Molecular dynamics simulations and instantaneous normal-mode analysis of the vibrational relaxation of the C-H stretching modes of N-methylacetamide-d in liquid deuterated water

Nonequilibrium molecular dynamics (MD) simulations and instantaneous normal mode (INMs) analyses are used to study the vibrational relaxation of the C-H stretching modes (ν(s)(CH?)) of deuterated N-methylacetamide (NMAD) in aqueous (D2O) solution. The INMs are identified unequivocally in terms of the equilibrium normal modes (ENMs), or groups of them, using a restricted version of the recently proposed Min-Cost assignment method. After excitation of the parent ν(s)(CH?) modes with one vibrational quantum, the vibrational energy is shown to dissipate through both intramolecular vibrational redistribution (IVR) and intermolecular vibrational energy transfer (VET). The decay of the vibrational energy of the ν(s)(CH?) modes is well fitted to a triple exponential function, with each characterizing a well-defined stage of the entire relaxation process. The first, and major, relaxation stage corresponds to a coherent ultrashort (τ(rel) = 0.07 ps) energy transfer from the parent ν(s)(CH?) modes to the methyl bending modes δ(CH?), so that the initially excited state rapidly evolves into a mixed stretch-bend state. In the second stage, characterized by a time of 0.92 ps, the vibrational energy flows through IVR to a number of mid-range-energy vibrations of the solute. In the third stage, the vibrational energy accumulated in the excited modes dissipates into the bath through an indirect VET process mediated by lower-energy modes, on a time scale of 10.6 ps. All the specific relaxation channels participating in the whole relaxation process are properly identified. The results from the simulations are finally compared with the recent experimental measurements of the ν(s)(CH?) vibrational energy relaxation in NMAD/D?O(l) reported by Dlott et al. (J. Phys. Chem. A 2009, 113, 75.) using ultrafast infrared-Raman spectroscopy.     

A Monte Carlo simulation of energy transfer processes in thermal unimolecular reactions. II. An applications to polyatomic dissociation

The Monte Carlo method has been used to provide a numerical solution to the ro-vibrational master equation for the low pressure unimolecular decomposition of a polyatomic molecule. This type of solution is made possible through the use of a simple exponential transition probability function, that represents the efficiency with which energy transfer takes place between the reactant molecule and an unspecified heat bath gas. The Monte Carlo technique is used to generate random variables that are distributed in a manner prescribed by the transition probability function. In the case of the present simulation, these variables correspond to random energy jumps induced in the molecule through single collision events. In order to account for the energy dependence of the vibrational state densities, we have proposed that vibrational relaxation in the polyatomic takes place from a single vibrational mode. Under equilibrium conditions we are able to show that with this assumption, the Monte Carlo model is capable of reproducing molecular quantities, such as the average vibrational energy per molecule and the vibrational specific heat, that compare favourable with the corresponding values calculated from equilibrium statistical mechanics. The model has been applied to a study of the low pressure unimolecular decomposition of a series of polyatomics. For three of the molecules, CH₄, CD₄, and C₂H₆ the agreement between the calculated and the high temperature experimental rate constants is very good. The calculations indicate that a significant proportion of the molecules that dissociate are rotationally as well as vibrationally excited. Very few of the reactive molecules have a vibrational energy content equal to or greater than E₀, the dissociation energy. The extent of rotational excitation is found to be temperature dependent.     

Vibrational projection analysis: New tool for quantitatively comparing vibrational normal modes of similar molecules

A new method for quantitatively comparing calculated vibrational modes is described that relies on projecting the vectors describing the normal modes of one molecule onto those of a basis molecule. The procedure virtually automates the assignment of vibrational modes from one molecule to a second, structurally similar one. We illustrate the concept by using the classical Wilson modes of benzene as a basis for describing normal modes of the monosubstituted benzene derivatives phenol, phenol-d5, and phenol radical cation. These examples demonstrate the method's power for accurately assigning and comparing the normal modes of molecules perturbed by chemical substitution, isotopic substitution, or oxidation state. The vibrational projection analysis method—a special case of vector projection analysis—is compared and contrasted with total energy distribution analysis, perhaps the most commonly used technique for quantitatively comparing vibrational modes, and is found superior in each case when comparing normal modes. Vibrational projection analysis need not be limited to single molecules and quantum calculations, because normal modes may be obtained for much larger systems using molecular mechanics or molecular dynamics techniques. The method should therefore prove useful for interpreting the normal modes of ordered periodic solids and structures perturbed by noncovalent contacts, including proteins and polymers. The method may also prove useful in evaluating new computational methods by allowing direct, quantitative comparison of the vibrational modes obtained from different techniques. The power of this technique will make vibrational projection analysis a valuable tool for computational chemists as well as those using calculations to complement vibrational spectroscopic measurements. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1663–1674, 1998     

