Anharmonic correction factor for vibrational sum of states

A 'small molecule' model is used to demonstrate, by comparison with the exact result, that the method of steepest descents yields an excellent approximation to the sum of states for a collection of independent Morse oscillators. It is then shown that the anharmonicity correction factor due to Haarhoff is grossly inaccurate at high energies.     

Configuration selection within vibrational multiconfiguration self-consistent field theory: application to bridged lithium compounds

A configuration selection scheme has been used to speed up vibrational multiconfiguration self-consistent field calculations. Deviations with respect to reference calculations were found to be negligible while yielding an acceleration of about two orders of magnitude. Its application to bridged lithium compounds (Li(2)H(2), Li(2)F(2), Li(2)O(2), and Li(3)F(3)) based on high-level coupled-cluster potential energy surfaces provides accurate vibrational transitions for all fundamental modes. The explicit inclusion of 4-mode couplings was found to be important for Li(2)H(2).     

Anharmonic oscillator model of overtone spectra for D3h symmetry molecules

The bond stretching vibrations of XF₅ molecules with D_3h symmetry are treated computationally on the Morse oscillator model in which the bond oscillators are coupled harmonically. Each calculation involves four parameters for two types of Morse potential and three parameters for the kinetic-energy, potential coupling terms. The eigenvalue formula for overtone and combination states up to three are presented and can be used to predict all the vibrational energy levels from local mode molecules through normal mode molecules. For PF₅, AsF₅ and VF₅, the coupled Morse oscillator model gives a prediction in good agreement with the experimental data.     

Anharmonic vibrational levels of the two cyclic isomers of SiC3

Using coupled-cluster approach full six-dimensional analytic potential energy surfaces for two cyclic SiC(3) isomers [C-C transannular bond (I) and Si-C transannular bond (II)] have been generated and used to calculate anharmonic vibrational wave functions. Several strong low-lying anharmonic resonances have been found. In both isomers already some of the fundamental transitions cannot be described within the harmonic approximation. Adiabatic electron affinities and ionization energies have been calculated as well. The Franck-Condon factors for the photodetachment processes c-SiC(3) (-)(I)-->c-SiC(3)(I) and c-SiC(3) (-)(II)-->c-SiC(3)(II) are reported.     

Raman probing of overtone and combination bands to study the vibrational energy distribution produced by multiple-photon excitation

Vibrational energy distribution in CF₃Br, produced by multiple-photon excitation, is studied with the use of Raman probing of fundamental bands and also overtone and combinations bands. On a collision-free time scale, statistical energy distribution among vibrational modes is found at energies over 7200 cm⁻¹. Possible physical causes of this effect are discussed.     

Renormalized perturbation theory by the moment method for degenerate states: Anharmonic oscillators

We apply renormalized perturbation theory by the moment method to an anharmonic oscillator in two dimensions with a perturbation that couples unperturbed degenerate states. The method leads to simple recurrence relations for the perturbation corrections to the energy and moments of the eigenfunction. We calculate accurate energy eigenvalues, illustrate the general features of the method, and comment on the application of the approach to other quantum mechanical models. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 261–272, 1998     

Anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second-order perturbative approach

The paper reports main results of a comprehensive study of the vibrational spectrum of ketene computed using second-order perturbation theory treatment based on quartic, cubic and semidiagonal quartic force constants. Two different models--a homogeneous model using the same density functionals and basis functions for the harmonic calculations and anharmonic corrections, and a hybrid model in which the two parts of the calculation are conducted using different density functionals and basis sets--have been employed in the present calculations. Different DFT and CCSD methods and DZ and TZ extended basis sets involving diffuse and polarization functions have been used to calculate optimized and vibrationally averaged geometrical parameters, the harmonic and anharmonic vibrational frequencies and the spectroscopic constants such as anharmonicity constants, rotational constants, rotation-vibration coupling constants, Nielsen's centrifugal distortion constants and Coriolis coupling constants. Homogeneous model is found to be superior to the hybrid model in several respects. Difficulties in the hybrid model may arise due to one of the following reasons: (a) the basic requirement that the geometry optimization and frequency calculations must be done at the same level of theory to have valid frequencies is not met in the hybrid model; (b) the molecular structure gets reoptimized at the low level for anharmonic corrections; (c) in addition, the perturbation could also diverge for the above reasons, particularly for the very low, very anharmonic terms where the harmonic approximation is not close enough to make the perturbation work.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

Ab-initio self-consistent field theory for the treatment of interface between two different quasi-one-dimensional chains

The solution of the problem how to treat an interface between two quasi-one-dimensional polymers has been formulated combining Dyson's equation with the mutually consistent field (self-consistent field solutions for the change of the bulk states of the polymers and for the extraband “interface” states) method. A numerical procedure for the implementation of an appropriate program (which needs as input only the ab initio self-consistent field crystal orbital solutions of the two infinite periodic polymers as well as some cluster calculations of the interface and its neighbors at both sides) is outlined. The necessary program is under development.     

Linear-scaling implementation of molecular electronic self-consistent field theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.     

