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.     

Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.     

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.     

Torsional anharmonicity in the conformational analysis of beta-D-galactose

Schemes to include a treatment of torsional anharmonicity in the conformational analysis of biological molecules are introduced. The approaches combine ab initio electronic energies and harmonic frequencies with anharmonic torsional partition functions calculated using the torsional path integral Monte Carlo method on affordable potential energy surfaces. The schemes are applied to the conformational study of the monosaccharide beta-d-galactose in the gas phase. The global minimum structure is almost exclusively populated at 100 K, but a large number of conformers are present at ambient and higher temperatures. Both quantum mechanical and anharmonic effects in the torsional modes have little effect on the populations at all temperatures considered, and it is, therefore, expected that standard harmonic treatments are satisfactory for the conformational study of monosaccharides.     

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.     

Rate constants from the reaction path Hamiltonian. II. Nonseparable semiclassical transition state theory

For proton transfer reactions, the tunneling contributions to the rates are often much larger than thermally activated rates at temperatures of interest. A number of separable tunneling corrections have been proposed that capture the dependence of tunneling rates on barrier height and imaginary frequency size. However, the effects of reaction pathway curvature and barrier anharmonicity are more difficult to quantify. The nonseparable semiclassical transition state theory (TST) of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)] accounts for curvature and barrier anharmonicity, but it requires prohibitively expensive cubic and quartic derivatives of the potential energy surface at the transition state. This paper shows how the reaction path Hamiltonian can be used to approximate the cubic and quartic derivatives used in nonseparable semiclassical transition state theory. This enables tunneling corrections that include curvature and barrier anharmonicity effects with just three frequency calculations as required by a conventional harmonic transition state theory calculation. The tunneling correction developed here is nonseparable, but can be expressed as a thermal average to enable efficient Monte Carlo calculations. For the proton exchange reaction NH2 + CH4 <==> NH3 + CH3, the nonseparable rates are very accurate at temperatures from 300 K up to about 1000 K where the TST rate itself begins to diverge from the experimental results.     

Effect of model potential of adsorptive bond on the thermodynamic properties of adsorbed CO molecules on Ni(111) surface

The effect of anharmonicity on the adsorption of CO molecules on the Ni(111) surface has been investigated. The DFT calculations are used to obtain the effective adsorption potential of the CO molecule on the Ni(111) surface. First, using an appropriate slab model, the geometry of adsorption system corresponding to hcp, fcc, bridge, and on-top sites with p(2 x 2) arrangement and coverage of 0.25 ML is optimized by the DFT calculations using a plane wave basis set and ultrasoft pseudopotentials; this gives the hcp site as the most stable site with De = 185 kJ/mol, for which the equilibrium distance of CO from the surface and C-O bond length on the surface are found to be 1.31 and 1.192 A, respectively. Then, the potential function of adsorption versus adsorptive bond distance was plotted, which is significantly different from that of a harmonic oscillator, i.e., the anharmonicity for the adsorptive bond is significant. Also the harmonic and anharmonic shifts of vibrational frequencies of adsorptive and C-O bonds are calculated to be -22.6 and 7.8 cm(-1), respectively. Hence, two potential models are selected for which their Schr?dinger equations are solved analytically, namely the hard repulsion-soft attraction (HS) and Morse potential (MP) models. The adsorption isotherms, internal energy, isochoric heat capacity, and entropy of adsorbed CO molecules have been calculated for the mentioned model potentials and compared with those of the harmonic oscillator (H). As a result, the adsorption isotherms are not considerably sensitive to the model potential. The anharmonicity of CO-Ni bond, which is included in HS and MP models, gives an average deviation in pressure as much as 1.4% for HS and 5.8% for MP, compared to 6.1% for the H model. However, isochoric heat capacity and entropy depend on the model potential significantly, and the differences may be as high as 69% and 55% for isochoric heat capacity and entropy, respectively.     

