Vibrational modes in partially optimized molecular systems

In this paper the authors develop a method to accurately calculate localized vibrational modes for partially optimized molecular structures or for structures containing link atoms. The method avoids artificially introduced imaginary frequencies and keeps track of the invariance under global translations and rotations. Only a subblock of the Hessian matrix has to be constructed and diagonalized, leading to a serious reduction of the computational time for the frequency analysis. The mobile block Hessian approach (MBH) proposed in this work can be regarded as an extension of the partial Hessian vibrational analysis approach proposed by Head [Int. J. Quantum Chem. 65, 827 (1997)]. Instead of giving the nonoptimized region of the system an infinite mass, it is allowed to move as a rigid body with respect to the optimized region of the system. The MBH approach is then extended to the case where several parts of the molecule can move as independent multiple rigid blocks in combination with single atoms. The merits of both models are extensively tested on ethanol and di-n-octyl-ether.     

Comparative study of various normal mode analysis techniques based on partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine‐stretch, the spectrum of quinine and a bis‐cinchona derivative, and the low frequency modes of the LAO binding protein. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Mechanisms of local and global molecular quantum gates and their implementation prospects

We explore how the globality of quantum logic operations is ensured in the context of optimal control theory when qubits are encoded in vibrational eigenstates of different normal modes and specially shaped laser fields act as quantum logic operations. In a two-qubit model system, transition mechanisms for optimized laser fields generating single qubit flips, local NOT and global NOT and controlled-NOT (CNOT) gates are investigated and compared. We evaluate the participation of vibrational eigenstates beyond the qubit basis in the global gate mechanisms and how different features of CNOT and NOT gates relate to the characteristics of the vibrational manifold. When a non-qubit normal mode interacting via anharmonic resonances is introduced, neither the global gate mechanisms nor the optimized laser fields show a significant increase in complexity. Similar features of the global quantum gates in both model systems indicate a generality of the deduced principles. Finally, a primary concept for a realization of global quantum gates in an actual experiment referring to state-of-the-art techniques is presented. The possible reconstruction of optimized laser fields with sequences of simple Gaussian subpulses is demonstrated and some critical parameters are deduced.     

Application of THz Vibrational Spectroscopy to Molecular Characterization and the Theoretical Fundamentals: An Illustration Using Saccharide Molecules

This work illustrates several theoretical fundamentals for the application of THz vibrational spectroscopy to molecular characterization in the solid state using two different types of saccharide systems as examples. Four subjects have been specifically addressed: (1) the qualitative differences in the molecular vibrational signatures monitored by THz and mid‐IR vibrational spectroscopy; (2) the selection rules for THz vibrational spectroscopy as applied to crystalline and amorphous systems; (3) a normal mode simulation, using α‐l ‐xylose as an example; and (4) a rigorous mode analysis to quantify the percentage contributions of the intermolecular and intramolecular vibrations to the normal mode of interest.     

Quantum calculation of highly excited vibrational energy levels of CS2(X) on a new empirical potential energy surface and semiclassical analysis of 1:2 Fermi resonance

We report a refined potential energy function for the ground electronic state of CS2 based on a least-squares fitting to several low-lying experimental vibrational frequencies. Energy levels up to 20,000 cm(-1) have been obtained on this empirical potential using the Lanczos algorithm and potential optimized discrete variable representation. Among them, 329 levels below 10,000 cm(-1) are assigned with approximate normal mode quantum numbers (n1, n(0)2, n3), based on expectation values of one-dimensional (1D) reference Hamiltonians. An effective Hamiltonian is extracted from these assigned levels. The agreement with experimental data, including those of several isotopically substituted species, is excellent. In addition, some Fermi and anharmonic resonances are analyzed. The nearest neighbor level spacing and delta3 distributions indicated that the vibrational spectrum of CS2 is largely regular in the energy range up to 20,000 cm(-1). Semiclassical phase space analysis, including bifurcation analysis of the spectroscopic Hamiltonian, is used to interpret subtle anomalies signaled by expectation values used in normal mode assignments. The meaning of Fermi resonance is clarified by contrasting the semiclassical analysis of CS2 and CO2.     

Theoretical investigation of the structure and vibrational spectra of carbamoyl azide

Molecular structure and vibrational frequencies of carbamoyl azide NH2CO-NNN have been investigated with ab initio and density functional theory (DFT) methods. The molecular geometries for all the possible conformers of the molecule were optimized using DFT-B3LYP, DFT-BLYP and MP2 applying the standard 6-311++G** basis set. From the calculations, the molecule was predicted to exist predominantly in cis conformation with the cis-trans rotational barrier of about 7.91-9.10 kcal/mol depending on the level of theory applied. The vibrational frequencies and the corresponding vibrational assignments of carbamoyl azide in Cs symmetry were examined theoretically and the calculated Infrared and Raman spectra of the molecule in the cis conformation were plotted. Observed frequencies for normal modes were compare with those calculated from normal mode coordinate analysis carried out on the basis of ab initio and DFT force fields using the standard 6-311++G** basis set of the theoretical optimized geometry. Theoretical IR intensities and Raman activities are reported.     

