronic states of GeF + are computed using the complete active space self-consistent field (CASSCF) followed by first- and second-order configuration interaction (FOCI, SOCI) methods that included up to 1.6 million configurations. Our computed spectroscopic constants of the 1,~ + electronic state fit well with the experimentally observed X ground state. Other yet to be observed properties of several excited electronic states are reported.

I. Introduction

The GeF ÷ ion is a potentially important species in plasma etching and sputtering applications. Fluorine-containing discharge plasmas reacting with Si and Ge produce in large abundance species such as SiF ÷ and GeF ÷. Yet the spectroscopic characterization of GeF + is limited only to the ground state of the ion. In spite of its industrial importance, until 1989 the GeF ÷ ion was spectroscopically unknown. Akiyama et al. [1] observed the GeF ÷ in a hollow cathode discharge of GeF4 mixed with He. They obtained the first high-resolution infrared laser diode spectrum of GeF ÷. The spectroscopic constants of the ground state were derived through the analysis of the absorption lines belonging to the fundamental band which were identified for five Ge isotopes. In a subsequent study on GeF ÷, Tanaka et al. [2] obtained the millimeter wave spectrum of GeF ÷ in the ground vibrational state for four isotopic species. In this study the effect of magnetic field was used to differentiate the absorption lines of the ions and neutral species. The Dunham coefficients for the ground

state were determined using the millimeter wave spectrum and the previous infrared laser diode spectrum. There are several experimental studies [3-11] on the related group I V - V I I diatomic positive ion exhibiting closed shell ground states such as SiCI ÷ [9], SiF ÷ [4], CC1 ÷ [7], CF ÷ [3,5,6], and so o.n. O n e o f the most recent studies is due to Sumiyoshi et al. [9] who have obtained the infrared diode laser spectrum of SiCI ÷. It appears that these species may not possess low-energy highly bound excited states above the ground state. Consequently, it is believed that techniques such as laser-induced fluorescence (LIF) may not be useful in the characterization of the electronic states of these species, and thus it is difficult to obtain spectroscopic information on the excited states. Tsuji et al. [10] have reported the first emission spectrum SiCI + attributed to the a 3 ] - I X 1~+ system. Nishimura et al. [11] have carried out ab initio computations on SiCI ÷ which have revealed that the a 3 H state is weakly bound while the A t I I state is repulsive. There are also related ab initio studies on SiF ÷ [12,13].

0009-2614/95f$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0009-2614(95)00291-X

8

H. Xu, K. Balasubramanian / Chemical Physics Letters 237 (1995) 7-13

Table 1 Atomic energy separations of GeF + obtained from asymptotic molecular energy separations at the dissociation limit Molecular states

Atomic states

1]~-(2), 1~-, 1ii(2), 1A 3~ +(2), 3~-, 3ii(2), 3A 3]~+, 3]~-(2), 3ii(2), 3A 5]~+, 5E-(2), Sii(2), 5A 1]~+, l[I 3]~+, 3H 1]~+ (2), I]~-, 1[](3), 1A(2)' lqb 3]~+(2), 1]~-, 3i-1(3)' 3A(2) ' 3qb

Ge ÷ 2p 4p (4s14p2) 2S (4s25s 1) 2D (4s14p2)

Energy (cm 1) F 2p 2p 2p Zp

FOCI 0 48173 64696.5 65267.2

SOCI 0 49052

exp. a 0 51531.4 61224 63934

a From Ref. [17].

The above survey of experimental and theoretical studies on I V - V I positive ions suggest the need for accurate computational studies on the potential energy curves and spectroscopic properties of G e F ÷. In this study we carry out relativistic complete active space m u l t i - c o n f i g u r a t i o n self-consistent field ( C A S - M C S C F ) followed by first- and second-order configuration interaction (FOCI, SOCI) computations. Potential energy curves and spectroscopic constants of several electronic states of G e F ÷ are obtained.

