Computer simulation of the rotational structure of vibronic bands of CF

MOLECULAR PHYSICS, 1987, VOL. 62, NO. 1, 175-192

Computer simulation of the rotational structure of vibronic bands of CF~ and SiF + / ) 2A l--C2 Tz by S. M. M A S O N and R. P. T U C K E T T Department of Chemistry, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, England

(Received 14 April 1987, accepted 11 May 1987) A computer simulation of the rotational structure of vibronic bands of the recently discovered emission spectra in CF2 and SiF2 D2Al-(72T 2 (Molec. Phys., 60, 761, 771) is presented. The model allows for Coriolis splitting, spinorbit splitting and Jahn-Teller distortion in the (7 2T2 state, and can be applied to /~i-(7 vibronic bands of either ion which do not involve the Jahn-Teller active vibrations. In CF2 (7 there is no Jahn-Teller distortion, and a simulation of the 1~ band at 381 nm compares excellently with the experimental spectrum obtained at a low rotational temperature. Estimates of the two rotational constants are made from the C" and/~ state photoelectron bands of CF,, and the simulation then gives values for the Coriolis and spin-orbit splitting in CF2 (72T2 . In SiFt a simulation can only be made of the 0~ band at 551 nm because both v2 and v4 vibrations in (72T2 are Jahn-Teller active; the distortion is shown to be dynamic in nature. The simulation is not so satisfactory because estimates for the rotational constants are less accurate than in CF 2 and the Jahn-Teller effect in (7 2T2 means that more constants are needed to determine the rotational structure. The spin-orbit splitting in the (72T2 state of both ions is small and positive, and the Coriolis constant in CF~ has a value substantially reduced from its limiting value of + 1. The results are interpreted in terms of the molecular orbital diagram for CF4 and SiF4.

1.

Introduction

In two recent papers [1, 2], we have reported the observation of discrete electronic emission spectra of the tetrahedral ions C F 2 and SiF2 in the gas phase. A supersonic molecular beam of CF4 or SiF 4 , cooled to a low rotational temperature, is crossed at right angles with an ionizing electron beam, and fluorescence from the crossing region is dispersed in a monochromator. Since the electron impact ionization involves little transfer of rotational angular momentum, the parent molecular ions CF~" or SiFt- are produced at a low rotational temperature; hence, any vibronic bands due to CF,~ or SiF2 are observed at a low rotational temperature, and are substantially narrowed compared to the same band at r o o m temperature. In C F 2 [1], a careful study of the discrete band system between 360 and 4 2 0 n m showed that the observed vibronic bands are cooled to a low rotational temperature, and are due to transitions between two highly excited electronic states/) 2A 1 and ~ 2T2 , 25.1 and 21.7eV above the ground state of CF4. Bands are only observed in the totally symmetric vl ( C - F stretching) manifold, and an accurate value of v~ in both electronic states is obtained; the values compare excellently with lower resolution photoelectron (PE) data of C F , for ionization to the ~ a n d / 5 states [3, 4]. Since bands involving non-totally symmetric vibrations are not observed, both electronic states of C F 2 have To symmetry and there is no Jahn-Teller distortion in the lower

176

S.M. Mason and R. P. Tuckett

triply-degenerate (7 2T2 state. Spin-orbit splitting is resolved in the (7 state, and the relative intensities of the two spin-orbit components in a/3-(7 vibronic band suggest strongly that the spin-orbit constant is positive. We were not able fully to resolve rotational structure, but the best resolved band contour shows heads degraded to the blue, suggesting that B ' > B". In SiF2 [2], the s a m e / 3 2 A I - ( 7 2 T 2 electronic band system is observed between 530 and 600 nm. Now, bands involving v~, v~ and v~ are observed, showing that the (7 state is distorting from Td symmetry by dynamic Jahn-Teller distortion, almost certainly to C3v symmetry. Spin-orbit splitting is resolved in the origin band, but its sign cannot be determined unambiguously; its magnitude is quenched in bands involving the v~ and v~ Jahn-Teller vibrations. To understand the fine detail of these spectra, and in particular to characterize fully the Jahn-Teller effect in SiFt" (7 2T2, rotationally resolved spectra need to be obtained. Such experiments are planned (see w5). In anticipation of obtaining such spectra, we have developed a computer program to calculate the rotational structure of a 2A1-2T2 vibronic band of a tetrahedral molecule. This paper reports the results. The program can be applied to all vibronic bands of CF~- /3-(7 (where no Jahn-Teller effect is operative), but only to bands of SiF2 /3--(7 which do not involve v~ or v~. A simulation of the band contour can then be made at any resolution. In C F 2 , estimates of the two rotational constants, the spin-orbit and Coriolis constant in the (72T2 state, and the rotational temperature can be made. The agreement with experiment is then excellent. In part, this arises because approximate values for B' and B" can be obtained from an analysis of the/3 and (7 state PE band contours; only 3 constants therefore need to be guessed a priori. In SiF2 more constants have to be estimated a priori because of the Jahn-Teller effect in (7 2T2 , and the agreement is not so satisfactory. Section 2 describes an analysis of the (7 and/3 state PE bands of CF 4 which give first estimates for the C - F bond distance and hence rotational constants in CF2 (7 and /3, The same analysis and results for SiFt" are described briefly. Section 3 describes the rotational structure of a 2A1-2T2 transition in emission, and defines the spectroscopic constants which may be determined. Section 4 shows the results of simulations for both CF~- and SiF2. These results are discussed in w5 and some concluding comments made.

