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     

Vibrational spectral diffusion of azide in water

Vibrational spectral diffusion denotes the time-dependent fluctuations of a solute's vibrational frequencies due to local environmental dynamics. Vibrational line shapes are weakly sensitive to spectral diffusion, whereas three-pulse vibrational echoes are much more sensitive. We report here on theoretical studies of spectral diffusion of the asymmetric stretch of the azide anion in heavy water. We run a classical molecular dynamics simulation of rigid azide in rigid water, and at every time step we calculate the azide's anharmonic asymmetric stretch frequency using an optimized quantum mechanics/molecular mechanics method developed earlier. This generates a frequency trajectory, which we use to calculate the absorption line shape and integrated three-pulse echo intensity. Our results for both the line width and the integrated echo intensity are in excellent agreement with experiment. Our calculated frequency time-correlation function is in excellent agreement with experiment for long times (greater than 250 fs) but differs considerably from experiment at short times; our theoretical correlation function has a very pronounced oscillation, presumably due to intermolecular azide-water hydrogen-bond stretching dynamics.     

Optimized quantum mechanics/molecular mechanics strategies for nitrile vibrational probes: acetonitrile and para-tolunitrile in water and tetrahydrofuran

The nitrile (Ctriple bondN) group is a powerful probe of structure and dynamics because its vibrational frequency is extraordinarily sensitive to the electrostatic and chemical characteristics of its local environment. For example, site-specific nitrile labels are useful indicators of protein structure because their infrared (IR) absorption spectra can clearly distinguish between solvent-exposed residues and residues buried in the hydrophobic core of a protein. In this work, three variants of the optimized quantum mechanics/molecular mechanics (OQM/MM) technique for computing Ctriple bondN vibrational frequencies were developed and assessed for acetonitrile in water. For the most robust variant, the transferability of the OQM/MM methodology to different solutes and solvents was evaluated by simulating the IR absorption spectra of para-tolunitrile in water and tetrahydrofuran and comparing to experiment and density functional theory (DFT) calculations. The OQM/MM frequencies compared favorably to DFT for para-tolunitrile/water, and the calculated IR absorption spectra are in qualitative agreement with experiment. This suggests that a single parametrization of the OQM/MM technique is reasonable for the calculation of nitrile line shapes when the probe is attached to different chemical moieties and when the label experiences local environments of different polarity.     

Role of quantum chemical calculations in molecular biophysics with a historical perspective

We discuss how the basic principles of quantum chemistry and quantum mechanics can be and have been applied to a variety of problems in molecular biophysics. First, the historical development of quantum concepts in biophysics is discussed. Next, we describe a series of interesting applications of quantum chemical methods for studying biologically active molecules, molecular structures, and some of the important processes which play a role in living organisms. We discuss the application of quantum chemistry to such processes as energy storage and transformation, and the transmission of genetic information. Quantum chemical approaches are essential to comprehend and understand the molecular nature of these processes. To conclude our work, we present a short discussion of the perspectives of quantum chemical methods in modern biophysics, the field of experimental and theoretical chiral vibrational and electronic spectroscopy.     

Vibrational dynamics of the floppy LiNC/LiCN molecular system

Modern spectroscopical techniques allow the efficient experimental investigation of highly excited vibrational states in molecular systems. On the theoretical side, powerful computational methods have also been developed for the calculation of the corresponding energy levels and wave functions, and their interpretation. In this paper we use a combination of two such methods, namely, the distribution of zeroes in the Husimi function and energy-level correlation diagrams, to discuss a classification scheme, for the lowest hundred vibrational levels of the LiNC/LiCN floppy molecular system, based on their dynamical characteristics.     

Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties

A number of recently developed theoretical methods for the calculation of vibrational energies and wave functions are reviewed. Methods for constructing the appropriate quantum mechanical Hamilton operator are briefly described before reviewing a particular branch of theoretical methods for solving the nuclear Schr?dinger equation. The main focus is on wave function methods using the vibrational self-consistent field (VSCF) as starting point, and includes vibrational configuration interaction (VCI), vibrational M?ller-Plesset (VMP) theory, and vibrational coupled cluster (VCC) theory. The convergence of the different methods towards the full vibrational configuration interaction (FVCI) result is discussed. Finally, newly developed vibrational response methods for calculation of vibrational contributions to properties, energies, and transition probabilities are discussed.     

