Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.     

Application of the effective harmonic oscillator method to computing the thermal averages for a system of coupled anharmonic oscillators

By treating the Hamiltonian for coupled oscillators with polynomial anharmonicity by the Gibbs-Bogoliubov inequality, the effective harmonic oscillator (EHO) method is developed and applied to computing the thermal averages for polyatomic molecules. Practical utility is demonstrated with calculations of electron diffraction quantities, namely the distance r_a and amplitude l, and of the vibrational partition functions for CO₂, CS₂, SO₂ and H₂O from spectroscopic data on the force fields. The results are compared with those in the literature obtained by more accurate techniques. A comparison of r_a and l was also made with the results of electron diffraction measurements.     

Vibrational spectroscopy of the G...C base pair: experiment, harmonic and anharmonic calculations, and the nature of the anharmonic couplings

The results of harmonic and anharmonic frequency calculations on a guanine-cytosine complex with an enolic structure (a tautomeric form with cytosine in the enol form and with a hydrogen at the 7-position on guanine) are presented and compared to gas-phase IR-UV double resonance spectral data. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces; the improved PM3 potential surfaces are obtained from standard PM3 theory by coordinate scaling such that the improved PM3 harmonic frequencies are the same as those computed at the RI-MP2/cc-pVDZ level. Comparison of the data with experimental results indicates that the average absolute percentage deviation for the methods is 2.6% for harmonic RI-MP2/cc-pVDZ (3.0% with the inclusion of a 0.956 scaling factor that compensates for anharmonicity), 2.5% for harmonic RI-MP2/TZVPP (2.9% with a 0.956 anharmonicity factor included), and 2.3% for adapted PM3 CC-VSCF; the empirical scaling factor for the ab initio harmonic calculations improves the stretching frequencies but decreases the accuracy of the other mode frequencies. The agreement with experiment supports the adequacy of the improved PM3 potentials for describing the anharmonic force field of the G...C base pair in the spectroscopically probed region. These results may be useful for the prediction of the pathways of vibrational energy flow upon excitation of this system. The anharmonic calculations indicate that anharmonicity along single mode coordinates can be significant for simple stretching modes. For several other cases, coupling between different vibrational modes provides the main contribution to anharmonicity. Examples of strongly anharmonically coupled modes are the symmetric stretch and group torsion of the hydrogen-bonded NH2 group on guanine, the OH stretch and torsion of the enol group on cytosine, and the NH stretch and NH out-of-plane bend of the non-hydrogen-bonded NH group on guanine.     

Decoherence in an anharmonic oscillator coupled to a thermal environment: a semiclassical forward-backward approach

The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.     

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.     

Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory

Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.     

Quantum solution of coupled harmonic oscillator systems beyond normal coordinates

Normal coordinates can be defined as orthogonal linear combinations of coordinates that remove the second order couplings in coupled harmonic oscillator systems. In this paper we go further and explore the possibility of using linear although non-orthogonal coordinate transformations to get the quantum solution of coupled systems. The idea is to use as non-orthogonal linear coordinates those which allow us to express the second-order Hamiltonian matrix in a block diagonal form. To illustrate the viability of this treatment, we first apply it to a system of two bilinearly coupled harmonic oscillators which admits analytical exact solutions. The method provides in this case, as an extra mathematical result, the analytical expressions for the eigenvalues of a certain type of symmetrical tridiagonal matrices. Second, we carry out a numerical application to the Barbanis coupled oscillators system, which contains a third order coupling term and cannot be solved in closed form. We demonstrate that the non-orthogonal coordinates used, named oblique coordinates, are much more efficient than normal coordinates to determine the energy levels and eigenfunctions of this system variationally.     

Revealing anharmonic couplings and energy relaxation in DNA oligomers by ultrafast infrared spectroscopy

The identification and characterization of NH 2 hydrogen-bonded stretching vibrations [nu(NH 2)] in DNA oligomers is usually hampered by the all-dominating absorption of the water stretching band in the spectral range of 3050-3600 cm(-1). Here, we use the two-color IR pump-probe technique to overcome the limitations of linear absorption spectroscopy by exciting adenine-thymine (A-T) oligomer vibrations in the fingerprint region and analyzing induced transient spectral changes in the nu(NH2) spectral region. These transient changes are related to anharmonic couplings to the modes excited in the fingerprint region and to modes populated by intra- and intermolecular energy redistribution and relaxation. The combination of calculated anharmonic coupling parameters and experimental transient IR data allows the assignment of a transition at 3215 cm(-1) to the nu(NH2) vibration of adenine in dA(20)-dT(20) DNA oligomers.     