Ab initio and DFT studies of the molecular structures and vibrational spectra of succinonitrile

The Molecular structure, conformational stability and vibrational frequencies of succinonitrile NCCH2CH2CN have been investigated with ab initio and density functional theory (DFT) methods implementing the standard 6-311++G* basis set. The potential energy surfaces (PES) have been explored at DFT-B3LYP, HF and MP2 levels of theory. In agreements with previous experimental results, the molecule was predicted to exist in equilibrium mixture of trans and gauche conforms with the trans form being slightly lower in energy. The vibrational frequencies and the corresponding vibrational assignments of succinonitrile in both C2h and C2 symmetry were examined theoretically and the calculated Infrared and Raman spectra of the molecule were plotted. Observed frequencies for normal modes were compared with those calculated from normal mode coordinate analysis carried out on the basis of ab initio and DFT force fields using the standard 6-311++G* basis set of the theoretical optimized geometry. Theoretical IR intensities and Raman activities are reported.     

Rapid anharmonic vibrational corrections derived from partial Hessian analysis

Vibrational analysis within a partial Hessian framework can successfully describe the vibrational properties of a variety of systems where the vibrational modes of interest are localized within a specific region of the system. We have developed a new approach to calculating anharmonic frequencies based on vibrational frequencies and normal modes obtained from a partial Hessian analysis using second-order vibrational perturbation theory and the transition optimized shifted Hermite method. This allows anharmonic frequencies for vibrational modes that are spatially localized to be determined at a significantly reduced computational cost. Several molecular systems are examined in order to demonstrate the effectiveness of this method including organic molecules adsorbed on the Si(100)-2×1 surface, model peptides in solution, and the C-H stretching region of polycyclic aromatic hydrocarbons. Overall, for a range of systems, anharmonic frequencies calculated using the partial Hessian approach are found to be in close agreement with the results obtained using full anharmonic calculations while providing a significant reduction in computational cost.     

Tandem interactions in the self-assembly of ionic block copolymers

The aim of the present review is to show how the phenomena of block copolymer self-assembly and interactions of ionic (or ionizable) groups in polymer systems can be combined to produce materials with versatile and unique behavior. In our discussion, we consider two classes of tandem interactions. First, block copolymers containing short ionic blocks and long nonionic blocks are investigated in organic media. In systems of this type, block copolymer self-assembly and short-range electrostatic interactions act in tandem, forming regular and highly-stable spherical structures. Next, we consider ionic (or ionizable) block copolymers dissolved in aqueous media. In this case, block copolymer self-assembly acts in tandem with the hydrophilic nature of the soluble blocks, resulting in a wide range of unique morphologies.     

Theoretical calculation of positron annihilation spectrum using positron-electron correlation-polarization potential

The positron-electron correlation-polarization potential model is used to calculate annihilation spectra of carbon disulfide and benzene. We assume that the positron is captured in the vibrationally excited states of the target molecule through vibrational Feshbach resonances. Using the standard normal mode representation, we calculated the resonance energies and widths for each vibrational mode. The resonance widths were calculated with Fermi's Golden Rule approximation, where the time-dependent wave packet approach has been applied. We found that vibrational resonances of infrared-active modes play a dominant role in resonant annihilation; however, infrared-inactive modes also contribute to the annihilation spectrum through polarizability changes along normal mode coordinates.     

Density functional theory calculations of the internal rotations and vibrational spectra of 2-, 3- and 4-formyl pyridine

The torsional potentials, molecular conformations and vibrational spectra, of 2-, 3- and 4-formyl pyridine have been investigated using density functional theory (DFT) method with 6-31+G* basis set. From the calculations, 2-formyl pyridine and 3-formyl pyridine were predicted to exist predominantly in cis conformation with the cis-trans rotational barrier of 9.38 kcal/mol and 8.55 kcal/mol, respectively. The two equivalent planar structures of 4-formyl pyridine are separated by an energy barrier of 7.18 kcal/mol. The vibrational wavenumbers and the corresponding vibrational assignments of molecules in C(s) symmetry were examined theoretically and the calculated Infrared of the molecules in the cis conformation was plotted. Observed wavenumbers for normal modes were compared with those calculated from normal mode coordinate analysis carried out on the basis of DFT force fields using the standard 6-31+G* basis set of the theoretical optimized geometry.     