Direct Vibrational Energy Transfer in Monomeric Water Probed with Ultrafast Two Dimensional Infrared Spectroscopy

Vibrational relaxation dynamics of monomeric water molecule dissolved in d-chloroform solution were revisited using the two dimensional Infrared (2D IR) spectroscopy. The vibrational lifetime of OH bending in monomeric water shows a bi-exponential decay. The fast component (T₁=(1.2±0.1) ps) is caused by the rapid population equilibration between the vibrational modes of the monomeric water molecule. The slow component (T₂=(26.4±0.2) ps) is mainly caused by the vibrational population decay of OH bending mode. The reorientation of the OH bending in monomeric water is determined with a time constant of τ=(1.2±0.1) ps which is much faster than the rotational dynamics of water molecules in the bulk solution. Furthermore, we are able to reveal the direct vibrational energy transfer from OH stretching to OH bending in monomeric water dissolved in d-chloroform for the first time. The vibrational coupling and relative orientation of transition dipole moment between OH bending and stretching that effect their intra-molecular vibrational energy transfer rates are discussed in detail.     

Communication: Probing non-equilibrium vibrational relaxation pathways of highly excited C≡N stretching modes following ultrafast back-electron transfer

Fifth-order nonlinear visible-infrared spectroscopy is used to probe coherent and incoherent vibrational energy relaxation dynamics of highly excited vibrational modes indirectly populated via ultrafast photoinduced back-electron transfer in a trinuclear cyano-bridged mixed-valence complex. The flow of excess energy deposited into four C≡N stretching (ν(CN)) modes of the molecule is monitored by performing an IR pump-probe experiment as a function of the photochemical reaction (τ(vis)). Our results provide experimental evidence that the nuclear motions of the molecule are both coherently and incoherently coupled to the electronic charge transfer process. We observe that intramolecular vibrational relaxation dynamics among the highly excited ν(CN) modes change significantly en route to equilibrium. The experiment also measures a 7 cm(-1) shift in the frequency of a ～57 cm(-1) oscillation reflecting a modulation of the coupling between the probed high-frequency ν(CN) modes for τ(vis) < 500 fs.     

Vibrational analysis of a rate-slowing conformational kinetic isotope effect

An enthalpy-entropy approach to analyzing a rate-slowing conformational kinetic isotope effect (CKIE) in a deuterated doubly-bridged biaryl system is described. The computed isotope effect (k_H/k_D?=?1.075, 368?K) agrees well with the measured value (k_H/k_D?=?1.06, 368?K). The rate-slowing (normal isotope effect) nature of the computed CKIE is shown to originate from a vibrational entropy contribution defined by the twenty lowest frequency normal modes in the ground state and transition state structures. This normal entropy contribution is offset by an inverse vibrational enthalpy contribution, which also arises from the twenty lowest frequency normal modes. Zero point vibrational energy contributions are found to be relatively small when all normal modes are considered. Analysis of the H_ZPE, H_vib, and S_vib energy terms arising from the low frequency vibrational modes reveals their signs and magnitudes are determined by larger vibrational energy differences in the labeled and unlabeled ground state structures.     

Torsionally broken symmetry assists infrared excitation of biomimetic charge-coupled nuclear motions in the electronic ground state

The concerted interplay between reactive nuclear and electronic motions in molecules actuates chemistry. Here, we demonstrate that out-of-plane torsional deformation and vibrational excitation of stretching motions in the electronic ground state modulate the charge-density distribution in a donor-bridge-acceptor molecule in solution. The vibrationally-induced change, visualised by transient absorption spectroscopy with a mid-infrared pump and a visible probe, is mechanistically resolved by ab initio molecular dynamics simulations. Mapping the potential energy landscape attributes the observed charge-coupled coherent nuclear motions to the population of the initial segment of a double-bond isomerization channel, also seen in biological molecules. Our results illustrate the pivotal role of pre-twisted molecular geometries in enhancing the transfer of vibrational energy to specific molecular modes, prior to thermal redistribution. This motivates the search for synthetic strategies towards achieving potentially new infrared-mediated chemistry.

Channelling vibrational excitation energy to achieve ground-state charge-transfer (CT)-assisted isomerization in a donor-bridge-acceptor molecule in solution.     

