Unified time‐path approach to the effect of anharmonicity on the molecular vibrational spectroscopy in solution (original) (raw)
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Anharmonic vibrational eigenfunctions and infrared spectra from semiclassical molecular dynamics
The Journal of chemical physics, 2018
We describe a new approach based on semiclassical molecular dynamics that allows simulating infrared absorption or emission spectra of molecular systems with inclusion of anharmonic intensities. This is achieved from semiclassical power spectra by computing first the vibrational eigenfunctions as a linear combination of harmonic states, and then the oscillator strengths associated with the vibrational transitions. We test the approach against a 1D Morse potential and apply it to the water molecule with results in excellent agreement with discrete variable representation quantum benchmarks. The method does not require any grid calculations, and it is directly extendable to high dimensional systems. The usual exponential scaling of the basis set size with the dimensionality of the system can be avoided by means of an appropriate truncation scheme. Furthermore, the approach has the advantage to provide IR spectra beyond the harmonic approximation without losing the possibility of an in...
Calculation of anharmonic vibrational spectroscopy of small biological molecules
PhysChemComm, 2002
The role of anharmonic effects in the vibrational spectroscopy of small biological molecules and their 1 : 1 complexes with water is discussed. The strengths and limitations of the vibrational self-consistent field (VSCF) method and its extensions as a computational tool for this purpose are examined. Anharmonic coupling between different vibrational modes is found to be very important for these systems, even for fundamental transitions, and incorporation of these effects seems essential for quantitative interpretation of experimental data. Both analytical, empirical force fields, and potential surfaces computed from electronic structure methods are used in VSCF calculations of several benchmark systems and compared with experimental spectroscopic data. Glycine in several conformers, the glycine-water complex, and N-methylacetamide are among the systems discussed. The main conclusions are: (1) Electronic structure methods such as MP2/DZP and density functional B97, give very good agreement with experimental data. Thus, MP2 and B97 clearly provide an accurate description of the anharmonic interactions. VSCF calculations, including all modes, with MP2, B97 and other successful methods are presently feasible for molecules with up to 15-20 atoms. (2) The electronic structure methods seem to give spectroscopic predictions in much better accord with experiment than standard empirical force fields such as AMBER or OPLS. The anharmonic couplings provided by these methods differ greatly, in the cases tested to date, from the ab initio ones. The implications of these results for future modeling of small biomolecules are discussed. Comments are provided on future directions in this subject, including extensions to large biomolecules.
A new methodology for dealing with time-dependent quantities in anharmonic molecules I: theory
Theoretical Chemistry Accounts, 2014
Morse oscillator coherent states tool has not witnessed much use or applications in quantum dynamics and non-equilibrium statistical mechanics due to the lack of rules of operations and hence the inability to deal with the Morse time evolution operator while still in the coherent states representation. This paper is about developing these needed operation rules of Morse coherent states and applying them to evaluate time correlation functions and thus be able to look at dynamics. This paper further provides two different approaches to dealing with the Morse oscillator propagator while still in coherent states representation, avoiding resorting to eigenstate representation or any other path integral techniques, such as initial value representation approach. Two approaches (one exact and another approximate) are developed to show how to handle anharmonic time evolution operator when acting on Morse coherent states, and calculate time correlation functions analytically. The Morse oscillator partition function is reproduced using the two approaches so as to test the correctness and applicability of the herein methodology. Additionally, the autocorrelation function is derived for a Morse wavepacket pumped on to the excited state, which is represented by a displaced Morse oscillator. A unitary transformation is utilized in order to move from the ground-state nuclear Hamiltonian to excited-state Hamiltonian. Evaluating this autocorrelation function using Morse coherent states representation without the alludedto-unitary transformation in the future may become possible as more progress is made on this novel approach. Absorption spectra are calculated. It is noticed in those spectra that while the zero-phonon line (ZPL) does not seem to be measurably affected by anharmonicity and only the phonon-side band (PSB) is shifted and broadened in case of weak linear electron-phonon coupling [Huang-Rhys factor (S) is less than unity], both the ZPL and PSB are noticeably affected in case S [ 1. It is further observed that a Voigt profile (a product of Lorenzian and Gaussian in the time domain) predominates the spectrum in case of an appreciable anharmonicity in the molecule. It is inferred that anharmonicity can be critically significant even at low temperature. It is finally concluded that quadratic exponential in the Morse oscillator energy eigenvalue that emerges presents itself as a Gaussian envelope in the autocorrelation function, leading to broadening, whereas the red shift is attributed only to the anharmonicity.
2008
The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotationalvibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.
Toward anharmonic computations of vibrational spectra for large molecular systems
The subtle interplay of several different effects makes the interpretation and analysis of experimental spectra in terms of structural and dynamic characteristics a very challenging task. In this context, theoretical studies can be very helpful, and this is the reason behind the rapid evolution of computational spectroscopy from a highly specialized research field toward a versatile and widespread tool. However, in the case of vibrational spectra of large molecular systems, the most popular approach still relies on a harmonic treatment, because of the difficulty to explore the multidimensional anharmonic potential energy surface. These can be overcome considering that, in many cases, the vibrational transitions are well localized and only some of them are observed experimentally. To this aim, the procedure for the simulation of vibrational spectra of large molecular systems beyond the harmonic approximation is discussed. The quality of system-specific reduced dimensional anharmonic approaches is first validated by comparison with computations taking into account all modes simultaneously for anisole and glycine. Next, the approach is applied to two larger systems, namely glycine adsorbed on a silicon surface and chlorophyll-a in solution, and the results are compared with experimental data showing significant improvement over the standard harmonic approximation. Our results show that properly tailored reduced dimension anharmonic approaches stand as feasible routes for state-of-the-art computational spectroscopy studies and allow to take into account both anharmonic and environmental effects on the spectra even for relatively large molecular systems.
