The anharmonic potential energy surface of methyl fluoride

A large experimental spectroscopic data set sensitive to the cubic anharmonic potential energy surface (PES) of methyl fluoride has been compiled from the literature for six symmetric and asymmetric top isotopomers of methyl fluoride: 12CH3F, 13CH3FF, 12CD3F, 13CD3F, 12CHD2F and 12CH2DF. This empirical data set has been used to critically assess the best available literature ab initio cubic force field and various 'improved' theoretical force fields. A perturbation-resonance approach to the calculation of the observables from the force constants has been utilized and existing PESs were found to reproduce the data poorly. The careful treatment required for the correct theoretical reproduction of empirical spectroscopic constants arising from highly correlated least-squares fits to the original data is discussed. A new fit to the data has been performed (optimising 19 of the 38 cubic force constants) resulting in a much improved PES. The latter has been used to predict currently unknown spectroscopic constants for the least well-characterised isotopomer 12CH2DF. The prospects for a future empirical determination of the complete cubic force field of methyl fluoride are discussed and new data most likely to yield new information on the PES identified.     

Energy levels of two interacting particles in an anharmonic potential

Energy levels of two interacting mass points in an anharmonic model potential (Morse type) have been studied. Analytic expression for the energy levels has been worked out. The model potential is shown to support bound states under certain conditions. The number of such states has been found to depend on the parameters of the potential. The potential is expected to be more realistic, particularly in presence of environments for diatomic molecules and artificial atoms. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Third-order anharmonic potential constants and equilibrium structures of the formyl and hydroperoxyl radicals

Observed vibration—rotation constants for HCO/DCO and HO₂/DO₂ are combined with vibrational frequencies and ground-state rotational constants in order to derive harmonic as well as third-order anharmonic potential constants, and also equilibrium structure parameters for the formyl and hydroperoxyl radicals. The “diagonal” terms of the third-order anharmonic constants thus obtained for the stretching modes are discussed in terms of the diatomic-molecule model.     

A new approach to solve the Schrodinger equation with an anharmonic sextic potential

In this study, the N-dimensional radial Schrodinger equation with an anharmonic sextic potential is solved by the extended Nikirov-Uranov method. We prove that the radial function can be factorised as the product between an exponential function and a polynomial function solution of the biconfluent Heun equation. The approach investigated in this article aims to be an alternative to other known methods of solving, as it has the advantage of dealing with simple, first-order differential and algebraic equations and avoiding numerous and laborious coordinate transformations and series expansions.

     

A simple method for determining potential parameters for anharmonic molecular vibrations

Analytical formulae allowing one to find in a simple way the parameters of a model potential for anharmonic molecular vibrations are presented.     

Parametrization of an anharmonic Kirkwood-Keating potential for AlxGa1-xAs alloys

We introduce a simple semiempirical anharmonic Kirkwood-Keating potential to model A(x)B(1-x)C-type semiconductors. The potential consists of the Morse strain energy and Coulomb interaction terms. The optical constants of pure components, AB and BC, were employed to fit the potential parameters such as bond-stretching and -bending force constants, dimensionless anharmonicity parameter, and charges. We applied the potential to finite temperature molecular-dynamics simulations on Al(x)Ga(1-x)As for which there is no lattice mismatch. The results were compared with experimental data and those of harmonic Kirkwood-Keating model and of equation-of-motion molecular-dynamics technique. Since the Morse strain potential effectively describes finite temperature damping, we have been able to numerically reproduce experimentally obtained optical properties such as dielectric functions and reflectance. This potential model can be readily generalized for strained alloys.     

The highly anharmonic BH5 potential energy surface characterized in the ab initio limit

The strong sensitivity to level of theory of the salient features of the ground state potential energy surface of BH(5) has been overcome by rigorously converged ab initio computations employing correlation-consistent basis sets cc-p(C)VXZ (X=2-6), explicitly correlated R12 corrections, and coupled-cluster theory complete through quadruple excitations (CCSDTQ). Extrapolations via our focal point method yield a C(s)-symmetry global minimum of BH(3)-H(2) type featuring interfragment B-H distances of (1.401, 1.414) A, an H(2) bond length elongated to 0.803 A, and a BH(3)+H(2) dissociation energy D(e)(D(0))=6.6 (1.2) kcal mol(-1). The classical barriers for H(2) internal rotation and hydrogen scrambling are 0.07 and 5.81 kcal mol(-1), respectively, above the BH(5) minimum. Our thermochemical computations yield Delta(f)H(0) ( degrees )[BH(5)(g)]=-111.3+/-0.2 kcal mol(-1)+Delta(f)H(0) ( degrees )[B(g)], which is limited in accuracy only by persistent uncertainties in the enthalpy of formation of gaseous boron. As a first step in investigating the extremely anharmonic 12-dimensional vibrational dynamics of BH(5), a complete quartic force field has been computed at the all-electron cc-pCVQZ CCSD(T) level of theory. Previous matrix isolation infrared assignments of the nu(2) and nu(9) stretching modes of BH(5) compare favorably with our computed vibrational fundamentals, but the experimental assignment of the nu(6) bending mode of the BH(3) moiety is not supported by computed isotopic shifts.     