2.

Analysis of the photoelectron spectra of C F 4 and SiFt" : ionization to r z and/~ 2A l

In w3 we shall see that the main features of a CF~ vibronic band are determined by two rotational constants, the Coriolis splitting and spin-orbit constant in (7 2T2 , and the rotational temperature. If estimates of all five constants had to be made a priori, an accurate simulation might be possible even with incorrect constants, since changes in some of the constants (especially B" and the Coriolis constant) are highly correlated. Fortunately, it is possible to use the vibrational band intensities from photoelectron spectroscopy to calculate Ar for ionization of CF4 .~ to CF~ /3 and (7 (r = C - F bond distance); values for B' and B" respectively can then be obtained. Furthermore, these Ar values can be checked, since data available for the vibrational intensities of CF~ /3 --. (7 (table of [1]) can be used to calculate Ar for this electronic transition of the ion.

Rotational structure of CF~ and SiF~ D 2A1-C 2T2

177

Table 1. Experimental and calculated relative intensities for CF 4 )~(v = 0) ~ CF~ (~(v0. vl

Expt t

2.0

3"0

0

1.3 2-7 5.2 8.7 9.3 10 9-3 8.0 6-7 5.3

3-6 8.9 10 6-7 3.1 0-9 0.2 ----

0.3 1.8 4.8 8.2 10 9.3 6.8 4.1 2-0 0.8

1

2 3 4 5 6 7 8 9

~trial

3.2

3"4

4.0

0.2 1.1 3.3 6.6 9.3 10 8-6 6-1 3-6 1.7

0.1 0-7 2.2 5-0 8.0 10 10 8-2 6.6 3-3

-0-1 0.4 1-3 3.1 5.5 7.9 9.7 10 8.9

I" The intensities are the peak heights from figure 2(a) of [4] normalized to 10 at vt = 5.

The different methods of obtaining geometry changes upon ionization have been reviewed by Eland [5]. The simplest method assumes that the vertical ionization potential (IP) accesses the classical turning points of the potential energy curve of the ion, and (IPvertieaFIPaaiabatic) can then be related directly to Ar. This semiclassical approximation is valid only when one vibrational m o d e is excited in the PE spectrum, and that motion can then be described by a variation in one single internal molecular coordinate (in this case the C - F bond distance). It is also applicable only where I P v e r t i e a l a c c e s s e s the classical part of the potential energy curve, i.e. when long vibrational progressions are involved. This method is used for the CF 4 ~" ~ C F ~ C ionization. A more general method calculates F r a n c k - C o n d o n factors and compares the vibrational intensity pattern with experiment. This method is applicable even if the (0, 0) transition is the most intense. H a r m o n i c oscillator potentials are assumed for CF 4 X, CF~ /~ and C F ~ C, and analytical expressions are used to calculate Ar for the three processes described above.

2.1. CF4 (2t2) -1 ionization to CF~ C 2 T 2 The fourth PE band of CF 4 has an adiabatic I P of 21.67eV, and shows a long progression in the vl (al) C - F stretching vibration peaking at v = 5 [4]. The long progression is consistent with the 2t 2 molecular orbital of CF4 (formed by overlap of carbon 2p and fluorine 2ptr) being strongly bonding [3, 4]. Using our high resolution value of vl (C)=729___ l c m -1 or 0.09eV [1], we obtain IPve,t IPad b = 0"45 eV. Eland has shown that in the semi-classical approximation Ar 2 = 5.44 x 105 IPvert - #r

IPadb,

(1)

with Ar in A, (IPvert--IPadb) in eV, # in amu and v' in cm -1. With # = 4 x 19 = 7 6 a m u and v' = 729cm-1, we obtain ]At] = 0.078A. The sign is assumed to be positive, because the 2t 2 molecular orbital is bonding rather than anti-bonding in nature I-3, 4]. The intensities of the ten vibrational bands observed in the vl progression are given in table 1, and the F r a n c k - C o n d o n method is now used to calculate a more accurate value of At. This method has been described by Smith and W a r s o p for

178

S.M. Mason and R. P. Tuckett

polyatomic molecules in the harmonic oscillator approximation [6,1. In general, we wish to calculate the transition moment

R(v', v") = f ~bv,(Q') . d/r

. aQ,

(2)

where Q is a normal co-ordinate. Defining Q' = Q" + d, for photoelectron spectroscopy this simplifies to

R(v, O) = f ~bo(Q" + d) . ~bo(Q"). dQ.