2. Method of calculations Relativistic effective core potentials (RECPs) which included the outer 4sZ4p l and 2s22p 5 shells of Ge + and F, respectively, in the valence space taken from Ref. [14] were employed in this investigation. The general method of C A S S C F (complete active space self-consistent field) followed by F O C I / S O C I (first-order and second-order configuration interaction) calculations has been described in a previous w o r k of our group on GeBr [15]. In addition to the SOCI, the effect of unlinked quadruple clusters was included through a multi-reference Davidson correction. The resulting value, which is a full-CI estimate, is labelled SOCI + Q result. The valence Gaussian basis set of the ( 3 s 3 p l d ) type [14] was used for Ge, while for the F atom we contracted the (4s4p) basis set [14] to (3s3p) and augmented it with two sets of d functions (oq = 0.45 and 0.1125), which resulted in the F ( 4 s 4 p 2 d / 3 s 3 p 2 d ) basis set. For the 12~+ and 31-1 states more accurate C A S S C F / F O C I / S O C I computations were made using the F ( 5 s 5 p 2 d / 4 s 4 p 2 d ) by augmenting the smaller basis set with diffuse s and p functions with a S =

0.1171 and OZp= 0.0816. Likewise, a comparable ( 4 s 4 p l d ) extended basis set on Ge ÷ was also used. W e computed the properties of two electronic states of GeF ÷ using the RECPs which retained all but 14 outer electrons of Ge in the core. That is, valence space composed of 3dl°4s24p 2 for Ge using different RECPs were considered. These RECPs were used together with G e ( 4 p 4 p 5 d / 4 s 4 p 3 d ) basis set and F ( 5 s 5 p 2 d / 4 s 4 p 2 d ) basis set. W e found that the spectroscopic properties were nearly the same as the ones obtained using the RECPs which retained all but four valence electrons on Ge in the core. Of course inclusion of more electrons in the valence space leads to greater magnitude of computations. All ten active electrons of G e F + were distributed in all possible ways in the active space consisting of four al, two b 2 and two b t orbitals. W e carried out separate C A S S C F / F O C I / S O C I calculations for each electronic state of different spin multiplicity and spatial symmetry in the C2v group. The C A S S C F calculation included up to 384 configuration spin functions (CSFs) while the FOCI and SOCI included up to 39 thousand and 1.6 million CSFs, respectively. All calculations were made using one of the author's [16] modified version of A L C H E M Y II codes 1 which included RECPs.

3. Results and discussions Table 1 shows the possible low-lying electronic states of G e F + and their dissociation limits. In the same table we have shown our computed FOCI and

1 The major authors of ALCHEMY II are B. Lengsfield, B. Liu and M. Yoshimire.

H. Xu, K. Balasubramanian

o.s? 0.4 ;,

i

/ Chemical Physics Letters 237 (1995) 7-13 0.7

Gel:'

0.6

;I\~,~"'nil) (i~>

o.3 i

9

0 ll=

0.5

;o, i

ii "r i,m

/

0.4

! 0,0

\'~/

~ - , ~ L

1.0

L ~ . L

2.0

•

~

L

~

L

3.0 4,0 R(Angstrom)

~ _ L A _ ~ _ _ ~

5.0

0.3 1.0

J

6.0

Fig. 1. Potential energy curves of GeF+ arising from Ge ÷ (2p)+ F(2p).

SOCI energy separations at the asymptotic limit together with the experimental atomic energy separations [17]. In general, the SOCI data should be considered as more accurate as these included the effects o f higher-order electron correlation. Comparison of our results at the asymptotic limit with the experimental atomic energy separations show that our basis set and level o f treatment of electron correlation effects are reasonable enough for the computation o f energy separations. Even at the FOCI level 2 p _ 4 p , 4p_2 S and 2 S - 2 D energy separations are computed with reasonable accuracies as seen from Table 1. Fig. 1 shows the computed C A S S C F / F O C I potential energy curves of all electronic states o f G e F + dissociating into the 2p ground state of the Ge + ion and the 2p ground state o f the F atom. The grid for the plot varied from 0.05 to 0.1 A for shorter intero nuclear distances or near minima. For r > 3.0 A, the grid varied in steps of 1.0 ~,. A s seen from Fig. 1, 1 + 3 1 the ~ , H and I I states exhibit minima while the a ~ +, 3y,- and 3A states exhibit shallower potential wells. Figs. 2 and 3 show the potential energy curves of the higher-lying states of G e F ÷ which dissociate

2.0

3.0

4.0

5.0

6.0

R(Angstrom) Fig. 2. Potential energy curves of GeF + arising from Ge ÷ (4p)+ F( 2 p).

