Harmonic analysis of large systems. II. Comparison of different protein models

A series of normal mode analyses of bovine pancreatic trypsin inhibitor (BPTI) has been performed. The results of modifying the long-range truncation of electrostatics, reducing the conformational space of the system (reduced basis normal mode analysis), and using different parameter sets and models for the potential function are reported. Both explicit (904 atoms) and polar hydrogen (580 atoms) representations of BPTI were examined and produced nearly identical normal mode vectors but slightly modified vibrational frequencies. The truncation methods—no cutoff, shift, and switch—were examined, and the use of a short switching function was found to alter harmonic motion greatly. A table relating the different cutoff methods to several previously published frequencies for BPTI indicates that the diversity of published lowest frequencies is due to the use of different electrostatic models rather than to inherent differences in the models or energy parameters. Examining reduced basis results demonstrates that a dihedral basis yields similar normal mode vectors, though the vibrational frequencies are shifted to higher values. The analysis of BPTI harmonic dynamics using a spherical harmonic reduced basis set yields significantly altered dynamics, indicating that BPTI is not well represented as a homogeneous object at low temperatures. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Harmonic analysis of large systems. III. Comparison with molecular dynamics

Atomic motions in bovine pancreatic trypsin inhibitor (BPTI), derived from molecular dynamics, harmonic analysis, and quasiharmonic analysis, are compared when a single protein model, energy parameters, and environment are employed. Molecular dynamics (MD) was carried out for 2 nanoseconds. An average structure was determined from the last nanosecond of the MD simulation, when no major structural changes were observed. This structure was used for several harmonic analysis calculations as well as for a reference structure for the quasiharmonic analysis, for both full basis and reduced basis sets. In contrast to the harmonic analysis results, the quasiharmonic reduced basis calculation using a spherical harmonics reduced basis provided good agreement with the full basis calculation, suggesting that when anharmonic effects are considered, BPTI can behave as a homogeneous object. An extensive analysis of the normal modes from a diverse set of 201 minimized MD simulation frames was performed. On only the sub-picosecond time scale were energy minima revisited after a transition to another state. This analysis shows that the dynamics average structure is not representative of the simulation frames in terms of energy and vibrational frequencies. For this model of BPTI, 42% of the motion (mean-squared fluctuation) can be attributed to harmonic limit behavior. A spectral analysis of the correlation function of deformation for a particular normal mode or quasiharmonic mode can be used to determine the time scales of motions which correspond to harmonic vibration, large-scale drift, or sharp transitions between local substrates. © 1995 John Wiley & Sons, Inc.     

Conformational dynamics of polypeptides and proteins in the dihedral angle space and in the cartesian coordinate space: Normal mode analysis of deca-alanine

Effects of different treatments of the degrees of freedom of bond length stretching and bond angle bending in computational analysis of conformational dynamics of proteins and polypeptides are assessed. More specifically, the normal mode analysis of conformational dynamics of α-helix of deca-alanine has been carried out both in the dihedral angle space (DAS) and in the Cartesian coordinate space (CCS). Almost perfect one-to-one correspondence has been found between normal modes in the CCS with frequencies less than 128 cm^?1 and those in the DAS with frequencies less than 164 cm^?1. Patterns of atomic displacements in the corresponding modes are very similar. This indicates that the effects of fixing degrees of freedom of bond length stretching and bond angle bending on the very-low-frequency normal modes in the CCS with frequencies less than 128 cm^?1 are almost solely to increase the frequencies by about 20%. The conclusion indicates that the different treatment of these degree does not lead to qualitatively different results as long as low-frequency motions are concerned. Based on the results of calculation, mechanical property of the α-helix of deca-alanine is discussed.     

Evaluating the conformational entropy of macromolecules using an energy decomposition approach

We have developed a novel method to compute the conformational entropy of any molecular system via conventional simulation techniques. This method only requires that the total energy of the system is available and that the Hamiltonian is separable, with individual energy terms for the various degrees of freedom. Consequently the method, which we call the energy decomposition (Edcp) approach, is general and applicable to any large polymer in implicit solvent. Edcp is applied to estimate the entropy differences due to the peptide and ester groups in polyalanine and polyalanil ester. Ensembles over a wide range of temperatures were generated by replica exchange molecular dynamics, and densities of states were estimated using the weighted histogram analysis method. The results are compared with those obtained via evaluating the P ln P integral or employing the quasiharmonic approximation, other approaches widely employed to evaluate the entropy of molecular systems. Unlike the former method, Edcp can accommodate the correlations present between separate degrees of freedom. In addition, the Edcp model assumes no specific form for the underlying fluctuations present in the system, in contrast to the quasiharmonic approximation. For the molecules studied, the quasiharmonic approximation is observed to produce a good estimate of the vibrational entropy, but not of the conformational entropy. In contrast, our energy decomposition approach generates reasonable estimates for both of these entropy terms. We suggest that this approach embodies a simple yet effective solution to the problem of evaluating the conformational entropy of large macromolecules in implicit solvent.     