(3)

The F r a n c k - C o n d o n factor, which is proportional to the PE vibrational band intensity, is then I R(v, 0) 12. Defining fl = (v"/v') 1/2, at2 = 4n2v'c/h (v' in c m - 1) and y = ~d, Ansbacher [7,1 has shown that R(1, 0) (2)l/2f12y R(0, 0) - 1 + f12 "

(4)

Using the recursion formula for Hermite polynomials [8"I, a simple recursion formula is also obtained

R(/3 --[--1, 0) (2)1/2fl2~ ( /3 ~1/2(1 -- f12~ R(/3- 1, O) R(v, 0) - (1 + fl2Xv + 1) 1/2 "4- \ V - " ~ J \ ~ ] "R('~, 0)

(5)

For CF4 ~ IA1 vl = 908cm -1 [9,1, so for the process CF4 X (v = 0 ) ~ CF~ ~ (v0 fl = (908/729) 1/2 = 1.116. A trial value of the dimensionless quantity y is chosen, and R(1, 0)/0,0) is calculated. The recursion formula is then used to obtain values of R(v, O)/R(O, 0) up to /3 = 9. The transition moments are squared, and relative F r a n c k - C o n d o n factors of the different vibrational bands are obtained, y is adjusted until the best agreement with experiment is reached. In practice, we match the positions of the observed and calculated intensity maxima, rather than the fine detail of the calculated values. Intensity distributions for five different values of ~ are given in table l, and we obtain Ybest= 3"2 ___0"2. This value of y (and hence the normal coordinate d = y/c0 can easily be converted into a change in the C - F bond distance internal coordinate Ar because the normal coordinates of v 1 do not mix with the other three vibrational modes. Hence from equations (20) and (22) of [6,1

d = AQ = (mF)l/24 - l/2(~r I + ~r 2 -t- ~r 3 d- t~r4),

y = 2ctm~/2Ar.

(6)

A value of y = 3-2 _+ 0.2 thus gives Ar = 0.078 _+ 0.005/~ in perfect agreement with the value obtained from the semi-classical calculation. Using a value of r o = 1.320/~ for CF 4 .~ 1A 1 [10,1, we obtain r o = 1-398 A for CF~" ~ 2 T 2 . 2.2. CF4 (4al)- 1 ionization to CF~ ~ 2A l The fifth PE band of CF 4 has an adiabatic IP of 25.12eV, and shows a short progression in the v I vibration with excitation to v = 0, 1 and 2 only [4]. From figure 2 (b) of [4], we estimate the relative intensities of these three peaks to be 10 : 3-7 : 0.9 respectively, and the 4al molecular orbital of CF 4 (formed by overlap of carbon 2s with fluorine 2ptr) is therefore predominantly non-bonding in nature (see below). The semi-classical method clearly cannot be used to calculate Ar, and

Rotational structure of CF~ and SiF,~ D 2 A t - ~ 2T2

179

the F r a n c k - C o n d o n method will only give an approximate value simply because of the lack of information in the PE band. Our high resolution work for CF~ /3-~ gives vl (/5 2A1) = 800 + 1 cm-1 [-1], so for the CF4 ~" ~ CF~ /3 ionization process fl = (908/800) 1/2 = 1.065. In this instance ~ is adjusted to give the best agreement for the relative intensity of the v = 1 to the v = 0 band. We obtain ? = 0.80 + 0-04, giving I Arl = 0.019 + 0.001 A. The error in Ar is unrealistically small. There is now some controversy about the sign of Ar. Ab initio calculations of Brundle et al. [3] suggest a slight bonding character for the 4al molecular orbital of CF4 (giving Ar positive) whereas Leung et al. [11] interpret their (e, 2e) experimental results as showing that this orbital is anti-bonding (giving Ar negative). We believe that 4al is bonding in character and hence Ar is positive for two reasons. Firstly, the vl vibrational frequency in CF~ /~ (800cm-1) is less than in neutral CF4 (908 cm-1). Secondly, intensity calculations for CF2 /5-~ (w2.3) are only consistent with these results if the positive sign of Ar is taken. We therefore obtain r0 = 1.339 A for CF~ /32A1 from the/3 state PE band analysis. 2.3. CF,~ ~ (v = O) ~ C (vl) ion emission spectrum The CF~- ion emission spectrum shows a progression of six members from /) (v = 0) ~ ~ (vl = 0-5) peaking in intensity at vl = 1-2 [1]. The relative intensities of the bands are 6 (vl = 0) : 10 : 10 : 6 : 4 : 1 (v~ = 5). If we regard /3 (v = 0) as the lower state of a photoionization process, the method of w2.1 can be used to calculate Ar for CF~- /$-~. With fl = (800/729) 1/2 = 1-048 the best agreement with experiment is obtained with ? = 2-0 + 0.1, giving a calculated intensity distribution of 4 . 3 : 9 . 6 : 1 0 : 6 - 5 : 3.2: 1.1. This converts to a IArl value of 0-049 + 0.003A, and the positive sign is taken because the 2t2 molecular orbital of CF4 has more bonding character than the 4al orbital (see earlier). It is possible to find Ar for the CF4 ,$" ~ CF~ /3 photoionization by a different method from w2.2, i.e. by combining the Ar values for the CF4 X ~ C F 2 t~ and CF~- /3 ~ CF~ C processes. We then find Ar for CF~ ~ ~ CF~ /5 to be 0.078 0.049 = +0-029 A. The positive sign is consistent with the 4al molecular orbital having slight bonding character. We believe that this value of Ar is more accurate than that of 0.019 A obtained directly from the CF4 ~" -* CF~ /5 PE band intensities. In the former case two long progressions have been analysed to yield Ar, whereas in the latter case we have analysed one short progression in which the relative intensity of v = 1 to v = 0 (difficult to measure accurately) is highly correlated to Ar. Hence the best value of r o (CF~ /) 2A1) is 1.320 + 0.029 = 1.349A. Using the quoted moment of inertia for CF4 of 1-466 x 10 -45 kg m 2 [10], these bond distances can be converted to rotational constants. The data are collected in table 2. These rotational constants for CF~ /~ and ~ are used as first estimates in the high resolution rotational simulations. -

