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.     

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 vibrational properties of explosives from temperature-dependent Raman

Raman spectra from 50 to 3500 cm(-1) and 4-296 K are analyzed for molecular crystal powders of the explosives pentaerythritol tetranitrate (PETN), beta-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), and 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) and the inert naphthalene. Temperature-dependent Raman spectroscopy is utilized for its sensitivity to anharmonic couplings between thermally populated phonons and higher frequency vibrations relevant to shock up-pumping. The data are analyzed with anharmonic perturbation theory, which is shown to have significant fundamental limitations in application to real data. Fitting to perturbation theory revealed no significant differences in averaged anharmonicities among the three explosives, all of which exhibited larger averaged anharmonicities than naphthalene by a factor of 3. Calculations estimating the multiphonon densities of states also failed to correlate clearly with shock sensitivity. However, striking differences in temperature-dependent lifetimes were obvious: PETN has long lived phonons and vibrons, HMX has long lived phonons but short lived vibrons, while TATB has short lived phonons and vibrons at low temperature. Naphthalene, widely used as a model system, has significantly different anharmonicities and density of states from any of the explosives. The data presented suggest the further hypothesis that hindered vibrational energy transfer in the molecular crystals is a significant factor in shock sensitivity.     

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.     

Anharmonic vibrational probe for N-methylacetamide in different micro-environments

In the present study, anharmonic vibrational properties of the amide modes in N-methylacetamide (NMA), a model molecule for peptide vibrational spectroscopy, are examined by DFT calculations. The 3N-6 normal mode frequencies, diagonal and off-diagonal anharmonicities are evaluated by means of the second order vibrational perturbation theory (VPT2). Good performance of B3LYP/6-31+G** is found for predicting vibrational frequencies in comparison with gas phase experimental data. The amide vibrational modes are assigned through potential energy distribution analysis (PED). The solvation effect on the amide vibrational modes is modeled within the PCM method. From gas phase to polar solvents, red shifts are observed for both harmonic and anharmonic vibrational frequency of amide I mode while the CO bond length increases upon the solvent polarity. Cubic and quartic force constants are further calculated to evaluate the origin of the anharmonicity for the amide I mode of NMA in different micro-environments.     

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.     

Anharmonic midinfrared vibrational spectra of benzoic acid monomer and dimer

Anharmonic vibrational calculations for the benzoic acid monomer and dimer in the mid-IR regime (500-1800 cm(-1)) are reported. Harmonic frequencies and intensities are obtained at the DFT/B3LYP level of theory employing D95(d,p) and cc-pVTZ basis sets. Anharmonic corrections obtained from standard perturbation theory lead to redshifts of 1%-3%. In almost all cases, the resulting frequencies deviate by less than 1% from previous measurements [Bakker et al., J. Chem. Phys. 119, 11180 (2003)]. Calculated intensities are in qualitative agreement with the absorption experiment, with the cc-pVTZ values being superior to the D95(d,p) ones for a few modes of the dimer. The antisymmetric out-of-plane bending mode of the dimer, which is strongly blueshifted with respect to the monomer frequency, represents a remarkable exception: The harmonic frequencies obtained for the two basis sets differ notably from each other, and the anharmonically corrected frequencies deviate from the experimental value by 8% [D95(d,p)] or 3% (cc-pVTZ). Nonperturbative calculations in reduced dimensionality reveal that the relatively small total anharmonic shift (few tens of cm(-1)) comprises of partly much larger contributions (few hundreds of cm(-1)) which are mostly canceling each other. Many of the individual anharmonic couplings are beyond the validity of second-order perturbation theory based on cubic and semidiagonal quartic force constants only. This emphasizes the need for high-dimensional, nonperturbative anharmonic calculations at high quantum-chemical level when accurate frequencies of H-atom vibrations in double hydrogen bonds are sought for.     

Anharmonic vibrational properties by a fully automated second-order perturbative approach

This paper describes the implementation of a fully automated code for the building of anharmonic force constants and their use in a second-order perturbative evaluation of vibrorotational parameters. Next, a number of test applications are discussed, which show the strengths and limits of various computational levels.     

Anharmonic vibrational spectroscopy and investigation of intramolecular mode couplings in adenine

Vibrational frequencies for the nucleobase adenine are calculated by the vibrational self-consistent field (VSCF) and correlation corrected vibrational self-consistent field (CC-VSCF) methods using Hartree-Fock (HF), density functional theory (DFT) and second order Møller-Plesset (MP2) theories. A large number of potential energy surface (PES) points were computed in the anharmonic calculations corresponding to each method. The quartic force field (QFF) approximation was used to generate the full grid of points for the VSCF solver. We have implemented our new procedure for computing the mode-mode coupling integrals in the 2-mode coupling representations of the quartic force field (2MR-QFF) for prediction of coupling magnitudes. Calculations were performed using the 6-31G(d,p) basis set. Comparison of the calculated ab initio anharmonic spectra with Ar matrix experimental data of adenine reported in the literature reveals that, the CC-VSCF (DFT) wavenumbers show the best agreement. The experimental geometric parameters of adenine are compared with the theoretically optimized molecular structural parameters. These are found to be in good agreement. Vibrational assignments are based on the calculated potential energy distribution (PED) values.     

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.     

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.     

Temperature-dependent vibrational dephasing in molecular crystals: a picosecond cars study of naphthalene

The temperature dependence of picosecond CARS of vibrational excitons in naphthalene is presented. Below ≈40 K relaxation is dominated by spontaneous emission of phonons. Above 40 K high-frequency phonons induce dephasing. The results are consistent with a phonon-promoted energy transfer process.     