Chemical Physics, 2009
It is well-known that the mirror image between absorption and fluorescence spectra is held for the displaced harmonic-oscillator system, and also this mirror image is independent to the chiral symmetry in which the excited-state potential energy surface is right-handed or left-handed with respect to the ground-state potential energy surface. As the first-order approximation of anharmonic correction is added into the displaced harmonic oscillator, this mirror image is broken down, and then the spectra can be depended on the chiral symmetry mentioned above. Both absorption and fluorescence coefficients are derived analytically within the first-order anharmonic approximation and numerical test is carried out to demonstrate the breaking down of the mirror image. Based on the same analysis, the electron transfer rate is derived analytically within the first-order anharmonic approximation. This rate might take the form of Arrhenius's equation but not form of Marcus's equation. Furthermore, it is found that this rate is also depending on the chiral symmetry.
Journal of Chemical Theory and Computation, 2010
We report some results on the calculation of vibrational spectra of molecules in condensed phase with accounting simultaneously for anharmonicity and solute-solvent interactions, the latter being described by means of the polarizable continuum model (PCM). Density functional theory force fields are employed as well as a new implementation of the PCM cavity and its derivatives. The results obtained for formaldehyde and simple peptide prototypes show that our approach is able to yield a quantitative agreement with experiments for vacuo-to-solvent harmonic and anharmonic frequency shifts.
Scalable Computing: Practice and Experience
Vibrational spectra of the two conformers of the free formic acid molecule are computed by two approaches, with a special emphasis on the region of O-H stretching modes. The first approach (referred to as a static one) is based on sequential computation of anharmonic O-H stretching vibrational potential and numerical solution of the vibrational Schr\"{o}dinger equation by the Numerov method. The second approach (referred to as a dynamic one) is based on molecular dynamics (MD) simulations performed within the atom-centered density matrix propagation scheme (ADMP) followed by spectral analysis of the velocity-velocity and dipole moment autocorrelation functions computed from the ADMP MD trajectories. All calculations are carried out within the density functional tight binding (DFTB) formalism. The computed properties are compared to the available experimental data and the advantages of the dynamic versus the static approach are outlined and analyzed in the context of detection o...
Advances in Quantum Chemistry, 2005
We here present a combined VA, VCD, Raman and ROA vibrational study of phenyloxirane. We have simulated the vibrational absorption (VA), also called IR, vibrational circular dichroism (VCD), Raman scattering and Raman optical activity (ROA) intensities utilizing the density functional theory (DFT) B3LYP hybrid exchange correlation functional and other exchange-correlation functionals (PBE, PW91, PBE1) with the 6-31G(d,p), 6-31++G(d,p), cc-pVDZ, aug-cc-pVDZ, cc-pVTZ and augmented correlation consistent polarized valence triple zeta (aug-cc-pVTZ) basis sets. Previously authors have focused on either the VA and VCD spectra or the Raman and ROA spectra of molecules, since the experimental and theoretical instruments and methods for calculating these quantities are quite distinct. Here we show that the combined analysis gives more information, especially with respect to the electric dipole, magnetic dipole, electric dipole-electric dipole polarizability, electric dipoleelectric quadrupole polarizability and electric dipole-magnetic dipole polarizability changes during the various induced transitions. The coupling of vibrational and electronic excitations may be used to aid in understanding the photo induced chemical reactivity observed in many systems. This work is a continuation of our goal to interpret the results of experimental studies on the basis of theoretical results, which can help to understand the structure and function of proteins, other biomolecules and ligands in their native environments. As the physical tools used to observe and study biological processes have evolved, so have the theoretical methods and models to interpret, understand and completely utilize the results of these new measurements. The work on developing methods for modeling amino acids, peptides, proteins and ligands in both the non aqueous (lipid) and aqueous environments has involved, of course, many groups. A review of our contributions to this field has recently been presented. In addition to interpreting existing and new experimental results, we will discuss structural, energetic, conformational, and vibrational studies on a variety of systems that have been used to test and validate levels of theory, and in addition to suggest modifications to existing levels of theory, which can make them even more useful than they currently are. Contents 1. Introduction 92 2. Methods and materials 93 3. Results 95 3.1. Structure 95 3.2. Vibrational absorption 99 3.3. Vibrational circular dichroism 101 3.4. Raman scattering 107
Chemical Physics Letters, 2007
Time-dependent density functional theory (TDDFT) is combined with the correlation-corrected vibrational self-consistent field method to calculate the fundamental vibrational frequencies of the electronic excited states of diatomic, triatomic, and tetraatomic molecules. Equation of motion coupled-cluster calculations are also carried out for comparison. TDDFT is shown to provide the harmonic and anharmonic frequencies for various excited states with reasonable accuracy by using hybrid functionals, except that several vibrational modes such as hydrogen atom stretching exhibit sizable discrepancies due to the lack of orbital relaxation process in TDDFT.