The vibration-rotation spectrum and anharmonic potential of H3

Some qualitative effects of anharmonicity on the spectra of H₃⁺ and D₃⁺ between low vibrational levels are described. Using large-basis vibration-rotation calculations with a Morse-based discrete variable representation for the vibrations and a symmetric-top basis for the rotations, new spectra of H₃⁺ and D₃⁺ have been assigned. This procedure was assisted by adjusting eight coefficients for H₃⁺ and six coefficients for D₃⁺ in the Meyer-Botschwina-Burton ab initio potential function, and eventually 621 new and old lines of H₃⁺ to levels up to 3ν₂ and 529 new and old lines of D₃⁺ to levels up to 2ν₂ have been fitted with standard deviations of 0.118 and 0.059 cm⁻¹, respectively. An attempt is made to compare five different potential energy functions for the H₃⁺ system, two ab initio and three adjusted to fit spectra of H₃⁺ or D₃⁺, by expanding them by the same procedure in the same variables. For extension of the present work to higher vibrational levels, more accurate boundary behaviour at linear configurations will be required, and some aspects of the use of hyperspherical coordinates are discussed.     

Anisotropic two-body problem under the Buckingham potential

Journal of Mathematical Chemistry - We present a qualitative study of the dynamics of two-point masses interacting via an anisotropic generalized Buckingham potential. We describe the asymptotic...     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

Anharmonic properties of the vibrational quantum computer

We developed an efficient approach to study the coherent control of vibrational state-to-state transitions. The approximations employed in our model are valid in the regime of the low vibrational excitation specific to the vibrational quantum computer. Using this approach we explored how the vibrational properties of a two-qubit system affect the accuracy of subpicosecond quantum gates. The optimal control theory and numerical propagation of laser-driven vibrational wave packets were employed. The focus was on understanding the effect of the three anharmonicity parameters of the system. In the three-dimensional anharmonicity parameter space we identified several spots of high fidelity separated by low fidelity planar regions. The seemingly complicated picture is explained in terms of interferences between different state-to-state transitions. Very general analytic relationships between the anharmonicity parameters and the frequencies are derived to describe the observed features. Geometrically, these expressions represent planes in the three-dimensional anharmonicity parameter space. Results of this work should help to choose a suitable candidate molecule for the practical implementation of the vibrational two-qubit system.     

Multireference space without first solving the configuration interaction problem

We further develop an idea to generate a compact multireference space without first solving the configuration interaction problem previously proposed for the ground state (GS) (Glushkov, Chem. Phys. Lett. 1995, 244, 1). In the present contribution, our attention is focused on low‐lying excited states (ESs) with the same symmetry as the GS which can be adequately described in terms of an high‐spin open‐shell formalism. Two references Møller–Plesset (MP) like perturbation theory for ESs is developed. It is based on: (1) a main reference configuration constructed from the parent molecular orbitals adjusted to a given ES and (2) secondary double excitation configuration built on the GS like orbitals determined by the Hartree–Fock equations subject to some orthogonality constraints. It is shown how to modify the MP zeroth‐order Hamiltonian so that the reference configurations and corresponding excitations are eigenfunctions of it and are compatible with orthogonality conditions for the GS and ES. Intruder states appearance is also discussed. The proposed scheme is applied to the GS, ES, and excitation energies of small molecules to illustrate and calibrate our calculations. © 2013 Wiley Periodicals, Inc.     

Anharmonic thermochemistry of cyclopentadiene derivatives

This paper focuses on the thermochemistry of some derivatives of cyclopenta‐1,3‐diene, namely, 5‐methylcyclopenta‐1,3‐diene, 5‐ethylcyclopenta‐1,3‐diene, 5‐formylcyclopenta‐1,3‐diene, 5‐methylcyclopenta‐1,3‐diene‐1‐yl radical, 5‐ethylcyclopenta‐1,3‐diene‐1‐yl radical, 5‐carbonylcyclopenta‐1,3‐diene radical, 1‐formylcyclopenta‐2,4‐diene‐1‐yl radical, 5‐methylenecyclopenta‐1,3‐diene radical, 5‐ethylidenecyclopenta‐1,3‐diene radical, and 3,6‐dimethylenecyclohexa‐1,4‐diene. Several different chemistries of these compounds are of interest in combustion modeling. Here, we present gas‐phase thermochemical properties for the above cited species, which are, except for 3,6‐dimethylenecyclohexa‐1,4‐diene, previously unknown. These were obtained from corrected (using bond additivity corrections) high‐level ab initio quantum chemistry calculations validated with well‐known compounds including cyclopentane, cyclopentene, cyclopenta‐1,3‐diene, and cyclopentadienyl radical. Heat capacities and entropies have been corrected for anharmonic molecular motions, in particular for internal rotations. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 453–463, 2003     