Asymmetric Reduction of Acetophenone with (−)-β-chlorodiisopinocampheylborane, and Derivatization with (−)-Menthyl Chloroformate. An Undergraduate Organic Synthesis, GC Analysis, and Molecular Modeling Project

Molecular vibration plays an important role in chemistry, both in chemical reactions and in the characterization and measurement of molecular structure and bonding. Normal modes provide the conceptual framework for understanding molecular vibrations. For example, the analysis of infrared spectra, an important tool for chemists, relies heavily on the concept of normal modes; yet, undergraduate students, even chemistry majors, seldom gain a thorough understanding of normal modes through the traditional chemistry curriculum. In fact, the most commonly used physical chemistry textbooks give only a cursory introduction to this concept, leaving out the substantive development. This occurs presumably because normal modes emerge from a multistepped mathematical analysis of the molecular dynamics. While the mathematical skill needed for each step typically has been covered in an introductory calculus course, the full development is a lengthy process and skipped in the texts. Thus, students have little opportunity to develop a sound conceptual understanding of vibrational modes and fundamental vibrational frequencies, even though they inevitably encounter these terms in their future work.     

Theoretical investigation of the Anti-Parkinson drug rasagiline and its salts: conformations and infrared spectra

The conformational analysis of rasagiline [N-propargyl-1(R)-aminoindan] was performed by the density functional theory (DFT) B3LYP method using the 6–31++G (d,p) basis set. A single point energy calculations based on the B3LYP optimized geometries were also performed at MP2/6-31++G (d, p) level. The vibrational frequencies of the most stable conformer of rasagiline was calculated at the B3LYP level and vibrational assignments were made for normal modes on the basis of scaled quantum mechanical force field (SQM) method. The influence of mesylate and ethanedisulfonate salts on the geometry of rasagiline free base and its normal modes are also discussed.      

Anharmonic vibrational probe for N-methylacetamide in different micro-environments

In the present study, anharmonic vibrational properties of the amide modes in N-methylacetamide (NMA), a model molecule for peptide vibrational spectroscopy, are examined by DFT calculations. The 3N-6 normal mode frequencies, diagonal and off-diagonal anharmonicities are evaluated by means of the second order vibrational perturbation theory (VPT2). Good performance of B3LYP/6-31+G** is found for predicting vibrational frequencies in comparison with gas phase experimental data. The amide vibrational modes are assigned through potential energy distribution analysis (PED). The solvation effect on the amide vibrational modes is modeled within the PCM method. From gas phase to polar solvents, red shifts are observed for both harmonic and anharmonic vibrational frequency of amide I mode while the CO bond length increases upon the solvent polarity. Cubic and quartic force constants are further calculated to evaluate the origin of the anharmonicity for the amide I mode of NMA in different micro-environments.     

Normal Coordinate Analysis in Cartesian Space I. Planar Symmetric Xn Molecules

Normal coordinate analysis of X_n type molecules can be carried out in the Cartesian space as well as in the internal space. Force constants in Cartesian coordinates for aromatic compounds belonging to D_nh group are calculated. The force constants of benzene are evaluated from vibrational frequencies both in the ground state and the ¹B_1u excited state. The calculated frequencies of planar carbon vibration of annulene of any N are tabulated. The normal coordinates derived from the calculation of 10-annulene are roughly the same of naphthalene derived more elaborated by Scherer. The normal modes in 10-annulene are indeed good approximations to the ones in naphthalene. This conclusion is valid for the other aromatic compounds.     

Ab-initio molecular geometry and normal coordinate analysis of tetrahydrothiophene molecule.