Extracting effective normal modes from equilibrium dynamics at finite temperature

A general method for obtaining effective normal modes of a molecular system from molecular dynamics simulations is presented. The method is based on a localization criterion for the Fourier transformed velocity time-correlation functions of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, a proper choice of the localization function leads to a novel method with a strong analogy with the usual normal mode analysis of equilibrium structures, where the Hessian system at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio molecular dynamics simulations. Three such examples are provided here. First we recover effective normal modes of an isolated formaldehyde molecule computed at 20 K in very good agreement with the results of a normal mode analysis performed at its equilibrium structure. We then illustrate the applicability of the method for liquid phase studies. The effective normal modes of a water molecule in liquid water and of a uracil molecule in aqueous solution can be extracted from ab initio molecular dynamics simulations of these two systems at 300 K.     

Author index to volume 48

The vibrational energy transfer in a polyatomic molecule is described by introducing an irreducible set of operators. Each operator represents a specific interaction induced by the intermolecular potential. We present a graphic method which significantly facilitates the solution if the number of quantum modes (M) is large.     

Electronic absorption,vibrational spectra,non-linear optical properties,NBO analysis and thermodynamic properties of 9-[(2-hydroxyethoxy) methyl] guanine molecule by density functional method

The Fourier transform infrared (FT-IR) and FT-Raman of 9-[(2-hydroxyethoxy) methyl] guanine (9-2HEMG) have been recorded in the regions 4000–100 and 4000–400 cm⁻¹, respectively. A complete assignment and analysis of the fundamental vibrational modes of the molecule were carried out. The observed fundamental modes have been compared with the harmonic vibrational frequencies computed using DFT (B3LYP) method by employing 6-31G(d,p) and 3-21G basis sets. The vibrational studies were interpreted in terms of potential energy distribution. The first order hyperpolarizability (β₀) and related properties (α, μ and Δα) of this molecular system are calculated using B3LYP/6-31G(d,p) method based on the finite-field approach. Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The results show that electron density (ED) in the σ* and π* antibonding orbitals and second-order delocalization energies (E(²⁾) confirm the occurrence of intramolecular charge transfer (ICT) within the molecule. UV–vis spectrum of the compound has been recorded and electronic properties such as excitation energies, oscillator strength and wavelength are calculated by TD-DFT and CIS methods using B3LYP/6-31G (d,p) basis set. Molecular electrostatic potential (MEP) and HOMO–LUMO energy levels are also constructed. The thermodynamic properties of the title compound have been calculated at different temperatures and the results reveal that the standard heat capacities (C_p,m), standard entropies (S_m) and standard enthalpy changes (H_m) increase with rise in temperature.     

Coherence transfer processes in vibrational relaxation of polyatomic molecules in condensed media

The vibrational relaxation of a polyatomic molecule in a condensed host is studied by a consideration of two molecular vibrations. Relaxation processes, intermode coupling terms and vibrational frequency fluctuation contributions are retained. Population decay (T₁), dephasing (T₂), and coherence transfer rates are evaluated through second order in the limit where the host bath dynamics are rapid compared to these molecular timescales. The rates are expressed in terms of temperature and frequency dependent bath correlation functions. For the special case of a three level system (the ground state and ones where one of the two vibrational modes is excited) the important effects of anharmonicity are incorporated. It is shown that certain coherence transfer terms involve zero frequency bath correlation functions, so they should be larger than the high frequency ones which obey modified energy gap laws. A discussion is presented of the types of interactions which may contribute to these coherence transfer processes.     

Infrared spectroscopy and intramolecular vibrational relaxation of c-C6F12 excited above the dissociation threshold

The IR spectrum of c-C₆F₁₂ at a vibrational energy of twice the dissociation threshold was investigated. Absorption of cw CO₂ laser radiation was measured at various frequencies. Our experimental conditions were chosen such that during absorption measurements all vibrational degrees of freedom were in equilibrium, the molecular rotation being at room temperature. The Boltzmann vibrational distribution allowed computer simulations of the spectrum to be made to determine the homogeneous contribution. The homogeneous half-width of the spectrum is γ=13±0.5 cm⁻¹ and the homogeneous spectrum of c-C₆F₁₂ at E= 60000 cm⁻¹ is non-Lorentzian. We attribute this to the influence of higher-order anharmonicities on the relaxation from the excited mode (v₂₇) to other modes in the molecule.     

Investigations of nuclear dynamics of LaI<Subscript>3</Subscript> molecule. I. Potential functions of normal vibrations in harmonic and anharmonic approximations

The potential energy surface of the LaI₃ molecule is scanned along the normal coordinate by a B3LYP/SDD, SDD method. It is shown that a nonplanar ν₂(A ₂″) vibrational potential function is most anharmonic. The effect of anharmonicity on the root mean square amplitudes of vibrations and the vibrational molecule spectrum is stated.     