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: application to formaldehyde

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.     

A molecular mechanics force field for conformational analysis of aliphatic acyclic amines

An improved molecular mechanics force field for conformational and vibrational studies of aliphatic acyclic amines is developed. The resulting force field reproduces molecular structures adequately and provides a good fit for energy differences between conformers and barriers to internal rotation for a large number of amines. In addition, vibrational frequencies are calculated in good agreement with available experimental data. When compared with existent force fields for amines, the present force field is considerably more simple and gives rise to calculated properties in closer agreement with experiment.     

QM/MM vibrational mode tracking

Vibrational spectroscopy is a powerful tool to investigate the structure and dynamics of biomolecules. When small subsystems of large molecules such as active centers of enzymes are studied, quantum chemical calculations based on quantum mechanics/molecular mechanics (QM/MM) coupling schemes are a valuable means to interpret the spectra. The goal of this work is a methodological pilot study on how to selectively and thus efficiently extract certain vibrational information for extended molecular systems described by QM/MM methods. This is achieved by an extension of the mode tracking algorithm and a comparison with the partial Hessian diagonalization approach. After validating the methodology for the CO stretching vibration of 2-butanone and a delocalized CO stretch in acetylacetone, the stretching and bending modes of the CO ligand in CO myoglobin are tracked. Such systems represent an ideal application for mode tracking, because only a few strongly localized vibrations are sought for, while the large remainder of the molecule is of interest only as far as it affects these local vibrations. This influence is treated exactly by mode tracking.     

trans-1,2-Dicyano-cyclopropane and other cyano-cyclopropane derivatives

In this work we present the experimental vibrational absorption (VA), vibrational circular dichroism (VCD) and Raman spectra for (+)-trans-1(S),2(S)-dicyanocyclopropane and its dideuterio derivative, trans-1(S),2(S)-dicyano-1(S),2(S)-dideuteriocyclopropane, along with VA, VCD, Raman and Raman optical activity (ROA) spectral simulations. Here we investigate the applicability of various local and non-local exchange-correlation (XC) functionals, hybrids and meta-hybrids to reproduce the vibrational spectra of this strained ring system, which also bears two cyano groups. At the highest level of theory, B3PW91/ aug-cc-pVTZ, we also investigated the trans-, cis- and gem-dicyanocyclopropane (trans-, cis-, and gem-DCCP), cyanocyclopropane (CCP) and the parent molecule cyclopropane (CP). In doing so we have investigated the electronic effects (coupling) between the cyano groups and the cyclopropane ring. In addition to providing an interpretation of the experimentally observed vibrational spectra for these molecules, this work also provides benchmark calculations for other methods, especially semi-empirical based wave function and density functional theory (DFT) based methods, such as SCC-DFTB and PM6. For the semi-empirical DFT based methods to be used for 3-membered ring systems, one ought to document their reliability for systems which were not used in the parameterization. The small 3- and 4-membered ring systems are good test systems because they contain non-standard bonding, which may be difficult to determine accurately with the approximations used in the SCC-DFTB and other semi-empirical methods. Like molecular mechanics force fields, semi-empirical methods, based on DFT and wave function quantum mechanics (WFQM), must be benchmarked against high level ab initio and DFT calculations and experimental data. In addition to bonding, the changes in the electric dipole moment, magnetic dipole moment, electric dipole-electric dipole polarizability, electric dipole-magnetic dipole polarizability and electric dipole-electric quadrupole polarizability with respect to nuclear displacement and nuclear velocity can be determined by the VA, VCD, Raman and ROA intensities. Hence it is important that the semi-empirical based DFT and wave function methods not only be parameterized to determine energies, gradients and Hessians, but also the electric and magnetic moments and their derivatives that determine the electronic and magnetic properties of these molecules and their interactions with matter and radiation. This will allow biochemists, biophysicists, molecular biologists, and physical biologists to use experimental and theoretical VA, VCD, Raman and ROA spectroscopies to probe biophysical and biochemical function and processes at the molecular level. Festschrift in Honor of Philip J. Stephens’ 65th Birthday.     