2.4. Bond length changes of SiF 4 upon ionization to SiF~ C 2 T2 and/$2A 1 The F r a n c k - C o n d o n method of Smith and Warsop can be used to calculate the change in Si-F bond distance upon ionization of SiF4 to the ~ a n d / ) states of the parent ion. The fourth PE band of SiF 4 (2t21 ionization to ~ 2T2) shows a progression in v t peaking at ol = 1 [12]; the relative intensities of vl = 0 - 4 are

180

S. M. M a s o n and R. P. Tuckett Table 2.

CF,,

X

Spectroscopic constants for electronic states of CF4 and CF2.

tA 1

CF~-/32A1 CF~- (~2T2

v1 (cm- 1)

ro (.~)

B0 (cm- 1)

I (kg m 2 x 1045)

908 [9] 800 [I] 729 [1]

1"320 [10] 1.349"I" 1-398:1:

0"189 0.181 0-168

1"466 [10] 1.531 1.644

i" This work. Analysis of the /~ state photoelectron band intensities gives r o = 1'339A, B o = 0-183cm -1 and I = 1-508 x 10-45kgm 2.

:~ This work. 5.8:10:9.1:7.5:4.8 (measuring peak heights from figure 3 of 1-12]). Using v " = 8 0 0 c m -1 I-9] and v ' = 7 0 6 - 6 c m -1 [2], f l = 1 . 0 6 4 and we find that = 1.9 + 0.2, giving a calculated intensity distribution of 4-9 (v~ = 0) : 10 : 9.6 : 5.7 : 2.4 (v 1 = 4). This converts to a change in S i - F b o n d distance u p o n ionization Ar = 0.047 + 0.005 A. The SiFt- /~(v = 0) ~ ~(vt) ion emission spectrum shows bands at v~ = 0, 1 and 2 in the intensity ratio 10 : 3.8 : 1-3 (Table of [2]). Using v~ ( / ) ) = 743.4 and v 1 ( ~ ) = 706-6cm -1 [2], the best agreement with the relative intensity of vl = 1 to vl = 0 is obtained with y = 0.85 + 0-03. This converts to Ar = 0-021 A. We c o m m e n t that b o t h the C state P E spectrum and t h e / ~ - C ion emission spectrum, in addition to progressions in the vt(at) totally symmetric vibration, show strong bands in the v4(t2) vibration [-2, 12]. This gives direct evidence that the triply degenerate 6" 2T2 state of SiFt- is distorting from tetrahedral symmetry by a dynamic J a h n - T e l l e r effect. It is not immediately clear h o w this distortion will affect the Ar values calculated above, calculations which have in effect assumed Ta s y m m e t r y in all electronic states of SiF 4 and SiF2. Since the 2t2 molecular orbital of SiF4 is bonding and 4a~ is p r e d o m i n a n t l y n o n - b o n d i n g I-4, 12], Ar for SiF4 Y7 --* SiF~ /3 is calculated to be 0.047 - 0.021 = + 0.026 A. This is a relatively large value, and for this Ar we can predict the relative intensity of v~ = 1 to vl = 0 in the/~ state photoelectron b a n d to be 0.61. Since vl is as large as 743.4cm - t or 0.092eV, we could expect vibrational structure to be resolved in this P E band. Lloyd and Roberts [4"] report its observation with H e II radiation at 21-5eV, and Lloyd 1-13] has reported to us that vibrational structure was not observed. In an unpublished H e II photoelectron spectrum, Potts [14] observes an unresolved shoulder to high energy of the adiabatic peak which could be v~(/~) = 1. F r o m his spectrum we estimate the intensity of v t = 1 to v = 0 to be only 0.28, which converts to Ar = 0.018 A. There is therefore some d o u b t a b o u t the Table 3. Spectroscopic constants for electronic states of SiF, and SiF2.

SiF 4 2 IA t I SiF~/3 2A 1 | SiFt /~ 2A 1 SiF2 (72T2

vI

ro

(cm- 1)

(A)

Bo (cm- 1)

800 [9] 743-4 [2] 7434 7066 [2]

1.540 [10] 1"558t 1-566~ 1.587w

0"140 0"137 0"136 0"132

I (kg m e x 1045) 1"994 2"040 2"062 2"118

[10]

t From an analysis of the /3 state PE band of Potts [14]. :~ From an analysis of the t~ state PE band and the SiFt /~-(7 ion emission band. See text. w From an analysis of the state PE band [12].

Rotational structure of CF2 and SiF2 D 2 A I - C 2T2

181

r o values for SiFt- /) and ~, which may arise because the effect of the Jahn-TeUer distortion in ~ 2T2 has not been considered in these calculations. These values and the corresponding rotational constants are collected in table 3. As far as the SiF2 D-C rotational simulations are concerned, perhaps the most important point to note is that A B - - - B o ( / ~ 2 A l ) - Bo(~ 2T2) is about one third its value in CF2 LS-~. This has a marked effect on the rotational structure of a 2 A t - 2 T 2 electronic transition (w4).