Vibrational spectroscopy of triacetone triperoxide (TATP): anharmonic fundamentals, overtones and combination bands

The vibrational spectrum of triacetone triperoxide (TATP) is studied by the correlation-corrected vibrational self-consistent field (CC-VSCF) method which incorporates anharmonic effects. Fundamental, overtone, and combination band frequencies are obtained by using a potential based on the PM3 method and yielding the same harmonic frequencies as DFT/cc-pVDZ calculations. Fundamentals and overtones are also studied with anharmonic single-mode (without coupling) DFT/cc-pVDZ calculations. Average deviations from experiment are similar for all methods: 2.1-2.5%. Groups of degenerate vibrations form regions of numerous combination bands with low intensity: the 5600-5800 cm(-1) region contains ca. 70 overtones and combinations of CH stretches. Anharmonic interactions are analyzed.     

Vibrational relaxation of HF colliding with helium. A coupled quantum treatment

Vibrationally inelastic, partial integral cross sections are computed for the HeHF system by solving the vibrational close-coupled (CC) equations via a spherical potential already suggested in the literature. Numerically converged results are obtained, at several collision energies, for single- and multiquantum transitions relevant to yield rate constants in the 1000–10 000 K range of temperatures. Very satisfactory agreements is found with the available experimental data; the highly quantum nature of the present system is surmised as causing the failing of more approximate approaches used before.     

Vibrational relaxation of oxygen in an argon cage

The vibrational relaxation of oxygen embedded in an argon cage through vibrational to local translation, rotation, and argon phonon modes has been studied using semiclassical procedures. The collision model is based on the trapped molecule undergoing the restricted motions (local translation and hindered rotation) in a cage formed by its twelve nearest argon neighbors in a face-centered-cubic structure. At 85 K in the liquid argon temperature range, the deexcitation probability of O(2)(v=1) is 5.8 x 10(-12) and the relaxation rate constant with the collision frequency from local translation is 23 s(-1). The rate constant decreases to 5.1 s(-1) at 50 K and to 0.016 s(-1) at 10 K in the solid argon temperature range. Transfer of the vibrational energy to local translation, rotation (both hindered and free), and argon phonon modes is the relaxation pathway for the trapped oxygen molecule.     

Membrane inclusions as coupled harmonic oscillators: effects due to anisotropic membrane slope relaxation

Membrane-mediated interaction between membrane-spanning peptides or protein segments plays an important role in their function and stability. Our rigorous "coupled harmonic oscillators" representation is extended to account for the complex boundary conditions permitting anisotropic relaxation of the membrane slope along the contours of the inclusions. Using this representation and applying a highly efficient finite-difference algorithm, we have analyzed the membrane-mediated interaction triggered by deformation of the hydrophobic tails of lipid molecules to match the lipophilic exterior of the inserted peptide. We establish that anisotropic relaxation crucially affects the interaction energy, leading to a short-range attraction between two inclusions, while conventional isotropic boundary conditions result in their strong repulsion. In a multi-inclusion cluster, this attraction is further enhanced and modified due to nonpairwise interactions. The results for dimyristoyl phosphatidylcholine and glyceryl monooleate membranes are compared, and the effects of the inclusion radius are considered. The possible role of slope relaxation in the reported stabilization of linked gramicidin channels and in proteins' functional cooperativity is outlined.     

On the wigner-kirkwood coordinate probability distribution of an asymmetric anharmonic oscillator; an addendum

In a recent publication we calculated the Wigner—Kirkwood coordinate distribution function for a symmetric single- or double-well anharmonic oscillator. By a simple transformation, the results are generalized for an asymmetric anharmonic oscillator.     

