From Concepts to Algorithms for the Treatment of Large Amplitude Internal Motions and Unimolecular Reactions

The formalism of the large amplitude path Hamiltonian provides a theoretical framework for the study of dynamical problems ranging from anharmonic vibrations to unimolecular reactions. A hierarchy of models at different degrees of sophistication can be elaborated and some of them have been put into practical use through the development of the DiNa package. The simplest level requires just the characterization of all the stationary points encountered along a large amplitude path and their quadratic environments. Perturbation theory can next be used to analyze the role of anharmonicity in the vibrational modulation of physico-chemical observables for semirigid systems. An extension of the same approach to saddle points allows the computation of reliable reaction rates taking into account curvature and tunneling effects. Finally, full characterization of the harmonic valley surrounding the path allows study of vibrational modulation in flexible systems and energy flow between different degrees of freedom during chemical reaction

Anharmonic, Temperature, and Matrix Effects on the Molecular Structure and Vibrational Frequencies of Lanthanide Trihalides LnX3 (Ln = La, Lu; X = F, Cl).

MP2 and CCSD(T) ab initio calculations have been carried out to elucidate geometrical structure and vibrational frequencies of representative lanthanide trihalides LnX3 (Ln = La, Lu; X = F, Cl) explicitly including temperature, anharmonic, inert-gas matrix, and spin−orbit effects. The results have been compared with gas-phase electron diffraction, gas-phase IR measurements, and IR spectra of molecules trapped in inert-gas matrices. On the Born−Oppenheimer surface LaCl3, LuF3, and LuCl3 adopt trigonal planar (D3h) geometry while LaF3 assumes a slightly pyramidal (C3v) structure. Because of normal-mode anharmonicities, the resulting thermal average bond angles are considerably lower than the equilibrium ones, while vibrationally averaged bond lengths are predicted to be longer. The inert-gas matrix effects, modeled by the coordination of two inert-gas molecules LnX3·IG2 (IG = Ne, Ar, Xe, and N2), are substantial and strongly depend on the polarizability of coordinating particles. Coordinating inert-gas units always favor the tendency of LnX3 molecules to adopt planar structure and induce noticeable frequency shifts

Ab initio Study on Spectroscopic Properties of GdF3 and GdCl3

The geometry and vibrational frequencies of the GdX3 (X = F and Cl) molecules have been analyzed at the ab initio level with extended basis sets, employing relativistic effective core potential, and evaluating electronic correlation by means of second-order perturbative (MP2) and coupled cluster (CCSD and CCSD(T)) methods. Anharmonicities, temperature, and inert-gas matrix effects have been explicitly included. The MP2, CCSD, and CCSD(T) calculations on the systems in the gas phase indicate a trigonal planar equilibrium structure for GdCl3 and a quasiplanar geometry for GdF3. Vibrationally averaged bond angle, evaluated by means of a simple one-dimensional treatment, is considerably smaller than the equilibrium value and both molecules have a pyramidal thermal average structure, in agreement with recent electron diffraction measurements. The theoretical estimate of Gd−X bond lengths depends on both the electronic correlation treatment and the basis set quality, thus indicating the desirability of high-level calculations. Experimental and theoretical comparison becomes quantitative after including thermal correction. Anharmonic vibrational frequencies have been computed through the vibrational self-consistent field method followed by the second-order perturbation correction. For both gadolinium trihalides, the ν2 out-of-plane bending potential shows a huge “negative” anharmonic form and hot bands fall at considerably higher energies than the fundamental one. Although the anharmonicities for the remaining modes are small, they are important for a correct interpretation of experimental IR spectra. The inert-gas matrix interactions, modeled by coordination of one and two inert-gas molecules GdX3·IGm (IG = Ne, Ar, Xe, and N2; m = 1 and 2), are substantial and GdX3 structures strongly depend on the number of coordinating molecules and on the interaction strength. As a consequence, all normal-mode frequencies slightly diminish as GdX3- -IGm interactions grow, while the ν2 out-of-plane bending frequency significantly increases