层状双金属氢氧化物微观结构与性质的理论研究进展

总结了近年来理论计算方法在研究层状双金属氢氧化物(LDHs)结构与功能方面的应用现状. 结合LDHs材料的结构特点, 归纳了量子力学、分子力学、几何建模及物理静电模型相结合对LDHs材料进行结构模拟的思路, 比较了各种方法在LDHs结构模拟上的优势及存在的不足. 量子力学方法能够精确获得水滑石材料的层板构成及作用机制、简单阴离子插层水滑石主客体间的超分子作用实质以及电子性质、反应机理等方面的信息. 与量子力学相比较, 分子力学方法可以快速得到插层水滑石材料的层间阴离子排布及取向、水合膨胀特性及宏观力学性质等. 几何模型和物理静电模型能构建直观、形象的数学模型, 大大简化了计算量,因此能计算接近实际LDHs尺寸的体系, 为推测LDHs结构信息提供了可能性. 随着理论方法和计算机硬件水平的发展, 使得计算机模拟技术逐渐成为获得LDHs材料微观结构参数、电子性质和动力学性质的一种有效手段.     

Quantum chemical studies of FT-IR and Raman spectra of methyl 2,5-dichlorobenzoate

In this paper, experimental and theoretical studies on the molecular structure and vibrational spectra of methyl 2,5-dichlorobenzoate (MDCB) are presented. Fourier transform infrared and Raman spectra of the title molecule in the solid phase were recorded and analyzed. The geometrical parameters were calculated using DFT (B3LYP) with 6-311G(d,p) and 6-311++G(d,p) basis sets, and compared with the experimental data. The vibrational frequencies, infrared intensities and Raman scattering activities were also reported. The detailed assignments were given based on the total energy distribution of the vibrational modes, calculated with scaled quantum mechanics method. The observed and calculated frequencies are found to be in good agreement.     

Dynamics of quantum wave packets in complex molecules traced by 2D coherent electronic correlation spectroscopy

Electronic and nuclear molecular wavepackets are a clear manifestation of the wavelike properties of matter at the very heart of quantum mechanics. In this work we demonstrate how electronic two-dimensional spectroscopy (2D) serves as a highly evolved tool for the simultaneous investigation of both phenomena. In further analysis and theoretical treatments, 2D spectra form an ideal basis for the discussion of electronic decoherence, vibrational relaxation and electron-phonon coupling.     

Density Functional Theory Investigations on Vibrational Spectra,Molecular Structure,and Properties of the L‐Serine,L‐Cysteine,and L‐Aspartic Acid Molecules

In this paper, we present a thorough investigation of the conformational space to characterize all possible gas‐phase structures of the neutral L‐serine, L‐cysteine, and L‐aspartic acid molecules. A total of 120 trial structures were generated for L‐aspartic acid and 96 trial structures for L‐serine and L‐cysteine by combining all internal single‐bond rotamers. Various combinations of the Hartree–Fock and density functional theory/B3LYP methods with different bases were used to optimize all possible trial structures. The theoretical studies on the structure, harmonic vibrational spectra, and molecular properties of these amino acids are presented. The assignments of the calculated wave numbers resulting from potential energy distributions were performed using the VEDA 4 program to allow a good interpretation of the theoretical vibrational spectra of the title compounds. The fundamental harmonic frequencies were found to be in good agreement with data in the literature. A natural bond orbital analysis was performed to investigate the charge delocalization throughout the molecules for the three test compounds. Moreover, an extensive discussion of the highest occupied molecular orbital–lowest unoccupied molecular orbital energy gap as well as other related molecular properties are reported.     

