Mixed time slicing in path integral simulations

A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be "collapsed" in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.     

On the direct calculation of the free energy of quantization for molecular systems in the condensed phase

Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate.     

N-萘基氨基甲酸甲酯振动光谱的理论研究

采用HF和DFT(B3LYP)方法及6-31G基组对N-萘基氨基甲酸甲酯的几何构型、振动谱性力场和红外光谱进行了研究,使用Pulay标度法对HF/6-21G和B3LYP/6-31G的理论力场进行标度。根据标度后的理论力场进行了简正坐标分析,得到势能分布和红外振动频率,与红外频率实验相比较,HF方法和DFT(B3LYP)方法的误差分别为37.8cm^-^1和8.68cm^-^1,此外,还根据B3LYP方法得到的势能分布和红外光谱强度对N-萘基氨基甲酸甲酯的振动基频进行了理论归属,并对前人的频率指认进行了修正和补充。     

Conformational dependence of Raman frequencies and intensities in alkanes and polyethylene

Raman vibrational frequencies and intensities of octane, dodecane and hexadecane conformers have been calculated using quantum mechanical ab initio methods. The results agree with various trends observed in the experimental spectra of alkanes, as well as several observations from the experimental Raman spectra of polyethylenes. The present data suggest that ab initio calculated Raman data on alkanes provide valuable information regarding the interpretation of polymer Raman spectra, in particular concerning issues where interpretation based on experimental verification is not possible.     

FC(O)NCS 分子振动光谱的理论研究

采用DFT(B3LYP)方法,以6-3G*为基组对FC(O)NCS的顺式和反式两种构型的几何结构,振动谐性力场和红外光谱进行了研究。B3LYP/6-31G*计算水平和大多数有机分子的一套固定标度因子进行标度。根据标度后的理论力场进行简正坐标分析得到的势能分布(PED)和红外光谱强度值对FC(O)NCS分子的顺式和反式两种构型的振动基频进行了理论归属。     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.     

2-氟-5-溴吡啶分子振动光谱的密度泛涵理论研究

用密度泛函理论方法B3LYP以及6-311++G(2df,2pd)基组对2-氟-5-溴吡啶分子 的平衡几何构型进行了优化并计算了该分子的振动谐力场。使用Pulay的标度方法 对理论力场进行了标度。采用Wilson的GF矩阵方法,根据标度后的理论力场进行了 简正坐标分析,对2-氟-5-溴吡啶分子的振动基频进行了理论研究,得到了势能分 布和红外振动频率。与红外频率的实验值相比较,理论频率的均方差为24 cm~(-1) 。此外,根据振动模式的势能分布对此分子的振动基频进行了理论归属,并对前人 的指认进行了修正和补充。     

Ab initio quantum mechanical calculations of energy,geometry, vibrational frequencies and IR intensities of tetraphosphorus tetrasulphide, α-P4S4(D2d), and vibrational analysis of As4S4 and As4Se4

Geometry, vibrational frequencies and IR intensities are calculated for α-P₄S₄ by scaled quantum mechanical calculations at the 6-31G*/SCF and STO-3G*/SCF levels. For both basis sets the frequencies are scaled with factors close to or equal to those found for P₄S₃, and based on these results a revised assignment is proposed. The α-P₄S₄ force field is transferred to the isostructural As₄S₄ and As₄Se₄ molecules and rescaled, and based on a good fit to experimental frequencies a new assignment is also proposed for these compounds.     

On a semiclassical approach to energy transfer in polyatomic molecules

A semiclassical method for energy transfer in polyatomic molecules is suggested. The method is based on a partial quantization of the vibrational degrees of freedom. The remaining degrees of freedom are treated classically. As an example a system with three quantum coordinates is considered. The Coriolis coupling terms are taken into account in the quantum mechanical part of the system and discussed for the N₂ + CO₂ system.     

Analysis of vibrational spectra of chlorotoluene based on density function theory calculations

The conformational behavior and structural stability of chlorotoluene were investigated by utilizing ab initio calculations with 6-31G* basis set at restricted Hartree-Fock (RHF) and density function theory (DFT) levels. The vibrational frequencies of chlorotoluene were computed at the RHF and DFT levels. Complete vibrational assignments were made on the basis of normal coordinate calculations for stable conformer of the molecule. RHF results without scaled quantum mechanical (SQM) force field procedure considered are in bad agreement with experimental values. Of the five DFT methods, BLYP reproduces the observed fundamental frequencies most satisfactorily with the mean absolute deviation of the non-CH stretching modes less than 10 cm(-1). Two hybrid DFT methods are found to yield frequencies, which are generally higher than the observed fundamental frequencies. When the calculated results are compared with 'experimental' frequencies, B3LYP method is found to be slightly more accurate for C-H stretching modes. The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features.     

Calculating intensities using effective Hamiltonians in terms of Coriolis-adapted normal modes

The calculation of rovibrational transition energies and intensities is often hampered by the fact that vibrational states are strongly coupled by Coriolis terms. Because it invalidates the use of perturbation theory for the purpose of decoupling these states, the coupling makes it difficult to analyze spectra and to extract information from them. One either ignores the problem and hopes that the effect of the coupling is minimal or one is forced to diagonalize effective rovibrational matrices (rather than diagonalizing effective rotational matrices). In this paper we apply a procedure, based on a quantum mechanical canonical transformation for deriving decoupled effective rotational Hamiltonians. In previous papers we have used this technique to compute energy levels. In this paper we show that it can also be applied to determine intensities. The ideas are applied to the ethylene molecule.     

