Force Field for SiF₄

Abstract

The force field of SiF₄ has been determined using both Coriolis coupling constants obtained from an investigation of the band contour of v₃ at 195 °K and isotopic shifts. The force fields are equally well determined using both methods and are in agreement.

In determining the general valence force field for silicon tetrafluoride from various sources of molecular information, McKean [1]¹ noted a significant discrepancy in the range of values for the stretch-bend interaction force constant characterized separately by the isotopic frequency shift Δv₄ and by the Coriolis constant ζ₄. Since the estimate of ζ₄ from the band shape of v₄ contains a relatively large uncertainty, as a consequence of an inability to locate precisely the P and R branch maxima, we examine in this communication the contour of the v₃ fundamental at 195 °K in order to obtain a reliable zeta value for constraining the force field. In addition to confirming the potential function for SiF₄ by comparing the force constants calculated from alternate methods, rotation-vibration interaction data from the two F₂ vibrations provide further tests concerning the utility of the band contour method for estimating Coriolis parameters.

The contours for both infrared active fundamentals, v₃ and v₄, were recorded at 310 and 195 °K with a double beam grating spectrophotometer equipped with interference filters to separate the orders. Spectral slit widths varied between 0.7 and 0.9 cm⁻¹. For low temperature measurements, a 5-cm path length copper cell, surrounded by an evacuated glass shell, was in contact with a solid CO₂ and acetone mixture.

Figure 1 displays a representative scan of the v₃ contour at 310 and 195 °K. A hot band at approximately 1029 cm⁻¹ distorts the contour sufficiently at 310 °K to preclude a valid P–R measurement for use in the Coriolis constant determination. The attenuation of the intensity of the hot band transition at 195 °K, however, reveals definite P, Q, and R branch features. Additional absorptions, attributed to the naturally occurring isotopes of ²⁹Si and ³⁰Si, are also observed. These values, summarized in table 1, agree well with Heicklen and Knight’s frequencies obtained from isotopically enriched compounds [2].

Figure 1. The vibration-rotation band contour for the v₃ fundamental of SiF₄.

(a) 310 °K, (b) 195 °K, (c) 195 °K. The frequencies are labeled in cm⁻¹.

Table 1. Observed data for Sif₄.

Δv_P-R represents the P–R separation in cm⁻¹. The frequencies are in cm⁻¹; the ζ_i are dimensionless.

	Frequency (cm−1)	Assignment
	1030.7 1029.5 1022.1 1013.5	28SiF4 hot band 29SiF4 30SiF4
	Observed frequency (cm−1)	ΔvP-R (cm−1)	ζi	∑ζi	Sum rule
v3 v4	1030.7 389.4	8.3 ± 0.5a,c 23.4 ± 1.0b	0.53 ± 0.03 −0.07 ± 0.05	0.46 ± 0.06	0.50

^a195 °K.

^b310 °K.

^cThe estimated uncertainty of 0.5 cm⁻¹ represents twice the maximum deviation from the value obtained from averaging twelve traces of the spectrum.

For v₃, an average value of 8.3 cm⁻¹ for Δv_P-R was determined from twelve expanded traces, recorded at several spectral slit widths. Repeated determinations of the P and R branch maxima by a second investigator suggests an uncertainty in Δv_P-R of less than 0.5 cm⁻¹. For the v₄ vibration, it is more difficult to determine Δv_P-R owing to the relative broadness of the P and R branch features. Measurements in a 10-cm path length cell at 310 °K, with varying sample pressures and instrumental conditions, give 23.4 ± 1.0 cm⁻¹for Δv_P-R, in agreement with Heicklen and Knight’s single value of 23.1 cm⁻¹.

Edgell and Moynihan’s expression (3) in terms of the rotational constant B and absolute temperature T, relates the Coriolis constant ζ_i to the measured $\text{Δ}{\nu }_{P-R}^i$ values. Perturbations to the contour from the ²⁹Si and ³⁰Si isotopes are ignored in this calculation. A summary of the calculated Coriolis constants appears in table 1. The zeta sum of 0.46 ± 0.06 for the two Coriolis values, compared to the theoretical sum of 0.50, supports the consistency of the data determined by the contour method.

The Coriolis coefficients ζ and the isotopic frequency shifts Δv, respectively, provide force field information through analogous expressions; namely

$$\zeta =L^{-1}C{\left(L^{-1}\right)}^{\prime },$$ (1)

and

$$\frac{2\text{Δ}\nu }{\nu }=L^{-1}\text{Δ}G{\left(L^{-1}\right)}^{\prime }.$$ (2)

L⁻¹ represents the normal coordinate vector matrix; C is a function of the atomic masses and the molecular geometry, and ΔG represents the change in the G matrix as a result of isotopic substitution. Since the L matrix relates the force field to the experimental parameters, figure 2 presents plots of the dependence of ζ_i and Δv₄ upon the interaction force constant F₃₄ for the F₂ symmetry species.

Figure 2. Plots of ${\zeta }_{33}^z$, ${\zeta }_{44}^z$, and Δv₄ (in cm⁻¹) as functions of F₃₄ for the F₂ symmetry species of SiF₄.

F₃₄ is in millidynes per angstrom.

The use of eq (2) with the L⁻¹ matrices for both the ²⁸S and ³⁰Si isotopes demonstrates the uncertainty in the force field fixed by a value for Δv₄. The lower portion of figure 2 displays the relevant plots. The solid circles locate the experimental point for Δv₄ of 3.0 ± 0.1 cm⁻¹ (1, 2), while the shaded areas represent the uncertainty in the experimental measurement. A vertical dotted line gives the average value for F₃₄ from the perturbation calculation. The solid circles and shaded areas in the upper portion of the figure represent the experimental Coriolis constants and their uncertainties, respectively. The vertical line originating from ζ₃ in the plot defines the preferred force field using the more certain Coriolis value. The L⁻¹ matrix for the ²⁸Si species formed the basis for the Coriolis plot in the figure. Definitions for the symmetry coordinates, as well as the details of the vibrational calculation, appear in reference [4].

The force constants, constrained by (a) Δv₄, (b) ζ₃ and ζ₄, and (c) ζ₃ alone appear in table 2. The dispersions in the F’s are assumed to arise from the uncertainties in the experimental data alone; that is, the errors due to anharmonicity and the uncertainty in the normal coordinates are neglected. The very good agreement for the force fields between the two types of constraints confirms the potential function for SiF₄. Although the frequency shift method reflects an optimistic estimate of ±0.1 cm⁻¹ uncertainty in the Δv₄ measurement (1, 2), the estimated dispersions in the crucial interaction force constant F₃₄ suggest that the Coriolis and the isotopic shift constraints are about equally effective for this molecule.

Table 2. SiF₄ force constants constrained by Δv₄, ζ₃ and ζ₄, and ζ₃, respectively.

The units of F are expressed in millidynes per angstrom.

Force constant	Δv4	ζ3 and ζ4	ζ3
F33	6.28 ± 0.22	6.21 ± 0.31	6.40 ± 0.16
F34	−0.23 ± 0.10	−0.20 ± 0.15	−0.28 ± 0.07
F44	.44 ± 0.01	.45 ± 0.02	.44 ± 0.01