0.7

'~~''~e1 0.6

z

Ge+(2D)+F(2P)

I110.5 ~ 0.4

~

1.0

~

2.0

,

~

~

i

3.0

, ~

,

~

I

~

4.0

,

,

,

I

5.0

,

~

~

,

I

6.0

R(Angstrom) Fig. 3. Potential energy curves of GeF + arising from Oe + (2D)+ F(2p).

10

H. Xu, K. Balasubramanian / Chemical Physics Letters 237 (1995) 7-13

Table 2 Computed FOCI spectroscopic properties of GeF + State

r e (A) FOCI

1E + 3II 3~+ 3A 1E 1A 3E111 11-I(II) 3II(III)

T~ (cm 1) exp.

1.666 1,700 2,167 2.310 2.338 2.344 2.341 1.785 2.102 2.031

1.665 a

toe (cm-1)

De (eV)

FOCI

exp.

FOCI

exp.

FOCI

0 39330 48166 48918 49158 49336 49379 54759 51656 73130

0

778 649 116 201 259 254 252

815 a 663 b

6.48 1.61 0.39 0.30 0.27 0.24 0.24

a Experimental results are for GeF + from Ref. [1]. b Experimental result is for GaF from Ref. [18].

Table 2 s h o w s the c o m p u t e d F O C I spectroscopic constants of the electronic states of G e F +. In c o m paring the results of the F O C I properties for the ground state and the e x p e r i m e n t a l data reported by A k i y a m a et al. [1], w e note that the F O C I b o n d length of the I E + ground state of G e + - F (1.666 ,~) is in g o o d a g r e e m e n t with the e x p e r i m e n t a l data o f 1.665 A. T h e F O C I toe v a l u e of the 1~+ ground state was found to be 778 c m - 1 w h i c h is in reasonable a g r e e m e n t w i t h the experimental toe v a l u e o f 816 c m -1. The smaller F O C I toe is consistent w i t h a p r e v i o u s c o m p u t a t i o n on G e F for w h i c h a similar level of theory y i e l d e d a w e that is 5 % less than the experimental result. T h e difference could be attributed to ECPs, basis set and the level of treatment. For the first excited 3I-I state, in T a b l e 2, w e list the e x p e r i m e n t a l data w h i c h c o m e s f r o m the iso-electronic G a F m o l e c u l e [18]. A s seen f r o m T a b l e 2, our

into the excited states o f the G e + ion and the ground state o f the F atom. A s seen f r o m Figs. 1 - 3 , the general trend is that m o s t excited electronic states exhibit m i n i m a w i t h the e x c e p t i o n of the 5H(II), 3 ~ + (II), 1A(II), 3A(II) and 3 ~ +(III) states w h i c h are repulsive. A s seen f r o m Fig. 1 and T a b l e 2, the ground state o f G e F + is a X 1Z+ state with r e ( G e - F ) -- 1.666 ,~ at the F O C I level. This state arises from the 10.220.230.21'rt 4 electronic configuration. If one of the 30" electrons is excited into the 2"rr orbital, 31-I (the first excited state) and ~l-I arising f r o m the 10"220"230"11"rra2a'r ~ electronic c o n f i g u r a t i o n w e r e formed. T h e other possibility is to r e m o v e an electron f r o m the la'r orbital o f the X aE+ ground state and p r o m o t e it to the 2rr orbital. T h i s yielded the 10.220.230"21"rr32~ 1 electronic c o n f i g u r a t i o n w h i c h results in the 3 ~ + , 3 ~ - , 3A, 1E - and 1A states.

Table 3 Computed SOCI spectroscopic properties of GeF + State

SOCI a x~+ 3R

Te (cm 1)

r e (,~) 1.669 1.711 (1.705) b

exp. 1.665

we (cm- l)

De (eV)

SOCI a

exp.

SOCI a

exp.

SOCI a

0 41020 (40688) b 39824 ~ (39705) c

0

770 639

815

5.64 0.56

exp.

The SOCI properties were computed using Ge(4s4pld) and F(5s5p2d/4s4p2d) basis sets except the De. b Numbers in parentheses are SOCI + Q values. c The Tc was obtained using more accurate 14-electron RECPs for Ge together with Ge(4s4p5d/4s4p3d) and F(5s5p2d/4s4p2d) basis sets.