3. Rotational structure of a ZArZT2 emission band in CF~ and SiF~ The full theory to describe a 2A~-2T2 electronic transition in a tetrahedral molecule has been developed by Watson in a series of papers analysing the Schtiler band system in the N D 4 free radical [15-17]. Following flash discharge of mixtures of N D 3 and D2, the 3p2T2,--3s2A~ Rydberg-Rydberg transition in N D 4 was photographed in absorption, and Watson was able to simulate the experimental spectrum at Doppler-limited resolution [17]. The first part of our work, therefore, was to develop a computer program to reproduce Watson's ND4 simulation (figure 2 of [17]); this was successful. We then applied our program to simulate 2A~ ~ 2T2 emission bands of CF~ and SiF~ at low rotational temperature and inferior resolution. We comment that in the 3p 2T2 ~ 3s 2Ax spectrum of N D 4 the unpaired electron moves between two Rydberg orbitals some distance from the N D ~ ionic core. In the CF~ and SiFt- /~ 2A I ---,C2T2 emission spectrum, however, an electron hole is located in two different valence molecular orbitals in the two electronic states. Whilst the physical interpretation of the spectroscopic constants may therefore be different in CF~/SiF~- and N D 4 , the energy levels of 2T2 and 2A 1 electronic states are appropriate in either case. These levels are shown in figure 1. We use the notation developed by Watson, and the reader is referred to [16] for full details. The rotational levels are labelled N R where R = Iq - A is the pure rotational angular momentum quantum number and A is the orbital electronic angular momentum quantum number. The rest of this section is specific to the CF~ and SiF~ /~-C emission bands, so the single prime label refers to the/~ 2A 1 upper state and double prime to the ~2 T2 lower state. In the 2A~ upper state, A = 0, R' = Iq' and if the spin-rotation splitting is negligible, the two sub-levels J = N _ 89 are degenerate (,J = Iq + S is the total angular momentum quantum number). Thus the rotational energy levels are given by B'N'(N' + 1) if centrifugal distortion is ignored. Each rotational level is split into its tetrahedral components (x) and the rovibronic symmetries of the lowest levels are shown in figure 1. The magnitude of the splittings in an A ~ state are expected to be very small, and they are ignored in the rest of this paper. In the 2T2 lower state, A = 1 and the three fold degeneracy of the T2 state is split by first order Coriolis interaction. Three stacks of rotational levels labelled T - , T O and T § are obtained, with R" = N" -- 1, N" and N" + 1 respectively. The splitting of a given N is determined by the Coriolis constant (" where - 1 ~< (" ~< + 1, and the rotational energy levels are approximately given by [18] T - ( N ) = B"N(N + 1) - 2B"~"(N + 1), t !

T~

= B"N(N + 1) - 2B"~",

T+(N) = B"N(N + 1) + 2B"~"N.

I'

b

(7)

182

S . M . M a s o n and R. P. Tuckett

2A__!

l~ ~

A1.E-T1+T2

33 m

A2,T1*T2

22 ~

E+T2

11i 7 O0

I

p

~ 5~

/'*3 2 T~

T1 A1 Q

R

~ A2"E 55 ~. ~' 2_T_ 2_ E +rl 56 rl "r2 ~ A2+E 45 A1 ,T1,1-2 ~ *T"T1 2 4~.

AI~2+E ,2T1,r2 E*rl *2T2

Av.T1 3~ ~

3/. ~ . t 21

0.01 cm-1) has to be used before this term has any noticeable effect on the simulations. Again, therefore, we feel justified in constraining q~ to zero. Aarts has observed the same vibronic bands of CF~- /$-(7 by He+-impact ionization of CF 4 at room temperature. A high resolution spectrum of the 1~ band is shown in figure 2(b) of [1]. Briefly, the band is much broader than that obtained in the molecular beam/electron beam apparatus (reflecting the higher rotational temperature), and the intensities of the two spin-orbit peaks are approximately 1 : 1. In concluding this section on CF~ /$-(7 simulations, we have attempted to simulate

Rotational structure of CF2 and SiF,~ D 2A1-~ 2T2 Table4.

187

Spectroscopic constants obtained from CF~" and SiF~ / ~ 2 A l ' - - ~ 2 T2 band simulationst. Parameter

CF~

SiFt-

B'

0-180 (3), 0"168w 0"15 (15) 10.0 (5) 011 011 25 (5)

0-136 0"132 0"0 4.5 (2)~ 0 0 25

B" (" ~" q~ qT" TR

t Units cm- 1, except (" (dimensionless) and Ta (K). :~ The values in parentheses indicate realistic confidence limits. w Fixed from photoelectron analysis (table 2). II Constrained to zero (see text). 82Because the spectroscopic constants in SiF~ are heavily correlated (see text), it is not meaningful to estimate errors in most of these constants. The exception is ~" (see ~t). the 1~ band at 300K. This is not an easy problem with the existing model for two reasons. Firstly, at high rotational temperatures the transitions with high R dominate the rotational contour, and yet this is where the AR = 0 selection rule breaks down. Secondly, the tetrahedral splittings become much larger at high R, so the value of q~ becomes important. However, constraining all the spectroscopic parameters to the values in table 4 and assuming AR = 0 still holds, the simulations at 300 K do show the following features: (a) a broadening of the vibronic band to lower wavelength; (b) a retention of the two spin-orbit peaks (separation reduced to 12cm-~), but a smearing out of the 2 : 1 intensity ratio to closer to 1 : 1 ; (c) a shift in the positions of the two spin-orbit peaks to lower wavelength of approximately 0-1 nm. All these points are in agreement with the experimental observations contained in our previous paper [1].