Comparative semiempirical and ab initio study of the harmonic vibrational frequencies of aniline—I. The ground state

The harmonic vibrational frequencies of the ground state S₀ of aniline obtained from various ab initio methods [6-31G, 6-31G(*) and 6-31G* basis sets] and semiempirical methods (MINDO/3, MNDO, AM1 and PM3) have been compared to the experimental vibrational spectra. Detailed theoretical analyses of the atomic Cartesian displacements of all normal modes are presented. The semiempirical PM3 method reproduces the experimental frequencies of aniline with comparable accuracy to the ab initio methods. Ale PM3 method will be useful in predicting the vibrational spectra of larger aromatic amines.     

The effects of conformation and intermolecular hydrogen bonding on the structural and vibrational spectral data of naproxen molecule

The structural and vibrational properties of naproxen, an inhibitor of cyclooxygenase (COX) enzyme, were investigated by molecular modeling and experimental IR and Raman spectroscopic techniques. Possible conformers of the molecule were searched via a molecular dynamics simulation carried out with MM2 force field. The total energies, equilibrium geometries, force fields, IR and Raman spectral data of the found stable conformers were determined by means of geometry optimization and harmonic frequency calculations carried out using the B3LYP method and Pople-style basis sets of different size. The stability order obtained for the lowest-energy conformers was confirmed by high-accuracy thermochemistry calculations performed with G3MP2B3 composite method. Some electronic structure parameters of naproxen and the anharmonicity characters of its vibrational modes were determined by means of natural population analysis (NPA) and anharmonic frequency calculations at B3LYP/6-31++G(d,p) and B3LYP/6-311++G(d,p) levels of theory. A part of these calculations carried out for free naproxen molecule were repeated also for its energetically most favored dimer forms. Two different scaling procedures ((1) “SQM-FF methodology” and (2) “Dual scale factors”) were independently applied to the obtained harmonic vibrational spectral data to fit them to the corresponding experimental data. In the light of the obtained calculation results, which confirm the remarkable effects of conformation and intermolecular hydrogen bonding on the structural and vibrational spectral data, in particular, on those associated with the functional groups in the propanoic acid chain, a reliable assignment of the fundamental bands observed in the experimental IR and Raman spectra of the molecule was achieved.     

A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes

A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler–Lagrange equations for molecular fragments ϕ_n described by internal parameters ζ_n. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k_a, adiabatic force constants. Minimization of the kinetic energy of the vibrating fragment ϕ_n yields the adiabatic mass m_a (corresponding to 1/G_nn of Wilson's G matrix) and, by this, adiabatic frequencies ω_a. Adiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 : 1–9, 1998     

Simulations of vibrational spectra from classical trajectories: calibration with ab initio force fields

An algorithm allowing simulating vibrational spectra from classical time-dependent trajectories was applied for infrared absorption, vibrational circular dichroism, Raman, and Raman optical activity of model harmonic systems. The implementation of the theory within the TINKER molecular dynamics (MD) program package was tested with ab initio harmonic force fields in order to determine the feasibility for more extended MD simulations. The results suggest that sufficiently accurate frequencies can be simulated with integration time steps shorter than about 0.5 fs. For a given integration time step, lower vibrational frequencies ( approximately 0-2000 cm(-1)) could be reproduced with a higher accuracy than higher-frequency vibrational modes (e.g., O-H and C-H stretching). In principle, the algorithm also provides correct intensities for ideal systems. In applied simulations, however, the intensity profiles are affected by an unrealistic energy distribution between normal modes and a slow energy relaxation. Additionally, the energy fluctuations may cause weakening of the intensities on average. For ab initio force fields, these obstacles could be overcome by an arbitrary normal mode energy correction. For general MD simulations, averaging of many shorter MD trajectories started with randomly distributed atomic velocities provided the best spectral shapes. alpha-pinene, D-gluconic acid, formaldehyde dimer, and the acetylprolineamide molecule were used in the tests.     

Localization transition of instantaneous normal modes and liquid diffusion

We analyze the structure of instantaneous normal modes (INM) associated with the Hessian matrix of a liquid. Utilizing a scaling theory developed in the framework of Anderson localization studies, we unambiguously identify the crossover point in the INM spectrum between extended and localized modes. We establish a relation between the unstable, delocalized INMs and the liquid diffusion coefficient that appears valid over a large temperature range, covering both Arrhenius and non-Arrhenius regimes of temperature dependence. These results suggest a possible route to theoretically relate dynamics to thermodynamical properties of the liquid via the tomography of the INMs.