Anharmonic vibrational modes of nucleic acid bases revealed by 2D IR spectroscopy

Polarization-dependent two-dimensional infrared (2D IR) spectra of the purine and pyrimadine base vibrations of five nucleotide monophosphates (NMPs) were acquired in D(2)O at neutral pH in the frequency range 1500-1700 cm(-1). The distinctive cross-peaks between the ring deformations and carbonyl stretches of NMPs indicate that these vibrational modes are highly coupled, in contrast with the traditional peak assignment, which is based on a simple local mode picture such as C═O, C═N, and C═C double bond stretches. A model of multiple anharmonically coupled oscillators was employed to characterize the transition energies, vibrational anharmonicities and couplings, and transition dipole strengths and orientations. No simple or intuitive structural correlations are found to readily assign the spectral features, except in the case of guanine and cytosine, which contain a single local CO stretching mode. To help interpret the nature of these vibrational modes, we performed density functional theory (DFT) calculations and found that multiple ring vibrations are coupled and delocalized over the purine and pyrimidine rings. Generally, there is close correspondence between the experimental and computational results, provided that the DFT calculations include explicit waters solvating hydrogen-bonding sites. These results provide direct experimental evidence of the delocalized nature of the nucleotide base vibrations via a nonperturbative fashion and will serve as building blocks for constructing a structure-based model of DNA and RNA vibrational spectroscopy.     

Coriolis interaction and intramolecular vibrational redistribution: A high-resolution spectroscopic probe of the rotational contribution to vibrational

We present here high-resolution fluorescence excitation spectra of the 12₀² band of pyrimidine in a molecular beam, which provide compelling ev     

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.     

Evaluation of quantum correlation functions from classical data: Anharmonic models

The previously introduced method of evaluating quantum mechanical time correlation functions using as input only classical simulation data is generalized and applied to two anharmonic model systems, as a further test. The quantum correction approach utilizes the relation between a general quantum correlation function and its classical analog. For the tested models, we obtain numerical results of nonlinear correlation functions with comparable accuracy to that of the centroid molecular dynamics method, although the present method is much simpler to implement and not limited to real valued quantum correlation functions.     

尿嘧啶及其5位取代物分子的指纹区间的非谐性振动特征

在B3LYP/6-311++G~(**)水平上利用振动二阶微扰理论对2-吡啶酮,尿嘧啶及其5-取代物:5-溴-尿嘧啶、5-氯-尿嘧啶、5-氟-尿嘧啶、5-三氟甲基-尿嘧啶、5-腈-尿嘧啶、5-羟基-尿嘧啶(排斥式和氢键式)、胸腺嘧啶分子做了非谐性计算,研究这些分子在1 600~1 850 cm-1指纹区间振动模式的非谐性频率,非谐性常数与取代基影响的关系,并计算了费米共振峰,用振动激子模型模拟了耦合常数.和2-吡啶酮中的C=O和C=C伸缩振动相比,不同的5位取代基引起嘧啶分子中C=O跃迁偶极矩波动,取代基的电负性使C=C伸缩的跃迁偶极矩增加,并使得嘧啶分子中C=O和C=C伸缩振动之间的相互作用值改变显著,跃迁偶极耦合常数值和跃迁振动电子立方密度充分说明电子相互作用对模式间的耦合起着关键作用.     

Anharmonic vibrational frequencies and vibrationally averaged structures and nuclear magnetic resonance parameters of FHF-

The anharmonic vibrational frequencies of FHF(-) were computed by the vibrational self-consistent-field, configuration-interaction, and second-order perturbation methods with a multiresolution composite potential energy surface generated by the electronic coupled-cluster method with various basis sets. Anharmonic vibrational averaging was performed for the bond length and nuclear magnetic resonance indirect spin-spin coupling constants, where the latter computed by the equation-of-motion coupled-cluster method. The calculations placed the vibrational frequencies at 580 (nu(1)), 1292 (nu(2)), 1313 (nu(3)), 1837 (nu(1) + nu(3)), and 1864 cm(-1) (nu(1) + nu(2)), the zero-point H-F bond length (r(0)) at 1.1539 A, the zero-point one-bond spin-spin coupling constant [(1)J(0)(HF)] at 124 Hz, and the bond dissociation energy (D(0)) at 43.3 kcal/mol. They agreed excellently with the corresponding experimental values: nu(1) = 583 cm(-1), nu(2) = 1286 cm(-1), nu(3) = 1331 cm(-1), nu(1) + nu(3) = 1849 cm(-1), nu(1) + nu(2) = 1858 cm(-1), r(0) = 1.1522 A, (1)J(0)(HF) = 124+/-3 Hz, and D(0) = 44.4+/-1.6 kcal/mol. The vibrationally averaged bond lengths matched closely the experimental values of five excited vibrational states, furnishing a highly dependable basis for correct band assignments. An adiabatic separation of high- (nu(3)) and low-frequency (nu(1)) stretching modes was examined and found to explain semiquantitatively the appearance of a nu(1) progression on nu(3). Our calculations predicted a value of 186 Hz for experimentally inaccessible (2)J(0)(FF).     

Converged vibrational energy levels and quantum mechanical vibrational partition function of ethane

The vibrational partition function of ethane is calculated in the temperature range of 200-600 K using well-converged energy levels that were calculated by vibrational configuration interaction, and the results are compared to the harmonic oscillator partition function. This provides the first test of the harmonic oscillator approximation for a molecule with more than five atoms. The absolute free energies computed by the harmonic oscillator approximation are in error by 0.59-0.62 kcal/mol over the 200-600 K temperature range.