4.2. Rotational simulation of the 0 ~ band of SiF~ D-C at 551 nm Figure 4(a) shows the 0 ~ band of SiF~ / ) - ~ at 551 nm recorded at a low rotational temperature in the molecular beam apparatus (see figure 2 (a) of [2]). The spectrum is much more intense than the CF~ / ) - ~ system, the resolution can therefore be improved substantially over the CF~ vibronic bands, and figure 4(a) is recorded at a resolution W of 0-011 nm or 0.35 cm-1. As noted in our earlier paper [2], the spin-orbit doubling of ~ 2T2 is clearly observed, its magnitude is small (2/3 x the observed splitting of 6-9 cm-1), but the sign of r is now uncertain. The band shows a blue-degraded tail at its low wavelength end, and in addition shows a branch which has the appearance of a red-degraded tail at its high wavelength end. This anomaly was noted earlier [2], but was unexplained. The rotational simulation of this band is much more difficult and hence less successful than in CF~ for several reasons. Firstly, the photoelectron analysis of SiF4 (w2.4) is limited, and only very approximate values for B~ and B~ are obtained.

188

S. M. Mason and R. P. Tuckett I ~ Pz

(a)

I

-

25

(b)

I

20

I

I

15 10 %)/ cm-1

I

I

5

0

I

25

I

20

1

I

15 10 %) cm-1

I

5

I

0

Figure 4. (a) shows the 0o~ band of SiF~ /)-t~ at 551 nm recorded at a resolution of 0-35 cm-t. (b) shows the simulation obtained with the constants in table 4. The direction and shading of the six branches is shown (see text). Secondly, because of the presence of the Jahn-Teller 20 and 40 vibronic bands in SiF~ / ) - ~ , q~ and q~ are both expected to be non-zero: furthermore, q~ may be large enough that the AR = 0 selection rule breaks down. Finally, because AB is predicted to be very small, all the spectroscopic constants become highly correlated, and it may be possible to obtain an approximate simulation using a combination of incorrect constants. In the initial simulations, therefore, we simplified the problem and constrained B' and B" to their photoelectron values (table 3), set both q~ and q~ to zero, and assumed the same rotational temperature of 25 K as in the CF~- work. It was immediately clear that the small value of AB (0.004 cm-1) results in a very different rotational contour from that in CF~ (AB = 0.012 cm-1), and that the correct shading of the heads and tails could only be obtained with a positive spin-orbit splitting in ~ 2T2 . With these constraints, the most satisfactory simulation is shown in figure 4(b) and the constants are given in table 4. Despite the limitations of this model, we are satisfied that the broad features of the experimental spectrum are reproduced in the simulation. The six branches are shown in figure 4(b). The four associated with the upper spin-orbit component G312(P1, Q1, Qz and R2) have most of their intensity spanning v = 0-13 cm-1, and the two associated with the lower Es/2 component (P2, RI) span v = 1 3 - 2 5 c m - L As shown by the arrows, three of the branches (PI, P2 and Q1) form blue-degraded heads. Because AB is small, the PI head forms at a high value of R where the intensity of the lines is very weak at a low rotational temperature; this branch therefore has the appearance of a red-degraded tail. The P2 and Q1 heads appear narrower because all the lines pile up together. The R~ branch shows a blue-degraded tail as B' > B". Changes in ~", AB, q~ or q~ have the most effect on the appearance of the G3/2 sub-band. Increasing (" from zero sharpens the P1 head since it forms at a lower

Rotational structure of CF~ and SiF~ D 2At-C 2T2

189

value of R (see equation (10)), and increases the relative intensity of the Q1 to the P2 head. Increasing AB has the same effects. Increasing q~ from zero makes the P1, Q~ and Q2 branches increasingly narrow, whilst the R 2 branch opens out rapidly to high frequency; for q~ > 0-005 cm-1, the simulated spectrum bears no resemblance to the experimental spectrum. Increasing q~ from zero broadens all four branches of G3/2, and for 0 < q~ < 0.005 cm- 1 the simulated spectrum shows a closer resemblance to experiment. It is clear, however, that all these constants are heavily correlated and further progress cannot be made until fully resolved rotational spectra have been obtained.

5.