Anharmonic vibrational averages for formaldehyde

In order to interpret the measured average of any physical observable in an excited vibrational state it is necessary to consider the anharmonic force field. It is convenient to use first-order perturbation theory to form the anharmonic averages and, to this end, one requires the cubic force constants in normal-coordinate space. These have been derived from two model force fields and have been used to compute the anharmonic coefficients necessary for the interpretation of measured average dipole moments in the excited states of formaldehyde.     

Anharmonic nuclear dynamics in the mixed quantum-classical limit

This study employs mixed quantum-classical dynamics (MQCD) formalism to evaluate the linear electronic dipole moment time correlation function (DMTCF) in which a Morse oscillator serves to model the associated vibrations in a mixed quantum-classical (MQC) environment. While the main purpose of this work is to study the applicability of MQCD formalism to anharmonic systems in condensed phase, approximate schemes to physically evaluate the mathematically divergent integrals have been developed in order to deal with the essential singularities that arise while evaluating the Morse oscillator canonical partition function and the DMTCF in MQC systems in the classical limit. The motivation for numerically and analytically evaluating these divergent integrals is that a partition function of any system should lead to a finite value at any temperature and therefore this divergence is unphysical. Additionally, since a partition function is to signify the number of accessible states to the system at hand, divergent results are not physically acceptable. As such, straightforward approximate analytic expressions, at different levels of rigor, for both the classical Morse oscillator partition function and the DMTCF in MQC systems are derived, for the first time. Calculations of Morse oscillator partition function values using different approaches at various temperatures for CO, HCl, and I(2) molecules, showing good results, are presented to test the expressions derived herein. It is found that this divergence, due to singularity, diminishes upon lowering the temperature and only arises at high temperatures. The gradual diminishing of the singularity upon lowering the temperature is sensible since the Morse potential fits the parabolic potential at low temperatures. Model calculations and discussion of the DMTCF and linear absorption spectra in MQC systems using the molecular constants of CO molecule are provided. The linear absorption lineshape is derived by two methods, one of which is asymptotic expansion.     

A potential harmonic method for the three-body coulomb problem

A potential harmonic method that is suitable for the three-body coulomb systems is presented. This method is applied to solve the three-body Schroedinger equations for He and e ⁺ e ⁻ e ⁺ directly, and the calculations yield very good results for the energy. For example, we obtain a ground-state energy of −0.26181 hartrees for e ⁺ e ⁻ e ⁺, and −2.90300 hartrees for He with finite nuclear mass, in good agreement with the exact values of −0.26200 hartrees and −2.90330 hartrees. Compared with the full-set calculations, the errors in the total energy for ground and excited states of e ⁺ e ⁻ e ⁺ are very small, around −0.0001 hartrees. We conclude that the present method is one of the best PH methods for the three-body coulomb problem. Received: 5 September 1996 / Accepted: 14 July 1997     

Polarization-corrected molecular electrostatic potential for the cation binding problem

The molecular electrostatic potential (MESP) and polarization-corrected MESP (PMESP) minima for some small molecules are calculated on the surface generated by rolling cations (Li⁺ and Na⁺) on their van der Waals surfaces. The cation binding energies of these molecules are obtained with HF/6-31G^** level ab initio calculations. A noteworthy outcome of the present study is that the plot of these binding energies and the corresponding PMESP surface minimum values turns out to be remarkably linear with a slope close to unity. The PMESP is thus found to work as a powerful tool for unearthing the patterns of cation binding sites and energetics for molecular systems.     

Perturbation expansions,symanzik scaling,and padé-type approximants: The anharmonic oscillator problem

The problem of representing an observable F(z) in the Padé scheme from its formal perturbative (Taylor) expansion in z is considered. It is demonstrated how the representation could be improved by incorporating in a simple manner, in the course of constructing such approximants, the knowledge of asymptotic (z → ∞) power-law behavior of F(z). Comparison with the usual approximants is made with a thorough numerical survey on error estimates and variations of error with z, input information, and quantum number. Spectacular performance of the new strategy is exemplified. Test calculations chiefly involve various properties of the first five eigenenergy states of the quartic anharmonic oscillator system. A few consistency requirements, including the virial theorem, are also studied. © 1993 John Wiley & Sons, Inc.