H. Xu, K. Balasubramanian / Chemical Physics Letters 237 (1995) 7-13

computed properties of the excited 317 state are in reasonable agreement with analogous GaF. Table 3 compares the results of the FOCI computations with more accurate SOCI computations which included second-order correlation effects. As seen from Table 3, the 3I-I excited state is bound by 0.56 eV at the SOCI level and exhibits a good potential well characterized by r e = 1.711 .~ and toe = 639 cm-1. At the present time there are no experimental studies on the excited electronic states of GeF ÷. However, Tsuji et al. [10] have obtained the spectroscopic properties of the related SiCI ÷ ion in the 3I-I excited state through the analysis of the emission spectrum of SiCI +. The vibrational assignments yield the Te values of 317~- and 3II 1 states as 31836 and 31721 cm-1, respectively. Of course, the compounds formed with the second-row atoms of the periodic tables are likely to be somewhat different from the heavier species. For example, the Te of the 11-I state of GeO is 37766 cm-1 compared to the corresponding state of GeS which has the T~ value of 32889 cm -1 [18]. Thus, the T~ value of GeF ÷ is likely to be = 5000 cm-1 larger than the Te value of GeCI +. Since GeC1 ÷ and SiCI ÷ are expected to be similar, we correct the experimental Te of the 3II state of GeF ÷. This value is in very good agreement with our computed FOCI T~ of 39330 c m - 1. We note that the higher-order SOCI and SOCI + Q results are 41020 and 40668 cm -1, respectively. Karua and Grein [13] have obtained the T~ of the 31/ state of analogous SiF ÷ as 38715 cm -1 at the MRDCI level of theory. Consequently, we conclude that our FOCI results should have reasonable accuracies for the low-lying electronic states of GeF ÷. Our FOCI results should be 1000-4000 cm -1 higher than the true T~ values. The T~ of the 31/state relative to X 1E+ was also computed using the C A S S C F / F O C I / S O C I techniques in conjunction with 14-electron RECPs which retained all but 3dl°4s24p 2 shells of Ge in the core. These computations must be considered more accurate as they included more electrons in the computations. The Te value of the 317 state was computed as 39824 and 39705 cm-1, at the SOCI and SOCI + Q levels of theory. These values fall within 1200 cm -1 of the results obtained using the four-electron RECPs described before. However, the T~ obtained using 14-electron RECPs (39700 cm -1) should be closer to the experiment.

11

As seen from Table 3, our computations predict the Al17 state of GeF + to be above a 3 1 / with a FOCI T~ of 54759 cm-1. We expect this value to be higher by the same factor as the 317 state. Thus, the experimental Te of the 1H state should be = 52000 cm -1. This state has not yet been observed experimentally. The transition from X 1~+ to 11-I is dipole-allowed and should thus be strong. The other electronic transition of interest is from X 1E+ to 31-[(1I). At the FOCI level this is predicted to occur at 51656 cm-1 but we expect this value to be at least 15% higher than the true value. As we discussed before, our computations place the 31/ state of GeF ÷ considerably higher. Therefore, as seen from Fig. 1, the dissociation asymptote may be computed somewhat higher. Our FOCI D e value of 6.48 eV is thus higher than the D e of GaF which is established as 5.98 eV [18]. However, the SOCI method in the smaller basis set yields a lower D e of 5.64 eV. The SOCI method in conjunction with the l a r g e r b a s i s set [ G e ( 4 s 4 p l d ) , F(5s5p2d/4s4p2d)] used here resulted in a D e of 5.58 eV. The experimental dissociation energy of GeF ÷ can be obtained from the experimental De(GeF) [18], the ionization potential of GeF [18], and the atomic ionization potential of Ge [17]. As seen from Ref. [18], there are two ionization potentials for GeF. An approximate value of 7.46 eV was obtained from fitting the energies of B 2~+ and D 2E+ states of GeF [19]. Since only the first two members of an s series were used, this value was considered as an approximate estimate of the IP of GeF by Martin and Merer [19]. Harland et al. [20]

Table 4 Contributions of the electronic configurations in the FOCI wavefunctions State

G (-~)

Electronic configurations

1~+ 317 3E+

1.666 1.700 2.167 2.341 2.310 2.338 2.344 1.785 2,102 2.031

let 22o'23er 2l'n'4 lo'22 o'23o'1 l'rr 42"r¢1 lcr22~rZ3o'21~a2~r 1 lcr 22 o'23or 2l'rt 32"rr1 1o"22 o"23o-21,'rr32'rr 1 lo'22 o"z 3o'2 l'n'32'rr I ltr 22 o-23tr 2 l'rr 32'rt I 1er 22 o'23er 1l'n'427r 1 lo'22 ar 23o'24o" 11"r¢3 lo'22o'13o'21~42"rr 1