Discussion

5.1. Rotational constants The rotational simulations of vibronic bands of CF~ and SiF~ /~--(~ suggest that the rotational constants obtained from the PE band analyses are fundamentally correct. For CF~, the long progression in v1 in the ~ state PE band means that an accurate value for B" can be obtained, and the intensity data for CF~ /~ (v = 0) ~ CF~- C (vl) means that an approximate value for B' can also be obtained. We note that the value of B' from the/~-C rotational simulation (0-180 + 0.003 cm-1) is in excellent agreement with the B' value obtained by this method, whilst the value derived directly from t h e / ) state PE band (0-183 cm-~--table 2) is on the very edge of our confidence limit in B'. For SiF~ /3 and C, the PE analysis is not so satisfactory because the vibrational progressions are not so long, and no account is taken of the Jahn-Teller distortion in the ~ state. The calculations, however, do suggest that AB for the SiFt- /)-C ion emission spectrum is small (about one-third its value in CF~ /)-C"), and this is confirmed by the rotational simulations since the value of AB has a major effect on the rotational structure of a / ) - ~ vibronic band. In summary, this is an excellent example of how photoelectron spectroscopy and optical emission spectroscopy of molecular ions can complement each other, so long as vibrational structure is resolved in the PE spectrum.

5.2. Coriolis constant in CF~ and SiF~ C 2 T2 The small value of ~ in both CF,~ and SiF~ ~ 2T2 is slightly surprising. If the lone electron is located in a 2p/3p orbital on the central C/Si atom, then a value of ( of + 1 would be expected; ~ has this approximate value in the ND 4 3p 2T2 Rydberg state, where the lone electron is in a N(3p) Rydberg orbital some distance from the ND~" ionic core [17]. This t 2 molecular orbital of CFJSiF4, however, arises mainly from a bonding between C (2p)/Si(3p) and 4F (2p) [3, 11], and the (t2)5 electron configuration gives the C 2T2 electronic state. The electronic value of ( is then expected to be reduced from its limiting value of + 1. An unpublished SCF wavefunction for this state of CF~ gives [23] : ~b(~ 2T2) = 0.46 C (2p) + 0-32 F (2s) + 0.65 F (2pa) + 0.52 F (2p~r).

(11)

It would be instructive to calculate an ab initio value of ( for this wavefunction, to compare with the value from the/$-(~ rotational simulations of 0.15 + 0-15.

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S . M . Mason and R. P. Tuckett

In SiF~ ~ 2 T2 this pure electronic value of ( will be quenched by the Jahn-Teller (JT) effect and hence reduced in value. Watson [15, 24] has shown that this quenching of ( can be related to the JT parameters Di, where D i is the dimensionless ratio of the lowering of the potential energy due to JT distortion to the unperturbed vibrational frequency vi. Since the v2 and v4 bending vibrations are both JT active [2], we obtain -~-~e~ec(1 -- 3/4D 2 - 3/2D2).

(12)

Taking v4 as an example, the value of D 4 c a n be estimated from the ratio of the frequency interval (0~ - 4 ~ to (0~ - 4 ~ in the SiF~ / ) - ~ spectrum. This ratio is 761.9/431.0 = 1.77 [2]. Cossart-Magos and Leach [25] have shown that two values of D are usually obtained for one value of this ratio. In this instance, D 4 = 0-10 or 0.33, and it is often easy to obtain the correct value by comparing the calculated intensity distributions for the 4 ~ series with experiment. Thus D4 = 0.33 gives a more realistic estimate of the relative intensities of 0 ~ to 4 ~ and 4 o [2, 25]. Similarly from the frequency ratio (0~ - 2 ~ to (0~ - 2 ~ (314.3/159.0 = 1-98 [2]), D 2 = 0-02 or 0.80 and the former value gives the better agreement with the 2 ~ intensities. Hence the JT distortion in SiF~ t~ 2T2 is dynamic, with v4 contributing most to the lowering of the potential energy of the state, and we obtain ( = 0-84 (e~,c. Again, an ab initio calculation of the pure electronic Coriolis constant would be instructive. For reasons made clear in w no great confidence should be placed in the value of = 0 obtained from the SiF~ /)-C 0 ~ simulation (table 4), and a fully rotationally resolved spectrum of this band is needed to obtain an accurate experimental value for (.

5.3. Spin-orbit splitting in CF~ and SiF~ C 2T2 Since the C 2 T 2 state of both ions has the (t2) 5 electron configuration, this molecular orbital is more than half full, and the spin-orbit splitting is expected to be negative. In fact for both CF~ and SiF~ ~ 2T2 ~ is positive (table 4). This is a very surprising result, and it is one of the few examples where Hund's rules for the sign of a spin-orbit splitting give the wrong answer. For CF~, equally surprising is the small value of ~ ( + 1 0 - 0 c m -1) compared to the F atom splitting of - ( 1 . 5 x 2 6 6 ) - - - 3 9 9 c m -1 for a tetrahedral arrangement of four F atoms [5]. Even if the t 2 molecular orbital predominantly represents a tr bond between C(2p) and F(2p) with not dissimilar coefficients (as equation (11) suggests), the magnitude of the molecular spin-orbit splitting should be dominated by the contribution of the halogen atoms, since the magnitude of its atomic spin-orbit splitting is much greater than that of the central C(2p). Since there is no Jahn-Teller distortion in C 2 T2 ' one cannot invoke a quenching of ~ by the JT effect. One possibility is that configuration interaction with other states of 2T2 symmetry not only decreases the value of in C 2 T2 but also changes its sign. A detailed ab initio calculation of this splitting would be of great interest. In SiF~ ~ 2T2 the molecular spin-orbit splitting arises from contributions from Si 3p ( + 1 5 3 c m -1) and 4F 2pn ( - 3 9 9 c m - 1 ) . Again, the small magnitude of ~ ( + 4 - 5 c m -1) is surprising, and as mentioned above its sign should be negative. There may now be some quenching of ~ by JT distortion which may also change its sign, and as in CF~- C 2T2 configuration interaction could be important. We note that the spin-orbit splitting of SiF~ C 2 T 2 v4 = 1 is reduced