A quantum mechanical strategy to investigate the structure of liquids: the cases of acetonitrile, formamide, and their mixture

A computational strategy based on quantum mechanical (QM) calculations and continuum solvation models is used to investigate the structure of liquids (either neat liquids or mixtures). The strategy is based on the comparison of calculated and experimental spectroscopic properties (IR-Raman vibrational frequencies and Raman intensities). In particular, neat formamide, neat acetonitrile, and their equimolar mixture are studied comparing isolated and solvated clusters of different nature and size. In all cases, the study seems to indicate that liquids, even when strongly associated, can be effectively modeled in terms of a shell-like system in which clusters of strongly interacting molecules (the microenvironments) are solvated by a polarizable macroenvironment represented by the rest of the molecules. Only taking into proper account both these effects can a correct picture of the liquid structure be achieved.     

氟磺酸氯分子振动光谱的从头算研究

采用从头算HF方法以6-31G^*基组研究了对ClOSO₂F分子的几何结构、振动谐性力场和红外光谱.理论力场由Pulay的标度量子力学方法进行标度,算得的振动频率与实验值比较,平均偏差为6.0cm^-1.根据振动频率的势能分布和从头算红外光谱强度值对此分子的振动基频进行了理论归属.     

Density functional theory study of vibrational spectra, and assignment of fundamental vibrational modes of succinimide and N-bromosuccinimide

This work deals with the vibrational spectroscopy of succinimide and N-bromosuccinimide. The mid and far FTIR and FT-Raman spectra were measured in the condensed state. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT) using standard B3LYP/6-31G(*) and B3LYP/6-311+G(**) methods and basis set combinations. The vibrational spectra were interpreted, with the aid of normal coordinate analysis based on a scaled quantum mechanical force field. The infrared and Raman spectra were also predicted from the calculated intensities. Comparison of simulated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes. Unambiguous vibrational assignment of all the fundamentals were made using the total energy distribution (TED).     

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.     

Structures and vibrational frequencies of 2-naphthoic acid and 6-bromo-2-naphthoic acid based on density functional theory calculations

The solid phase mid FTIR and FT Raman spectra of 2-naphthoic acid (NA) and 6-bromo-2-naphthoic acid (BNA) have been recorded in the regions 4000-400 cm(-1) and 3500-100 cm(-1), respectively. The fundamental vibrational frequencies and intensities of the vibrational bands were evaluated using density functional theory (DFT) using standard B3LYP method and 6-311+G** basis set combinations. The vibrational spectra were interpreted, with the aid of normal coordinate analysis based on a scaled quantum mechanical force field. The infrared and Raman spectra were also predicted from the calculated intensities. Comparison of simulated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes.     

ClC(O)NCS分子振动光谱的理论研究

采用密度泛函理论DFT(B3LYP)方法,以6-31G^*为基组对ClC(O)NCS的反式和顺式两种构型的几何结构、振动谐性力场和红外光谱进行了研究.B3LYP/6-31G^*的理论力场由适用于B3LYP/6-31G^*计算水平和大多数有机分子的一套固定标度因子进行标度.根据标度后的理论力场进行简正坐标分析得到的势能分布(PED)和红外光谱强度值对ClC(O)NCS分子的顺式和反式两种构型的振动基频进行了理论归属.     

Thermodynamic integration from classical to quantum mechanics

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.     

Spectroscopic Properties of Lumiflavin: A Quantum Chemical Study

In this work, the electronic structure and spectroscopic properties of lumiflavin are calculated using various quantum chemical methods. The excitation energies for ten singlet and triplet states as well as the analysis of the electron density difference are assessed using various wave function‐based methods and density functionals. The relative order of singlet and triplet excited states is established on the basis of the coupled cluster method CC2. We find that at least seven singlet excited states are required to assign all peaks in the UV/Vis spectrum. In addition, we have studied the solvatochromic effect on the excitation energies and found differential effects except for the first bright excited state. Vibrational frequencies as well as IR, Raman and resonance Raman intensities are simulated and compared to their experimental counterparts. We have assigned peaks, assessed the effect of anharmonicity, and confirmed the previous assignments in case of the most intense transitions. Finally, we have studied the NMR shieldings and established the effect of the solvent polarity. The present study provides data for lumiflavin in the gas phase and in implicit solvent model that can be used as a reference for the protein‐embedded flavin simulations and assignment of experimental spectra.     

An evaluation of scaling factors for multiparameter scaling procedures based on DFT force fields

An extended database of scaling factors for calculating fundamental frequencies within multiparameter scaled quantum mechanical (SQM) force field, and effective scaling frequency factor (ESFF) methods, based on various DFT force fields is reported. Twenty-six density functionals have been examined in conjunction with various Pople's and Dunning's basis sets of VDZ and VTZ quality. The calculations were based on a standard training set of 30 molecules proposed by Baker et al., for which 660 vibrational modes were assigned. Six functionals turned out to be particularly well-suited to the calculations oriented toward determination of scaled frequencies. They are B3LYP, B3PW91, B97, B97-1, B97-2, and O3LYP; they are all capable of providing reasonable scaled frequencies even for the small, 6-31G* basis set (rms <15 cm(-1)). Correlations between the quality of the scaled frequencies and the basis set quality as well as the accuracy of the predicted molecular geometry were investigated. The 6-311+G** basis set turned out to be preferable. In addition, correlation between the rms values in the scaled frequencies and the errors in the predicted geometric parameters was found. Both 11- and 9-parameter scaling frames are compared. It is shown that 9-parameter scaling is preferable in the middle range of the vibrational spectrum (500-2500 cm(-1)), provided it was based on high-quality force fields. Finally, statistical uncertainties of the calculated scaling factors are reported.