Anharmonic frequencies of CX2Y2 (X, Y = O, N, F, H, D) isomers and related systems obtained from vibrational multiconfiguration self-consistent field theory

Accurate anharmonic frequencies are provided for molecules of current research, i.e., diazirines, diazomethane, the corresponding fluorinated and deuterated compounds, their dioxygen analogs, and others. Vibrational-state energies were obtained from state-specific vibrational multiconfiguration self-consistent field theory (VMCSCF) based on multilevel potential energy surfaces (PES) generated from explicitly correlated coupled cluster, CCSD(T)-F12a, and double-hybrid density functional calculations, B2PLYP. To accelerate the vibrational structure calculations, a configuration selection scheme as well as a polynomial representation of the PES have been exploited. Because experimental data are scarce for these systems, many calculated frequencies of this study are predictions and may guide experiments to come.     

Improved convergence in block copolymer self-consistent field theory by Anderson mixing

A modification to real space polymeric self-consistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing [D. G. Anderson, J. Assoc. Comput. Mach. 12, 547 (1965)], and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.     

Investigations of self-consistent field,scf ci and virtual stateconfiguration interaction vibrational energies for a model three-mode system

Self-consistent field vibrational energy eigenvalues are reported for a model three-mode system considered previously by Noid et al. These eigenvalues and those from configuration interaction calculations based on true SCF wavefunctions and virtual state wavefunctions are compared with the previous semiclassical and exact quantum ones of Noid et al.     

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.     

Eigenvalue independent partitioning and direct minimization in self-consistent field theory

It is pointed out that the matrix elements of a partitioning operator, f, introduced previously for constructing effective hamiltonians, provide natural sets of unconstrained and non-redundant variables in which to formulate self-consistent field theory. The elements of f are complementary to corresponding elements of the density matrix, the relation being essentially that between covariant and contravariant vectors. Some consequences for direct minimization SCF techniques are considered.     

Efficient correlation-corrected vibrational self-consistent field computation of OH-stretch frequencies using a low-scaling algorithm

The authors present a new computational scheme to perform accurate and fast direct correlation-corrected vibrational self-consistent field (CC-VSCF) computations for a selected number of vibrational modes, which is aimed at predicting a few vibrations in large molecular systems. The method is based on a systematic selection of vibrational mode-mode coupling terms, leading to the direct ab initio construction of a sparse potential energy surface. The computational scaling of the CC-VSCF computation on the generated surface is then further reduced by using a screening procedure for the correlation-correction contributions. The proposed method is applied to the computation of the OH-stretch frequency of five aliphatic alcohols. The authors investigate the influence of different pseudopotential and all-electron basis sets on the quality of the correlated potential energy surfaces computed and on the OH-stretch frequencies calculated for each surface. With the help of these test systems, the authors show that their method offers a computational scaling that is two orders of magnitude lower than a standard CC-VSCF method and that it is of equal accuracy.     

On non-exponential unimolecular dissociation of molecules prepared by vibrational overtone excitation

The sensitivity of vibrational overtone excitation experiments to non-RRKM behavior is considered. It is proposed that the experimental results are not inconsistent with intrinsically non-RRKM unimolecular lifetime distribution.     

Infrared overtone spectroscopy and vibrational analysis of a Fermi resonance in nitric acid: Experiment and theory

High resolution infrared spectra of nitric acid have been recorded in the first OH overtone region under jet-cooled conditions using a sequential IR-UV excitation method. Vibrational bands observed at 6933.39(3), 6938.75(4), and 6951.985(3) cm(-1) (origins) with relative intensities of 0.42(1), 0.38(1), and 0.20(1) are attributed to strongly mixed states involved in a Fermi resonance. A vibrational deperturbation analysis suggests that the optically bright OH overtone stretch (2nu1) at 6939.2(1) cm(-1) is coupled directly to the nu1 + 2nu2 state at 6946.4(1) cm(-1) and indirectly to the 3nu2 + nu3 + nu7 state at 6938.5(1) cm(-1). Both the identity of the zero-order states and the indirect coupling scheme are deduced from complementary CCSD(T) calculations in conjunction with second-order vibrational perturbation theory. The deperturbation analysis also yields the experimental coupling between 2nu1 and nu1 + 2nu2 of -6.9(1) cm(-1), and that between the two dark states of +5.0(1) cm(-1). The calculated vibrational energies and couplings are in near quantitative agreement with experimentally derived values except for a predicted twofold stronger coupling of 2nu1 to nu1 + 2nu2. Weaker coupling of the strongly mixed states to a dense background of vibrational states via intramolecular vibrational energy redistribution is evident from the experimental linewidths of 0.08 and 0.25 cm(-1) for the higher energy and two overlapping lower energy bands, respectively. A comprehensive rotational analysis of the higher energy band yields spectroscopic parameters and the direction of the OH overtone transition dipole moment.     

The model of a polyelectrolyte solution with explicit account of counterions within a self-consistent field theory

A theoretical approach to calculating the thermodynamic and structural functions of solutions of polyelectrolytes based on Gaussian equivalent representation for the calculation of functional integrals is proposed. It is noted that a new analytical result of this work is the direct assumption of counterions, along with an equation for the gyration radius of a polymer chain as a function of the concentrations of monomers and added low-molecular salt. An equation of state is obtained within the proposed model. Our theoretical results are used to describe the thermodynamic and structural properties of an aqueous solution of sodium polystyrene sulfonate with additions of NaCl.