Mixed second and third energy derivatives from auxiliary density perturbation theory†

Abstract

The working equations for the calculation of mixed second- and third-order energy derivatives in the framework of auxiliary density functional theory are presented. The perturbations with respect to nuclear displacements and external homogeneous electric field components are calculated with auxiliary density perturbation theory. The presented energy derivative working equations were implemented in deMon2k and validated by vibrational spectra simulations within the double harmonic approximation. The effect of the auxiliary functions on the IR and Raman spectra simulation were analysed for the C₆₀ fullerene. As applications, vibrational spectra of icosahedral carbon fullerenes with up to 540 atoms are calculated without employing symmetry constraints.     

Structural and spectroscopic investigation of the N-methylformamide–water (NMF···3H2O) complex

In this work, theoretical studies on the structure, molecular properties, hydrogen bonding, and vibrational spectra of the N-methylformamide–water (NMF···3H₂O) complex will be presented. The molecular geometry was optimised by using Hartree–Fock (HF), second Møller–Plesset (MP2), and density functional theory methods with different basis sets. The harmonic vibrational frequencies are computed by using the B3LYP method with 6-311++G(d,p) as a basis set and then scaled with a suitable scale factor to yield good coherence with the observed values. The temperature dependence of various thermodynamic functions (heat capacity, entropy, and enthalpy changes) was also studied. A detailed analysis of the nature of the hydrogen bonding, using natural bond orbital (NBO) and topological atoms in molecules theory, has been reported.     

Entropy of flexible liquids from hierarchical force–torque covariance and coordination

ABSTRACT

New theory is presented to calculate the entropy of a liquid of flexible molecules from a molecular dynamics simulation. Entropy is expressed in two terms: a vibrational term, representing the average number of configurations and momentum states in an energy well, and a topographical term, representing the effective number of energy wells. The vibrational term is derived in a hierarchical manner from two force–torque covariance matrices, one at the molecular level and one at the united-atom level. The topographical term comprises conformations and orientations, which are derived from the dihedral distributions and coordination numbers, respectively. The method is tested on 14 liquids, ranging from argon to cyclohexane. For most molecules, our results lie within the experimental range, and are slightly higher than those by the 2PT method, the only other method currently capable of directly calculating entropy for such systems. As well as providing an efficient and practical way to calculate entropy, the theory serves to give a comprehensive characterisation and quantification of molecular structure.     

Frequency spectra of CFC metals and correlated spectral density between bulk atoms

The Green's function generating coefficients method is applied to the calculation of frequency spectra and correlated spectral density for bulk atoms of copper and platinum. The mean square and mean correlated displacements are then deduced. The method is certainly a powerful tool allowing precise calculation of all quantities related to vibrational properties of solids.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

Equations-of-motion approach to quantum mechanics: application to a model phase transition

We present a generalized equations-of-motion method that efficiently calculates energy spectra and matrix elements for algebraic models. The method is applied to a five-dimensional quartic oscillator that exhibits a quantum phase transition between vibrational and rotational phases. For certain parameters, 10 x 10 matrices give better results than obtained by diagonalizing 1000 x 1000 matrices.     

On the convergence of zero-point vibrational corrections to nuclear shieldings and shielding anisotropies towards the complete basis set limit in water

ABSTRACT

The method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.     

The impact of vibrational wave function on low energy electron vibrational scattering from nitrogen molecule

The vibrational wave function of the target theoretically plays an important role in the calculation of vibrational excitation cross sections. By a careful study of the differential cross sections resulting from different vibrational wave functions we find that cross sections are susceptible to vibrational wave functions. Minor changes in the vibration wave function may cause a significant change in the cross section. Even more surprising is that by selecting a few numbers of potential models(which determine the vibrational wave functions) we can often calculate the differential scattering cross section in much closer agreement with experiment in the framework of body-frame vibrational close-coupling theory, which suggest that an accurate potential energy may play a more important role in scattering than we thought before.     

Matrix isolation studies and potential function for perfluorocyclobutane

The infrared and Raman spectra of perfluorocyclobutane isolated in argon matrices at 1:100 and 1:200 mole ratios have been measured between 200 and 2000 cm^?1. Although the ring-puckering fundamental (ν₁₆) was not observed directly, an assignment for the 2 ← 1 (30 cm^?1) transition of ν₁₆ has been deduced from sum and difference bands resolved in the infrared spectrum. Potential functions based upon valence force models are considered in detail and correlated with those of similar ring systems. By using the frequency of the 2 ← 1 transition for ν₁₆ and a vibrational reduced mass of 1501 amu, an approximate model potential function calculation yields a slightly puckered equilibrium conformation with a barrier on the order of 124 cm^?1. The vibrational assignment for perfluorocyclobutane is discussed in terms of the new matrix isolation spectra.     

Determination of vibrational energy levels and transition dipole moments of CO2 molecules by density functional theory

An efficient method is presented to calculate the intra-molecular potential energies and electrical dipole moments of CO₂ molecules at the electronic ground state by solving the Kohn-Sham (KS) equation for a total of 101 992 nuclear configurations. The projector-augmented wave (PAW) exchange-correlation potential functionals and plane wave (PW) basis functions were used in solving the KS equation. The calculated intra-molecular potential function was then included in the pure vibrational Schrödinger equation to determine the vibrational energy eigen values and eigen functions. The vibrational wave functions combined with the calculated dipole moment function were used to determine the transition dipole moments. The calculated results were compared with the experimental data.