Promotion of deep tunneling through molecular barriers by electronic-nuclear coupling

Deep electronic tunneling through molecular barriers in donor-bridge-acceptor complexes is studied using an analytically solvable model. The effective tunneling matrix element is formulated as a sum over vibronic tunneling pathways. For a symmetric system the frequency of tunneling oscillations is shown to increase with the strength of electronic-nuclear coupling at the bridge, the number of electronic-nuclear coupling sites, or the frequency of a bridge vibration. Acceleration by several orders of magnitude is demonstrated within the range of realistic molecular parameters.     

Phonon-assisted second harmonic generation in As(1)(-)(x)Bi(x)Te(3)-CaBr(2)-PbBr(2) glasses

We have found experimentally the IR-induced second harmonic generation (SHG) in glasses possessing different degrees of electron-phonon interactions. For the investigations, we have chosen As(1)(-)(x)()Bi(x)Te(3)-CaBr(2)-PbBr(2) (0 < x <1) glasses. General formalism is based on consideration of fifth-order nonlinear optical susceptibility. The effect is observed in the middle IR region (spectral range 0.92-10.5 microm) where the value of the electronic energy gap is commensurable to the energies of actual quasi-phonons participating in the anharmonic (non-centrosymmetric) electron-phonon interactions. Varying the As/Bi ratio allows us to operate by the degree of electron-phonon anharmonicity in a wide spectral range. The second harmonic generation (SHG) output signal shows a correlation with IR-induced anharmonic phonon modes within the 1.5-4.8 microm spectral range. A maximum value of SHG is achieved at pump-probe delaying times of about 12.5-20 ps, which are typical for relaxation of the anharmonic electron-quasi-phonon subsystem. The maximally achieved value of the phonon-assisted optical susceptibility was about 6 x 10(-38) m(4)/V(4). The SHG signal was saturated for the IR pump power densities of about 1.73 GW/cm(2), corresponding to output SHG signals of about 9.8 x 10(-4) with respect to the fundamental ones. By varying the degree of electron-phonon anharmonicity and changing content of glasses, it was unambiguously shown that the IR-induced SHG signal correlates well with changes of oscillator strengths of IR-induced anharmonic phonon modes.     

Anharmonicity of amide modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.     

Anharmonicity of a molecular oscillator

The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d³E/d Q ³ ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )_N = 0 and λ = (?k/?N) _Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Effects of anharmonicity on nonadiabatic electron transfer: a model

The effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabatic electron transfer is probed by examining the dependence of the transition probability on the exoergicity. The Franck-Condon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the first-order perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wave-packet propagations on a numerical grid. The transition-probability expression incorporating a high-frequency quantum mode and low-frequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarse-graining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.     

Analysis of local anharmonicity using Gaussian model potentials and cartesian oscillator basis sets: example, HCN

This paper examines local anharmonic vibrations in molecules using an analysis that starts with an ab initio potential energy surface, fits a model potential constructed of Gaussian basis functions, and proceeds to a quantum mechanical analysis of the anharmonic modes using Cartesian harmonic oscillator basis functions in a variational calculation. The objective of this work is to suggest methods, with origins in nuclear and molecular (electronic) quantum mechanics, that should be useful for the accurate analysis of the local anharmonic motions of hydrogen, and perhaps other atoms or small molecular fragments, residing in molecularly complicated but otherwise harmonic environments.     

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate: Formalism and Application to Azulene?

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.     

Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field (VSCF) method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy, entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates.     

Prediction of vibrational frequencies of UO2(2+) at the CCSD(T) level

Electronic structure calculations at the coupled cluster (CCSD(T)) and density functional theory levels with relativistic effective core potentials and large basis sets were used to predict the isolated uranyl ion frequencies. The effects of anharmonicity and spin-orbit corrections on the harmonic frequencies were calculated. The anharmonic effects are larger than the spin-orbit corrections, but both are small. The anharmonic effects decreased all the frequencies, whereas the spin-orbit corrections increased the stretches and decreased the bend. Overall, these two corrections decreased the harmonic asymmetric stretch frequency by 6 cm-1, the symmetric stretch by 3 cm-1, and the bend by 3 cm-1. The best calculated values for UO22+ for the asymmetric stretch, symmetric stretch, and bend were 1113, 1032, and 174 cm-1, respectively. The separation between the asymmetric and the symmetric stretch band origins was predicted to be 81 cm-1, which is consistent with experimental trends for substituted uranyls in solution and in the solid state. The anharmonic vibrational frequencies of the isoelectronic ThO2 molecule also were calculated and compared to experiment to calibrate the UO22+ results.     