Charge Distribution and Chemical Effects. XLII. Bond Dissociation Energy and Radical Formation

The problem of bond dissociation, R1R2 → R1• + R2•, is addressed from the viewpoint that the fragments, R1 and R2, may not be individually electroneutral in the host molecule, whereas the corresponding radicals certainly are. The mutual charge neutralization of R1 by R2 during the cleavage of the bond linking R1 to R2 is described by an expression featuring only molecular ground-state properties. This expression translates directly into a new energy formula for the dissociation energy, D*(R1R2) = ε(R1R2) + CNE − E*nb + RE(R1) + RE(R2), where both the molecule and the radicals are taken at their potential minimum. The charge neutralization energy, CNE, profoundly affects the relationship between the dissociation (D*) and contributing bond energy (ε), i.e., the energy in the unperturbed molecule. Nonbonded interactions between R1 and R2, E*nb, are almost negligible. The reorganizational energy, RE, measures the energy difference between R• and the corresponding electroneutral group found in the symmetric molecule RR. Numerical applications to alkanes reveal an important cancellation of individual CNE terms accompanying the mutual charge neutralization of alkyl groups during the cleavage of CC bonds, i.e., . Theoretical εCC's lead to valid CC bond dissociation energies. In CH bond dissociations, on the other hand, the sum εCH + CNE remains nearly constant although individual εCH's may differ from one another by as much as 6 kcal mol−1. The appropriate approximation, , shows in what manner charge neutralization energies disguise genuine contributing CH bond energies to create a perception of seemingly constant CH bond contributions

Bond Energies and Bond Dissociation Energies

The problem of bond dissociation, R1R2 → R1 • +R2 •, is addressed from the view point that the fragments, R1 and R2, may not be individually electroneutral in the host molecule, whereas the corresponding radicals certainly are. An expression is derived for the charge neutralization energy, CNE, accounting for the neutralization of R1 by R2. This leads to a new formula for the dissociation energy, D* = ε + CNE + ΔEnb + RE(R1) + RE(R2), where ε is the charge-dependent bond energy, ΔEnb is a small nonbonded contribution and the last two terms are reorganizational energies which measure the relaxation of an electroneutral fragment to yield the final product. This new formula is general. For diatomics it reduces to D* = ε. For a bond in the "interior" of a molecule (i.e. a bond linking sufficiently large groups), the appropriate expression is D* ≈ ε + RE(R1) + RE(R2). Peripheral bonds (e.g., C-X with X = H, Cl, Br, I) are described by D* ≈ constant + RE. Finally, bonds involving the "exterior" of a molecule (e-g., hydrogen bonds) are described by D* = CNE + ΔEnb. Even though the latter "bonds" may be relatively weak, any charge imbalance resulting from their formation is capable of inducing significant modifications in the "interior" of the bonded partners and thus can affect their reactivities. This is where detailed charge analyses and the calculation of charge-dependent bond energies can prove valuable

Potential Energy Surfaces for Chemical Reactions: An Analytical Representation from Coarse Grianed Data with an Application to Proton Transfer in Water

In this paper we address the issue of how to represent the potential energy surfaces that arise in chemical reactions from coarse grained electronic structure calculations. Using a reductionistic method based on the reaction surface model, we develop a computational protocol which combines tensor product spline fitting with bivariate interpolation. This approach is particularly useful when one wishes to retain a high degree of accuracy for a few special degrees of freedom. An application of the procedure has been developed for the transfer of a proton between two water molecules. Starting from MP2/6-311G** calculations on H5O2+ dimer, we construct the global potential energy surface governing the proton transfer as well as the pattern of charge distributions. In order to study large reactive systems embedded in an external medium, we show how a less demanding procedure can be implemented. It rests on a minimum coupling approach of second-order Taylor expansions of the potential about quasi-stationary points. The resulting potential energy surface is termed a “minimum coupling potential