An ab initio force field for the cofactors of bacterial photosynthesis

This article presents a new ab initio force field for the cofactors of bacterial photosynthesis, namely quinones and bacteriochlorophylls. The parameters has been designed to be suitable for molecular dynamics simulations of photosynthetic proteins by being compatible with the AMBER force field. To our knowledge, this is the first force field for photosynthetic cofactors based on a reliable set of ab initio density functional reference data for methyl bacteriochlorophyll a, methyl bacteriopheophytin a, and of a derivative of ubiquinone. Indeed, the new molecular mechanics force field is able to reproduce very well not only the experimental and ab initio structural properties and the vibrational spectra of the molecules, but also the eigenvectors of the molecular normal modes. For this reason it might also be helpful to understand vibrational spectroscopy results obtained on reaction center proteins.     

Multiple grid methods for classical molecular dynamics

Presented in the context of classical molecular mechanics and dynamics are multilevel summation methods for the fast calculation of energies/forces for pairwise interactions, which are based on the hierarchical interpolation of interaction potentials on multiple grids. The concepts and details underlying multigrid interpolation are described. For integration of molecular dynamics the use of different time steps for different interactions allows longer time steps for many of the interactions, and this can be combined with multiple grids in space. Comparison is made to the fast multipole method, and evidence is presented suggesting that for molecular simulations multigrid methods may be superior to the fast multipole method and other tree methods.     

Spectroscopic and theoretical studies on nickel(II) complex of maleonitriledithiolate and 2,2'-bipyridine

The complete IR spectra of the title complex Ni(mnt)(bpy) (mnt=maleonitriledithiolate, bpy=2,2'-bipyridine) and a new method to analyze vibrational spectra for such a complicated metal complex are reported in this paper. The molecular geometry, binding, electronic structure and spectroscopic property of it have been studied in detail by theoretical calculations. The geometry optimization from PM3 calculations give that this molecule is of a planar structure with the symmetry point group C(2v) and its ground state is the spin triplet state. The vibrational and electronic spectra were calculated by PM3 and ZINDO/S methods, respectively. The scientific method of analyzing vibrational spectra is established herein by giving main fixed points and pivotal vibrational units. Besides the regular symbols, the new defined symbols eta and M play an important role in describing the vibration modes accurately and vividly.     

Hydration of l-tyrosine in aqueous medium. An experimental and theoretical study by mixed quantum mechanical/molecular mechanics methods

Quantum mechanical/molecular mechanics (QM/MM) calculations were carried out in order to study the theoretical structures of l-tyrosine in both gas phase and in aqueous solution and observe the changes that occur on the structural and vibrational properties in two phases. Therefore, the molecule was characterized by infrared and Raman spectroscopy in solid phase and aqueous solution. Optimized geometries and relative stabilities for the zwitterion l-tyrosine derivatives have been calculated taking into account the solvent effects by using the self-consistent reaction field (SCRF) theory. For a complete assignment of the IR and Raman spectra of l-tyrosine in solid and aqueous solution phases, density functional theory (DFT) calculations were combined with Pulay's scaled quantum mechanical force field (SQMFF) methodology in order to fit the theoretical wavenumber values to the experimental ones. A good agreement between theoretical and available experimental results is found.     

Copper(II) and cobalt(II) complexes of 2,6-diacetylpyridine bis(<Emphasis Type="Italic">O</Emphasis>-methyloxime): A theoretical investigation

The molecular geometries and vibrational frequencies of the title compounds in the ground state are calculated using the Hartree-Fock (HF) and density functional theory (DFT/B3LYP) methods with the LANL2DZ basis set and compared with the experimental data. The calculated results show that the optimized geometries can well reproduce the crystal structural parameters, and the theoretical vibrational frequencies show good agreement with the experimental values. The energetic behavior of the title compounds in solvent media is examined using the B3LYP method with the LANL2DZ basis set by applying the Onsager and polarizable continuum model (PCM). In addition, molecular electrostatic potential (MEP) and frontier molecular orbital (FMO) analyses of the title compounds are investigated by theoretical calculations.