Normal mode analysis of oligomeric proteins: Reduction of the memory requirement by consideration of rigid geometry and molecular symmetry

A method is presented to reduce the memory requirement of normal mode analysis applied to systems containing two or more large proteins when these systems exhibit symmetry properties. We use a rigid geometry model (i.e., only the dihedral angles of the polypeptide chain are considered as variables). This model allows a reduction by a factor of 8 on average of the number of variables with a concomitant freezing of the high-frequency modes. The symmetry properties of the system are used to reduce further the number of variables that must be considered in the computation. Application of group theory leads to a factorization of the matrices of interest (the coefficient and the Hessian matrices) into independent blocks along the diagonal. The initial, reducible representation is thus transformed into a number of irreducible representations of smaller dimensions. In the case of the C₂ symmetry group, the method leads to a reduction of the size of the matrices that must be manipulated during the computation (coefficient matrix, Hessian matrix, and eigenvectors matrix) by a factor of 256 compared with the usual normal mode analysis in Cartesian coordinate space. The method is particularly well adapted to the study of the dynamics of oligomeric proteins because these proteins often display symmetry properties (e.g., virus coat proteins, immunoglobulins, hemoglobin, etc.). In favorable cases, in conjunction with X-ray diffuse scattering data, the study of systems showing allosteric properties might be considered. © 1994 by John Wiley & Sons, Inc.     

Amide I vibrational circular dichroism of dipeptide: Conformation dependence and fragment analysis

The amide I vibrational circular dichroic response of alanine dipeptide analog (ADA) was theoretically investigated and the density functional theory calculation and fragment analysis results are presented. A variety of vibrational spectroscopic properties, local and normal mode frequencies, coupling constant, dipole, and rotational strengths, are calculated by varying two dihedral angles determining the three-dimensional ADA conformation. Considering two monopeptide fragments separately, we show that the amide I vibrational circular dichroism of the ADA can be quantitatively predicted. For several representative conformations of the model ADA, vibrational circular dichroism spectra are calculated by using both the density functional theory calculation and fragment analysis methods.     

Langevin model of the temperature and hydration dependence of protein vibrational dynamics

The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.     

Density functional theory studies on the structures and vibrational spectra of 3,6-dichlorocarbazole and 3,6-dibromocarbazole

Becke 3-Lee-Yang-Parr density functional theory (DFT) calculations using 6-311G** and 6-311G(2df,p) basis sets were carried out to study molecular structures and vibrational spectra of 3,6-dichlorocarbazole and 3,6-dibromocarbazole. The optimized geometries, vibrational frequencies, IR intensities, and Raman activities have been obtained. On the basis of B3LYP calculations, a normal mode analysis was performed to assign the vibrational fundamental frequencies according to the potential energy distributions. The computational frequencies are in good agreement with the observed results.     

丙氨酸二肽分子二级结构与振动光谱特性

利用从头算方法探索蛋白质模型分子——丙氨酸二肽的二级结构布居特性以及体系势能变化. 引入对分子结构敏感的振动探针(酰胺振动吸收带), 借助其光谱表象, 寻求振动光谱参数与分子结构之间的联系. 研究结果表明: 丙氨酸二肽分子处于C_7eq构型(Φ/Ψ=-80°/80°)时具有最低能量值, 且分子易形成β折叠、PP_II、C₅及C₇等能量较低的稳定构型. 通过简正模式分析, 得到分子3N-6 个振动模式的吸收光谱, 并通过势能分布分析方法对分子骨架上酰胺振动吸收带的特征振动模式进行了指认. 重点考察分子骨架上酰胺-I带振动光谱参数与分子构型变化之间的相关性, 建立振动光谱参数与蛋白质二级结构之间的联系, 为在化学键水平上研究蛋白质的结构及其发挥作用的机制提供科学依据.     

Vibrational analysis of x-ray absorption fine structure thermal factors by ab initio molecular dynamics: the Zn(II) ion in aqueous solution as a case study

In this work, we consider a new combination of vibrational analysis and normal-like mode decomposition of Debye-Waller factors of solvated ions entirely based on molecular dynamics data. Such a novel time-dependent analysis procedure provides a direct link between x-ray absorption fine structure parameters and normal mode contributions for an ion-solvent system. The potentialities of such a methodology rely on two fundamental aspects which distinguish it from already available tools. First, a general vibrational analysis that does not require any Gaussian or harmonic model for describing atomic fluctuations in liquids. Second, a very accurate sampling of the short range motions around the structural probe via the recently developed atom centered density matrix propagation/general liquid optimized boundary method. This novel molecular dynamics methodology is based on an integrated ab initio/classical potential using localized basis functions and nonperiodic boundary conditions. As a case study we have chosen the Zn(II) ion in aqueous solution. The consistency of our results and the observed good agreement with experiments show how the key support to advanced structural techniques from molecular dynamics can be further expanded and investigated.