Vibrational spectroscopy of protonated imidazole and its complexes with water molecules: ab initio anharmonic calculations and experiments

The results of anharmonic frequency calculations on neutral imidazole (C3N2H4, Im), protonated imidazole (ImH+), and its complexes with water (ImH+)(H2O)n, are presented and compared to gas phase infrared photodissociation spectroscopy (IRPD) data. Anharmonic frequencies are obtained via ab initio vibrational self-consistent field (VSCF) calculations taking into account pairwise interactions between the normal modes. The key results are: (1) Prediction of anharmonic vibrational frequencies on an MP2 ab initio potential energy surface show excellent agreement with experiment and outstanding improvement over the harmonic frequencies. For example, the ab initio calculated anharmonic frequency for (ImH+)(H2O)N2 exhibits an overall average percentage error of 0.6% from experiment. (2) Anharmonic vibrational frequencies calculated on a semiempirical potential energy surface fitted to ab initio harmonic data represents spectroscopy well, particularly for water complexes. As an example, anharmonic frequencies for (ImH+)H2O and (ImH+)(H2O)2 show an overall average deviation of 1.02% and 1.05% from experiment, respectively. This agreement between theory and experiment also supports the validity and use of the pairwise approximation used in the calculations. (3) Anharmonic coupling due to hydration effects is found to significantly reduce the vibrational frequencies for the NH stretch modes. The frequency of the NH stretch is observed to increase with the removal of a water molecule or replacement of water with N2. This result also indicates the ability of the VSCF method to predict accurate frequencies in a matrix environment. The calculation provides insights into the nature of anharmonic effects in the potential surface. Analysis of percentage anharmoncity in neutral Im and ImH+ shows a higher percentage anharmonicity in the NH and CH stretch modes of neutral Im. Also, we observe that anharmonicity in the NH stretch modes of ImH+ have some contribution from coupling effects, while that of neutral Im has no contribution whatsoever from mode-mode coupling. It is concluded that the incorporation of anharmonic effects in the calculation brings theory and experiment into much closer agreement for these systems.     

Dynamics of anharmonic surfaces in harmonic crystals

Explicit expressions are given for the effective equations of motion for surface atoms placed in a general anharmonic potential and attached to semi-infinite harmonic bulk substrates. Three types of one-dimensional substrates are considered: i) continuous dispersionless, ii) discrete with nearest neighbours harmonic interactions, and iii) a substrate showing a strong spatial dispersion due to next-nearest neighbours interactions. The elimination of the harmonic degrees of freedom of the dispersionless substrate i) reduces the problem to the damped Duffing oscillator in the case of an external force applied to the surface atom, and to an extended Duffing oscillator with time-dependent coefficients in the case of scattering of a phonon incoming from the bulk. In both remaining cases [ii) and iii)]the resulting equations of motion are Volterra integro-differential equations. The equations of motion obtained allow for the study of transitive regimes, of higher harmonics generation and of chaotic behaviour, due to the surface anharmonicity.     

Vibrational spectroscopy of (SO4(2-)).(H2O)n clusters, n=1-5: harmonic and anharmonic calculations and experiment

The vibrational spectroscopy of (SO4(2-)).(H2O)n is studied by theoretical calculations for n=1-5, and the results are compared with experiments for n=3-5. The calculations use both ab initio MP2 and DFT/B3LYP potential energy surfaces. Both harmonic and anharmonic calculations are reported, the latter with the CC-VSCF method. The main findings are the following: (1) With one exception (H2O bending mode), the anharmonicity of the observed transitions, all in the experimental window of 540-1850 cm(-1), is negligible. The computed anharmonic coupling suggests that intramolecular vibrational redistribution does not play any role for the observed linewidths. (2) Comparison with experiment at the harmonic level of computed fundamental frequencies indicates that MP2 is significantly more accurate than DFT/B3LYP for these systems. (3) Strong anharmonic effects are, however, calculated for numerous transitions of these systems, which are outside the present observation window. These include fundamentals as well as combination modes. (4) Combination modes for the n=1 and n=2 clusters are computed. Several relatively strong combination transitions are predicted. These show strong anharmonic effects. (5) An interesting effect of the zero point energy (ZPE) on structure is found for (SO4(2-)).(H2O)(5): The global minimum of the potential energy corresponds to a C(s) structure, but with incorporation of ZPE the lowest energy structure is C2v, in accordance with experiment. (6) No stable structures were found for (OH-).(HSO4-).(H2O)n, for n相似文献   

The coherent state and anharmonic oscillator description of nonlinear oscillation

A perturbation solution of the nonlinear oscillation of the form $$\ddot x + \omega ^2 x + bx^2 + ax^3 = 0$$ is obtained, using the coherent states constructed out of quantum oscillator states. The equation of the spine obtained here is compared with that obtained by using an averaging procedure. It is found that the equation obtained in the present case is simpler and different from the other. Also the method used here has the distinct advantage that it is suitable for any nonlinear oscillator containing both even and odd higher order terms.     

Vibrational contributions to indirect spin-spin coupling constants calculated via variational anharmonic approaches

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.