The molecular geometry of tetrahydrothiophene (THT) was quantum mechanically calculated using the split valence 6-31G** basis set. Electron correlation energy has been computed employing MP2 method. The molecule showed a twist form puckered structure with a twist torsion angle of 13 degrees and has a total energy of -347,877.514 kcal/mol of which a 436.715 kcal/mol electron correlation energy. The envelope form of the molecule showed an inter-plane angle of 22 degrees and has a total energy of -347,874.430 kcal/mol involving -436.558 kcal/mol electron correlation energy. The normal coordinates of the molecule were theoretically analyzed and the fundamental vibrational frequencies were calculated. The IR and laser Raman spectra of THT molecule was measured. All the observed vibrational bands including combination bands and overtones were assigned to normal modes with the aid of the potential energy distribution values obtained from normal coordinate calculations. The molecular force field was determined by refining the initial set of force constants using the least square fit method instead of using the less accurate scaling factor methods. The determined molecular force field has produced simulated frequencies which best match the observed values. The lowest-energy modes of vibration were two molecular out-of-plane deformations, observed at 114 and 166 cm(-1). The barrier of ring twisting estimated from the observed ring out-of-plane vibrational mode at 114 cm(-1) was estimated.     

Synthesis of two new thioesters bearing ferrocene: Vibrational characterization and ab initio calculations. X-ray crystal structure of S-(2-methoxyphenyl)ferrocenecarbothioate

Structural and conformational properties of S-benzyl ferrocenecarbothioate (I) and S-(2-methoxyphenyl) ferrocenecarbothioate (II) are analyzed using data obtained from X-ray diffraction, vibrational data and theoretical calculations. According to chemical quantum calculations, the synperiplanar and antiperiplanar forms are found as the first and second more stable conformations, respectively, for the title compounds. The geometric parameters and normal modes of vibration were calculated using a density functional theory method (B3LYP) and the 6-31+G∗∗ basis set for all atoms except for iron. For this atom the calculations were carried out with the Lanl2dz basis set. The calculated parameters are in good agreement with the corresponding X-ray diffraction values. The combined experimental and theoretical approach allows a consistent assignment for most of the fundamental modes.     

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.     

Vibrational spectra and normal co-ordinate analysis of 2-aminopyridine and 2-amino picoline

The Fourier transform infrared (FT-IR) and Raman (FT-R) spectra of 2-aminopyridine and 2-amino picoline were recorded and the observed frequencies were assigned to various modes of vibration in terms of fundamentals by assuming Cs point group symmetry. A normal co-ordinate analysis was also carried out for the proper assignment of the vibrational frequencies using simple valence force field. A complete vibrational analysis is presented here for the molecules and the results are briefly discussed.     

Probing vibrational wave packets in molecular excited states

A time-dependent theoretical method is used to describe a UV pump?CUV probe strategy to trace, at a femtosecond time scale, the motion of vibrational wave packets created in excited states of the hydrogen molecule by measuring single ionization probabilities. We use a spectral method to solve the time-dependent Schr?dinger equation in full dimensionality, including correlation and all electronic and vibrational degrees of freedom. A pump pulse initially creates a vibrational wave packet in the intermediate electronic excited states of $\hbox{H}_2$ . The frequency of the probe is chosen to ionize the target leaving the ion in a bound vibrational state. By varying the time delay between pulses, non-dissociative single ionization is enhanced or suppressed. Energy differential ionization probabilities are reported and compared with a model based on the Franck?CCondon approximation.     

Comparing normal modes across different models and scales: Hessian reduction versus coarse‐graining

Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse‐graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the “implosion” of the all‐atom (AA) Hessian to a coarse‐grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass‐weighting. The dimension‐dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension‐independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Gō‐like model, a canonical elastic network model, and a network model with intentionally unphysical force constants. Published 2012 Wiley Periodicals, Inc.     

Maximum Interaction Model Force Constant Calculation of the Mlx (Co)6-x Type Molecule

C—O stretching frequency of inorganic carbonyl molecules is quite characteristic in the vibrational spectroscopy (the IR and Raman). Since such stretching modes are quite different from the skeletal modes, a non-mechanical coupling model has been proposed by Cotton¹⁾. The C—O stretching force constants and their interaction constants may be calculated semiquantitatively from their characteristic frequencies. The trouble is that the number of vibrational frequencies is always less than the number of force constants, whenever a symmetry irreducible representation contains more than one frequency. Cotton suggest that the interaction constants for octahedral type molecule from the dpπ bonding point of view^1-2). Instead of this, a model of maximum interaction between M—C—O bonds is proposed in this paper. Such model not only gives better remedy to the problem of octahedral complexes, but also is useful to solve the normal modes in molecules of trigonal bipyramidal and many other symmetries.     

