Ab initio vibrational state calculations with a quartic force field: applications to H2CO, C2H4, CH3OH, CH3CCH, and C6H6

For polyatomic molecules, n-mode coupling representations of the quartic force field (nMR-QFF) are presented, which include terms up to n normal coordinate couplings in a fourth-order polynomial potential energy function. The computational scheme to evaluate third-and fourth-order derivatives by finite differentiations of the energy is fully described. The code to generate the nMR-QFF has been implemented into GAMESS program package and interfaced with the vibrational self-consistent field (VSCF) and correlation corrected VSCF (cc-VSCF) methods. As a demonstration, fundamental frequencies have been calculated by the cc-VSCF method based on 2MR-QFF for formaldehyde, ethylene, methanol, propyne, and benzene. The applications show that 2MR-QFF is a highly accurate potential energy function, with errors of 1.0-1.9% relative to the experimental value in fundamental frequencies. This approach will help quantitative evaluations of vibrational energies of a general molecule with a reasonable computational cost.     

构造SO~2分子势能面的李代数方法

把李代数方法得到的SO~2分子的代数Hamiltonian,利用相干态基经典化并找到一个新的变换,将分子的键角引入,而得到SO~2分子的势能面。由该势能面计算的解离能,所给出的势能面的立体图和相应的等高线以及力常数与其他方法给出的相一致。该方法可以推广到多原子分子及反应体系。     

Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules

A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/torsion, and angle/angle/ torsion cross-term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments. © 1994 by John Wiley & Sons, Inc.     

Investigation of the role of the C-PCM solvent effect in reactivity indices

It has been shown recently, how the coupling between electronic degrees of freedom and vibrational modes is reflected in the properties of molecules. The necessary derivatives have been analyzed and their thermodynamic relations were demonstrated. This present work is focused on the analysis of a molecular system, under the influence of C-PCM induced solvent effect. The analysis is based on reactivity indices derived from DFT. The shift of frequency for diatomic molecules has been obtained. It has been identified as chemical force effect. The role of nuclear reactivity indices has been emphasized. This concept has been extended to obtain regional chemical potential values within C-PCM model for polyatomic molecules.     

多原子分子力场的模型势函法与MNDO,MINDO／3方法的研究

用量子力学方法获得分子的模型力场现已占有很重要的位置.然而由于理论上很难获得体系高精度解析势能面,使力场的理论计算遇到了困难.直到Pulay提出梯度法后,量子化学方法才被广泛用于多原子分子的振动分析.但由于该方法采用数值微分通过能量的第二阶导数所获得的力场矩阵对角元误差很大,需将其伸缩、变角对角力常数分别扣除10％、20％,才能获得与观测值相近的结果;且ab initio计算花机时太多,应用于大分子计算存在一定的困难.为此本文把前文提出的确定力常数的模型势函法与MNDO、MINDO/3等半经验方法结合起来,构造多原子分子的力场,并用于振动分析,获得了满意的结果.     

Ionisation Potential, Electron Affinity and Polar Bond: A First-order Correction Method for Interaction Energy

A new first-order method is proposed to improve the potential energy of the polar molecules. The nature of the polar bonding is illustrated by some examples, LiF, LiO, LiH, ScO, and AlO molecules, covering from strong to weak ionic cases. A simple first-order correction method using the dipole moment or the effective charge, and the experimental and theoretical ionisation potentials and electron affinities is explained. Application of this method to those molecules improves remarkably the spectroscopic constants. This method can be easily extended to polyatomic cases involving a polar bonding between an electropositive moiety (electron donor) and an electronegative functional group (electron acceptor).     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Inclusion of non-bonded interactions in calculations of vibrational frequencies

The consequences of including non-bonded interactions in the calculation of vibrational frequencies are examined by comparing the results of the consistent force field method (CFF)and a conventional spectroscopic force field calculation method. Sample calculations are given, using ethane as a test case. It is shown that the CFF method is more practical for the calculation of non-bonded interaction parameters for large molecules, provided that the molecular potential energy is first minimized.     

Application of potential constants: Electronic chemical potentials of polyatomic molecules—VIII

A new approach for the calculation of electronic chemical potentials of polyatomic systems is developed by applying the quadratic potential (force) constants which are available from normal coordinate analyses using spectroscopic data. The approach is constructed within the framework of density-functional theory into which the simple bond-charge model is incorporated. To evaluate the utility of such an approach, we have calculated electronic chemical potentials for various kinds of polyatomic molecules, and the calculated results have been compared favorably with experimental values as well as those obtained from ab initio SCF calculations. It seems that this approach offers the possibility of chemical potential calculations for polyatomic molecules whose quadratic stretching force constants are obtained by normal coordinate analyses.     

Theoretical investigation of the interactions between the π‐systems of molecular organic semiconductors and an analysis of the contributions of repulsion and electrostatics

A concept for the interactions between π‐systems is necessary to understand a number of phenomena in modern material sciences such as supramolecular properties and self‐assembly. In the present article, we investigate the intermolecular interaction energies between organic semiconductors with extended π‐systems using SAPT (symmetry‐adapted perturbation theory), LMO‐EDA (localized molecular orbital energy decomposition analysis), DFT‐D (density functional theory including dispersion corrections), and force‐field approaches. Both apolar organic molecules such as acenes and highly polarized π‐systems of merocyanines and squaraines were used to probe the influence of electrostatics on the shape of the potential energy surfaces (PES) governing the geometric structures of aggregates. Our results reveal that the shapes of the PESs result from variations in the short‐range, highly specific repulsion forces even for highly polar molecules. Using distributed quadrupoles, we show that it is nevertheless possible to mimic the intermolecular potentials with electrostatics. This is also possible with van‐der‐Waals potentials and a simple overlap‐based force‐field ansatz based on the overlap between p‐orbitals. © 2016 Wiley Periodicals, Inc.     