Including anharmonicity in the calculation of rate constants. II. The OH+H2-->H2O+H reaction

A recently developed method for calculating anharmonic vibrational energy levels at nonstationary points along a reaction path that is based on second-order perturbation theory in curvilinear coordinates is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the title reaction. Two different potential energy surfaces were employed for these calculations, an improved version of the author's surface 5 and the WSLFH surface of Wu et al. [J. Chem. Phys. 113, 3150 (2000)]. We present detailed comparisons of rate constants computed for the two surfaces with and without anharmonicity and with various approximations for incorporating tunneling along the reaction path. The results for this system are quite sensitive to the surface employed, the choice of coordinates (curvilinear versus rectilinear), and the inclusion of anharmonicity. A comparison with experiment provides information on the accuracy of these surfaces.     

Including anharmonicity in the calculation of rate constants. 1. The HCN/HNC isomerization reaction

A method for calculating anharmonic vibrational energy levels in asymmetric top and linear systems that is based on second-order perturbation theory in curvilinear coordinates is extended to the bound generalized normal modes at nonstationary points along a reaction path. Explicit formulas for the anharmonicity coefficients, x(ij), and the constant term, E0, are presented, and the necessary modifications for resonance cases are considered. The method is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the HCN/HNC isomerization reaction. Although the results for this system are not very sensitive to the choice of coordinates, we find that the inclusion of anharmonicity leads to a substantial improvement in the vibrational energy levels. We also present detailed comparisons of rate constants computed with and without anharmonicity, with various approximations for incorporating tunneling along the reaction path, and with a more practical approach to calculating the vibrational partition functions needed for larger systems.     

Importance of anharmonicity, recrossing effects, and quantum mechanical tunneling in transition state theory with semiclassical tunneling. A test case: the H2 + Cl hydrogen abstraction reaction

The hydrogen abstraction reaction from H2 by the Cl atom is studied by means of the variational transition state theory with semiclassical tunneling coefficients on the BW2 potential energy surface. Vibrational anharmonicity and coupling between the bending modes are taken into account. The occurrence of trajectories that recross the transition state is estimated by means of the canonical unified statistical method and by classical trajectories calculations. Different semiclassical methods for tunneling calculations are tested. Our results show that anharmonicity has a small but nonnegligible effect on the thermal rate constants, recrossing can be neglected, and tunneling is adequately described by the least-action approximation, and less successfully by the large-curvature version 3 approximation. However, the large-curvature version 4 and small-curvature approximations lead to a severe underestimation of tunneling. Thermal rate constants calculated using transition state theory including anharmonicity and tunneling agree very well with accurate quantal thermal rate constants over a wide temperature range, although the improvement over the harmonic transition state theory with the microcanonically optimized semiclassical tunneling approximation (based on version 3 of the large-curvature tunneling method) used in a previous study of this reaction is only marginal.     

Vibrational spectroscopy for glycine adsorbed on silicon clusters: Harmonic and anharmonic calculations for models of the Si(1 0 0)-2 × 1 surface

The vibrational spectroscopy of a glycine molecule adsorbed on a silicon surface is studied computationally, using different clusters as models for the surface. Harmonic frequencies are computed using density functional theory (DFT) with the B3LYP functional. Anharmonic frequency calculations are carried out using vibrational self-consistent field (VSCF) algorithms on an improved PM3 potential energy surface. The results are compared with experiments on Glycine@Si(1 0 0)-2 × 1.

The main findings are: (1) Agreement of the computed frequencies with experiment improves with cluster size. (2) The anharmonic calculations are generally in better agreement with experiment than the harmonic ones. The improvements due to anharmonicity are most significant for hydrogenic stretching. (3) An important part of the anharmonic effects is due to anharmonic coupling between different normal modes of the system. (4) The anharmonic coupling between glycine vibrational modes is much larger than the anharmonic coupling between glycine and “phonon” (cluster) modes.

Implications of the results for surface vibrational spectroscopy are discussed.