DFT and ab initio quantum chemical studies on p-cyanobenzoic acid

The Fourier transform infrared (FTIR) and FT-Raman spectra of p-cyanobenzoic acid (CBA) have been recorded in the range 4000-400 and 4000-100 cm(-1), respectively. The complete vibrational assignment and analysis of the fundamental modes of the compound were carried out using the observed FTIR and FT-Raman data. The vibrational frequencies determined experimentally were compared with theoretical wavenumbers obtained from ab initio HF and DFT-B3LYP gradient calculations employing 6-31G**, 6-311++G** and cc-pVTZ basis sets for the optimised geometry of the compound. The geometry and normal modes of vibration obtained from the HF and DFT methods are in good agreement with the experimental data. The normal coordinate analysis was also carried out with ab initio force fields utilising Wilson's FG matrix method. The interactions of cyano and carboxylic acid groups with the skeletal vibrational modes were investigated.     

Theoretical and experimental vibrational study of phenylurea: structure, solvent effect and inclusion process with the beta-cyclodextrin in the solid state

FTIR and Raman vibrational spectroscopic techniques as well as DFT quantum chemical calculation were used for characterizing conformational changes of phenylurea (a herbicide parent molecule) occurring from solid state to aqueous medium. Experimental infrared frequencies were assigned on the base of urea and benzenic derivatives spectroscopic data available in the literature and vibrational normal modes analytical calculation at the fully optimized geometry. Investigation of isotopic and solvent effects has revealed that the structure of phenylurea is particularly sensitive to the electrostatic environment via hydrogen non covalent bonds. The ability of beta-cyclodextrin (beta-CD) to form host-guest inclusion complex with phenylurea in the solid state was also evidenced by significant frequency shifts observed in the 1400-1800 cm(-1) spectral range.     

Semi-empirical and vibrational studies of flavone and some deuterated analogues

The infrared solid state, Raman solid state and tetrachloride solution spectra of flavone have been obtained. Assignments of most of the vibrational data have been performed by comparison between the spectra of flavone and three isotopic species, deuterated on the A, B and C rings, respectively. The vibrational frequencies for all the investigated compounds have been calculated from the conformational analysis of flavone using the semi-empirical AM1 method and compared with experimental values. The correlation is more or less satisfactory; however, for some vibrational modes, the calculated isotopic shifts agree better with experiment than do the frequencies themselves. Specific vibrational modes which retain a benzene ring mono-substituted and ortho-distributed character have been recognized in the spectra, according to literature data, isotopic frequency shifts and graphic representation of the atomic displacements.     

Coordinating Abilities Towards Sodium of Oxygenated Solvents

Tetracoordination of the sodium cation is indicated by the ²³Na-NMR. chemical shifts for NaClO₄ in binary mixtures of ether and alcohol solvents. Solvent exchange occurs by a sequential process, and involves one or several intermediates. In competition with tetrahydrofurfuryl alcohol, whereas glyme corresponds to monocyclic intermediates, diglyme and triglyme

1 For abbreviations see Table 1.

favor formation of bicyclic intermediates. The relevant conformational factors are analysed, and also serve to explain the better coordinating abilities of diglyme and triglyme, as compared to glyme. The mechanism for solvent exchange is discussed.     

X-ray diffraction method of the radial electron density distribution. Structure of nanophase supports and supported catalysts

The structure of the synthesized title compound is characterized by IR, UV-visible spectroscopy, and single crystal X-ray diffraction (XRD). The new compound (C₁₈H₂₃NS) crystalizes in the monoclinic P2₁/c space group. In addition to the crystal structure from the X-ray experiment, the molecular geometry, vibrational frequencies, atomic charge distribution, and frontier molecular orbital (FMO) analysis of the title compound in the ground state are calculated by density functional teory (B3LYP) with 6-311G(d,p) and 6-31G(d,p) basis sets. The results of the optimized molecular structure are presented and compared with the experimental values. The computed vibrational frequencies are used to determine the types of molecular motions associated with each of the observed experimental bands. To determine the conformational flexibility, the molecular energy profile of (1) is obtained by semi-empirical (AM1) and (PM3) calculations with respect to a selected degree of torsional freedom. Moreover, molecular electrostatic potential (MEP) and thermodynamic parameters of the title compound were calculated by the theoretical methods.