Rotational structure of CF,~ and SiF,~ D 2AI-t~ 2T2

191

compared to its value in v = 0, i.e. ~ is quenched in the JT active vibration. Its sign is as yet unknown. 5.4. Concluding remarks We have presented a rotational simulation of vibronic bands of CF~ and SiF~ /~2A1-C2T2 which allow for Coriolis splitting, spin-orbit splitting and Jahn-Teller distortion in the ~ 2T2 state. The model can be applied to all bands of CF~-, but only to those of SiFt- which do not involve the Jahn-Teller active vibrations. We are hoping to obtain Doppler-limited spectra of these ions on photographic plates in the near future. A hollow cathode source will be used with a temperature of ~ 300 K. Our simulations show, however, that analyses of these hot spectra will be considerably facilitated if, in addition, rotationally resolved cold spectra ( ~ 25 K) are available to refer to. These experiments are now in preparation. We thank Dr. R. A. Kennedy for many useful discussions, Dr. J. K. G. Watson for helpful correspondence, and Mr. G. Yarwood for computational assistance. We acknowledge the financial support of SERC (UK), and SMM thanks the University of Cambridge (Sims Scholarship) for a Research Studentship. Note added in proof.--The anomalous sign of the spin-orbit splitting constant in now been explained by R. N. Dixon and R. P. Tuckett (1987, Chem. Phys. Lett., paper submitted). It arises because the 2p orbitals on the four fluorine atoms have both a (pointing along the C/Si-F bonds) and n (lying perpendicular to the bonds) character. This is confirmed by the wavefunction in equation

CF~/SiF~ CET2 has

(11). References AARTS,J. F. M., MASON,S. M., and TuCr,EYr, R. P., 1987, Molec. Phys., 60, 761. MASON,S. M., and TUCKETT,R. P., 1987, Molec. Phys., 60, 771. BRUNDLE,C. R., ROBIN,M. B., and BASCH,H., 1970, J. chem. Phys., 53, 2196. LLOYD,D. R., and ROBERTS,P. J., 1975, J. electron Spectrosc., 7, 325. ELAND,J. H. D., 1984, Photoelectron Spectroscopy, 2nd edition (Butterworths). SMITH,W. L., and WARSOe,P. A., 1968, J. chem. Soc. Faraday II, 64, 1165. ANSBACHER,F., 1959, Z. Naturf. (a), 14, 889. PAULING,L., and WILSON, E. B., 1935, Introduction to Quantum Mechanics (McGrawHill). [9] HERZBERG, G., 1945, Molecular Spectra and Molecular Structure II, Infra-Red and Raman Spectra of Polyatomic Molecules (Van Nostrand), p. 167. [10] JANAFTHERMOCHEMICALTABLES,1970, NSRDS-NBS37, 2nd edition. [11] LEUNG,K. T., and BRION,C. E., 1984, Chem. Phys., 91, 43. [12] JADRNY,R., KARLSSON,L., MA'r'rSSON,L., and SIEGBAI-rN,K., 1977, Chem. Phys. Lett., 49, 203. [13] LLOYD,D. R., 1986 (private communication). [14] POTTS,A. W., 1986 (private communication). [15] WATSON,J. K. G., 1984, J. molec. Spectrosc., 103, 125. [16] WATSON,J. K. G., 1984, J. molec. Spectrosc., 107, 124. [17] ALBERT1,F., HUBER,K. P., and WATSON,J. K. G., 1984, J. molec. Spectrosc., 107, 133. 1-18] HOLLAS,J. M., 1982, High Resolution Spectroscopy (Butterworths). [19] KIRSCrrNER,S. M., and WATSON,J. K. G., 1973, J. molec. Spectrosc., 47, 347. [20] TtJcr,~TT, R. P., DALE, A. R., JAFFEY,D. M., JAm~Yr, P. S., and KELLY,T., 1983, Molec. Phys., 49, 475. [21] DEKOVEN, B. M., LEVY, D. H., HARRIS, H. H., ZERGARSrd, B. R., and MILLEg, T. A., 1981, J. chem. Phys., 74, 5659. [1] [2] [3] [4] [5] [6] [7] [8]

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[22] HERNANDEZ,S. P., DAGDIGIAN,P. J., and DOERING,J. P., 1982, Chem. Phys. Lett., 91, 409. [232 AARTS,J. F. M., 1986 (private communication). [24] WATSON, J. K. G., 1985, Proceedings of the 17th Int. Symposium on Free Radicals (Granby, U.S.A.), pp. 650-670. [25] COSSART-MAGOS,C., and LEACH,S., 1979, Chem. Phys., 41, 345; 1980, Ibid., 48, 349.