Towards a complete basis set limit of Hartree–Fock method: correlation-consistent versus polarized-consistent basis sets

In this paper the convergence pattern of correlation-consistent (cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree–Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules.     

Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant

The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats, treatment of electrostatic interactions, and system size (1000 molecules). The densities and enthalpy of vaporization from an independent data set based on simulations using the CHARMM General Force Field (CGenFF) presented by Vanommeslaeghe et al. (J. Comput. Chem.2010, 31, 671) are included for comparison. We find that, overall, the OPLS/AA force field performs somewhat better than GAFF, but there are significant issues with reproduction of the surface tension and dielectric constants for both force fields.     

多原子反应体系的高精度拟合势能面

本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。     

Ab Initio prediction of possible crystal structures for general organic molecules

The performance of a new crystal packing procedure for the ab initio prediction of possible molecular crystal structures is presented. The method is based upon only molecular information, i.e., no unit cell parameters are assumed to be known. The search for the global crystal energy minimum and all local minima inside an energy window is derived from Monte Carlo simulated annealing methods and has been applied to various organic molecules containing heteroatoms and polar groups. A systematic evaluation of the search method and of the quality of the potential energy function has been established. It is demonstrated that the packing of general organic molecules is possible even with standard force fields like CHARMM provided that the charges defining the electrostatic interactions are based upon physical models rather than transferable empirical parameters. Concepts of crystal packing that were based till now upon assumptions and speculations could be proved or disproved by solving directly the extended global optimization problem related to crystal packing. Crystal structures of molecules as complex as those treated in this article have not been, till now, predicted by a computational approach. In one case, a disagreement between the predicted and experimental structure was evident and, based upon the computations, we suspect that the published structure is the wrong one. © 1992 by John Wiley & Sons, Inc.     

二原子分子和三原子分子的周期表

门捷列夫元素周期表是自然科学中最重要的原则之一．然而,对于分子而言,却缺乏类似的表格．本文提出两个分别对应于二原子分子和三原子分子的周期表．这些分子周期表的格式和门捷列夫原子周期表相似．在这些表格中,分子依照它们各自的族数G和周期数P分类排列,G是价电子的数目而P则表示分子的尺寸．分子的基本性质,包括键长、结合能、力常数、电离势、自旋多重度、化学反应活性以及键角等等,都随着表中的G和P作周期性的变化．二原子分子和三原子分子的周期性因而被揭示开来．本文还进一步指出这种周期性是源出于分子的壳状电子构型．周期表中不仅包含了游离的分子,还包含了多原子分子中的“赝”分子．这些周期表可用来从本质上分类分子,广泛地预言分子的未知性质,了解在多原子分子中赝分子的作用,以及开拓新的研究领域,如芳香族、团簇或纳米微粒的周期性等．因此这些表格不仅能够引起多学科领域中科学工作者的关注,而且还能引起理科学生们的兴趣．     

Periodic tables of diatomic and triatomic molecules

The Mendeleev periodic table of atoms is one of the most important principles in natural science. However, there is shortage of analog for molecules. Here we propose two periodic tables, one for diatomic molecules and one for triatomic molecules. The form of the molecular periodic tables is analogous to that of Mendeleev periodic table of atoms. In the table, molecules are classified and arranged by their group number G, which is the number of valence electrons, and the periodic number P, which represents the size of the molecules. The basic molecular properties, including bond length, binding energy, force constant, ionization potential, spin multiplicity, chemical reactivity, and bond angle, change periodically within the tables. The periodicities of diatomic and triatomic molecules are thus revealed. We also demonstrate that the periodicity originates from the shell-like electronic configurations of the molecules. The periodic tables not only contain free molecules, but also the "virtual" molecules present in polyatomic molecules. The periodic tables can be used to classify molecules, to predict unknown molecular properties, to understand the role of virtual molecules in polyatomic molecules, and to initiate new research fields, such as the periodicities of aromatic species, clusters, or nanoparticles. The tables should be of interest not only to scientists in a variety of disciplines, but also to undergraduates studying natural sciences.     

The correlation of intermolecular effects in the vibration spectra of BF3 with alterations in its quadratic valence force field

The effect of weak and specific intermolecular interactions in the vibration spectra of molecules is considered and correlated with alterations in the potential energy of the molecule via the force field. The approach, which follows a previously developed method [3], shows how best to choose the perturbations in order to reproduce the intermolecular interaction and keep the internal consistency of the force field. The vibrational calculation is exemplified for XY₃molecules with D_3h symmetry and applied to the boron trifluoride molecule.     

On a semiclassical approach to energy transfer by atom/molecule-surface collisions

A semiclassical theory for energy transfer in polyatomic molecules has been extended to atom/molecule-surface scattering problems. The solid is treated     

The rotation–vibration coupling equations for polyatomic molecules in internal coordinates

An exact vibration–rotation kinetic energy operator for polyatomic molecules has been obtained on the basis of Sutcliffe's method, in terms of curvilinear internal coordinates and rotational angular moment operators. This operator is derived from the kinetic energy operator in Cartesian coordinates by the successive transformations using the chain rule. This kinetic energy operator can be used not only for the system of any triatomic and tetraatomic molecules and common polyatomic molecules in chemistry, but also for the investigation of the collision problems between two molecules after some modifications. Finally, using this Hamiltonian, the rotation–vibration coupling equations of polyatomic molecules have been derived and discussed. © 1992 John Wiley & Sons, Inc.