3~3A 1~1A 117 31I(11) 3II(III)

(95.2%) (94.0%) (92.5%) (93.6%) (93.3%) (93.4%) (93.4%) (91.9%) (78.3%) (74.5%)

12

H. Xu, K. Balasubramanian / Chemical Physics Letters 237 (1995) 7-13

Table 5 Mulliken populations of the low-lying electronic states of GeF+ State l~ + 3II 3~ + 3~-

3A l~1A x17 3II(II) 317(1II)

Gross population Ge

F

Ge(s)

Ge(p)

Ge(d)

F(s)

F(p)

F(d)

2.46 2.62 3.07 3.07 3.07 3.08 3.07 2.94 3.13 2.83

7.54 7.38 6.93 6.93 6.93 6.92 6.93 7.06 6.87 7.17

1.87 1.21 1.93 1.93 1.93 1.93 1.93 1.71 1.93 1.26

0.55 1.35 1.12 1.12 1.11 1.14 1.13 1.20 1.16 1.52

0.04 0.07 0.02 0.02 0.02 0.01 0.01 0.03 0.04 0.05

2.02 2.01 1.99 1.99 1.99 1.99 2.00 1.99 1.95 1.98

5.47 5.31 4.92 4.93 4.93 4.89 4.89 5.03 4.90 5.16

0,05 0.06 0,02 0.01 0.01 0.05 0.04 0.04 0.02 0.03

have deduced a value of 7.2 eV from the electron impact measurements. The D e of the neutral G e F obtained from therochemical mass spectrometry is somewhat more certain to be 5.00 eV. The experimental D e of G e F ÷ can be deduced from these values using the formula

atom. The bonding is considerably ionic, consistent with a large D e of 5.58 eV. The 3I-I state arises from the 2P(4s24p~) state of the Ge ÷ ion and thus has a different Ge Mulliken population compared to the ground state. There is less charge transfer in the 31I state compared to the X t ~ + ground state.

De(GeF + ) = IP(Ge) - IP(GeF) + De(GeF ) . Using the well-known IP(Ge) value of 7.88 eV, we obtain the experimental De(GeF +) as 5.42 eV using the IP(GeF) from the approximate Rydberg limit and 5.68 eV using the IP(GeF) = 7.2 eV from electron impact measurements. Our SOCI D e of 5.58 eV in the larger basis set is between these two experimentally deduced values. Karna and Grein [13] have computed the D e o f the related SiF ÷ ion to be 6.60 eV at the M R D C I level of theory. Table 4 shows the weights of the leading configurations contributing to the various electronic states of G e F +. As seen from Table 4, the X 12~+, 31-i, 3E+ ' 3~, 1ii , ~ and ~A states are well represented by their leading configurations which contribute more than 80%. The 3A, 3II(II) and 3II(III) state are somewhat more complex in that other and Rydberg configurations contribute to this state. Table 5 shows the Mulliken population analyses o f some low-lying electronic states of G e F + . As seen from this table, the total Ge populations in all electronic states of G e F + are below 3.13, while the total F populations are above 6.87. The ~E+ ground state of G e F ÷ is composed of 4s1"874p°553d°°4 which deviates considerably from the 4s24p ~ character of the ground state o f the Ge + ion. There is an obvious transfer of electronic charge density from Ge to the F

4. Conclusion The C A S S C F / F O C I / S O C I methods of calculations which included up to 1.6 million configurations were employed for the low-lying electronic states of G e F + dissociating into the ground state of Ge + and F and two other excited states of Ge +. Spectroscopic constants and potential energy curves were computed. Our computed r e, foe and Te values of the X ~ ÷ state are in good agreement with experiment. Our computed properties of the 31-I excited state of G e F ÷ were in reasonable accord with the anticipated values derived from SiC1 + for which this state has been observed. Properties of several other states were predicted that are yet to be observed. The G e - F bondings were analyzed through the leading configurations and Mulliken populations.

Acknowledgements This research was supported by the US National Science Foundation under Grant CHM 9417459. The authors thank Dr. Dingguo Dai for help in computations.

H. Xu, K. Balasubramanian / Chemical Physics Letters 237 (1995) 7-13

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