A two force-constant model for complexes B⋯M–X (B is a Lewis base and MX is any diatomic molecule): Intermolecular stretching force constants from centrifugal distortion constants DJ or ΔJ

Abstract

A two force-constant model is proposed for complexes of the type B⋯MX, in which B is a simple Lewis base of at least C2v symmetry and MX is any diatomic molecule lying along a Cn axis (n ≥ 2) of B. The model assumes a rigid subunit B and that force constants beyond quadratic are negligible. It leads to expressions that allow, in principle, the determination of three quadratic force constants F11, F12, and F22 associated with the r(B⋯M) = r2 and r(M-X) = r1 internal coordinates from the equilibrium centrifugal distortion constants DJ (e) or ΔJ (e), the equilibrium principal axis coordinates a1 and a2, and equilibrium principal moments of inertia. The model can be applied generally to complexes containing different types of intermolecular bond. For example, the intermolecular bond of B⋯MX can be a hydrogen bond if MX is a hydrogen halide, a halogen-bond if MX is a dihalogen molecule, or a stronger, coinage-metal bond if MX is a coinage metal halide. The equations were tested for BrCN, for which accurate equilibrium spectroscopic constants and a complete force field are available. In practice, equilibrium values of DJ (e) or ΔJ (e) for B⋯MX are not available and zero-point quantities must be used instead. The effect of doing so has been tested for BrCN. The zero-point centrifugal distortion constants DJ (0) or ΔJ (0) for all B⋯MX investigated so far are of insufficient accuracy to allow F11 and F22 to be determined simultaneously, even under the assumption F12 = 0 which is shown to be reasonable for BrCN. The calculation of F22 at a series of fixed values of F11 reveals, however, that in cases for which F11 is sufficiently larger than F22, a good approximation to F22 is obtained. Plots of F22 versus F11 have been provided for Kr⋯CuCl, Xe⋯CuCl, OC⋯CuCl, and C2H2⋯AgCl as examples. Even in cases where F22 ∼ F11 (e.g., OC⋯CuCl), such plots will yield either F22 or F11 if the other becomes available.

H3P⋯AgI: generation by laser-ablation and characterization by rotational spectroscopy and ab initio calculations

“…The compliance matrix elements ( F –1 ) nn are simply 1/ F nn under the approximations described above. It was shown in ref. 50 that zero-point constants and coordinates can be used in place of equilibrium values to a reasonable approximation.…”

“…To deal with such cases, we have recently described a two-force constant model which relates the quadratic force constants F M–X and F B···M (hereafter referred to as F 11 and F 22 , respectively) to either D e J or Δ e J under the assumption that the contribution of the cross term F 12 is negligible. 50 The model applies to all complexes of a Lewis base B with any diatomic molecule ( e.g. a hydrogen halide HX, a dihalogen XY, or a coinage metal halide MX) as long as the diatomic molecule lies along a C n ( n ≥ 2) symmetry axis of B in the equilibrium geometry.…”

“…The two-force constant model for a symmetric-top molecule such as H 3 P···AgI leads (with numbering of the Ag and I atoms and internal coordinates r 1 and r 2 shown in Fig. 2 ) to the expression 50 In eqn (3), I e bb is an equilibrium principal moment of inertia and the a n are equilibrium principal axis coordinates of atoms n = 1 and 2. The compliance matrix elements ( F –1 ) nn are simply 1/ F nn under the approximations described above.…”

Molecular geometries and other properties of H2O⋯AgI and H3N⋯AgI as characterised by rotational spectroscopy and ab initio calculations

“…We recently proposed a model 43 that allows in principle some of the quadratic force constants of L· · · M-X complexes to be established from centrifugal distortion constants determined experimentally. This model goes beyond that of Millen 44 by describing the centrifugal distortion constant D J (for symmetric top or linear complexes) or ∆ J (for asymmetrictop complexes) in terms of three quadratic bond-stretching force constants F 11 , F 22 , and F 12 , where the subscripts 1 and 2, respectively, refer to the M-X and L· · · M bonds (such that F 11 = F M-X and F 22 = F L · · · M ) with F 12 being the off-diagonal coupling term.…”

Geometries of H2S⋯MI (M = Cu, Ag, Au) complexes studied by rotational spectroscopy: The effect of the metal atom

“…The experimentally-determined force constants are calculated by applying a model 59 which accounts for contributions to the centrifugal distortion constants from both the MX and S•••M bonds. The force constants of these bonds are denoted by F11 and F22 respectively in Eq 3;…”