Modification of Morse potential in conventional force fields for applying FPDP parameters

Although the Morse potential function is widely used in molecular modeling software, newer potential functions that possess more parameters provide greater accuracy. Against this backdrop, the Four-Parameter-Diatomic-Potential (FPDP) was selected for converting its parameter into those of the Morse potential due to the former’s resemblance to the latter. A pair of modified Morse indices was extracted by imposing equal force constant for infinitesimal bond stretching and equal energy integral for complete interatomic separation. Results reveal very good agreement for both bond compression and bond stretching. The developed parameter conversion would enable all FPDP parameters to be converted into the modified Morse parameters. Only minor algorithm alterations are required for incorporating the modified Morse function into molecular modeling packages that adopt the conventional Morse potential for describing 2-body bonded interaction.     

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.     

Quantum mechanical guides to the potential energy curves of some simple molecules

The molecular orbital expression for the bond energy of a chemical bond is used to obtain some insight into the factors which produce the potential energy curves of a number of simple bonds. The resulting picture of bond formation and the potential energy curve is an electrostatic one and it depicts the potential energy curve as the sum of a long range attractive curve and a short range repulsive one. Broadly speaking, that part of the curve to the long bond length side of the minimum is determined essentially by the two electrons which form the bond and, in particular, by the `binding energy' of these two electrons. The position of the minimum and the shape of the short bond length side of the curve do depend in general on the other valence electrons of the two atoms. The long range attractive curve is easily calculated but it is difficult to get the short range repulsive curve accurately. The results may prove useful in the construction of potential energy surfaces where the long bond length side of the potential energy curve is the important part.     

Bond functions,covalent potential curves,and the basis set superposition error

In the current practice of quantum chemistry, it is not clear whether corrections for basis set superposition errors should be applied to the calculation of potential energy curves, in order to improve agreement with experimental data. To examine this question, spectroscopic parameters derived from theoretical potential curves are reported for the homonuclear diatomics C₂, N₂, O₂, and F₂, using a configuration interaction method. Three different basis sets were used, including double zeta plus polarization, triple zeta plus double polarization, and double zeta polarization augmented by bond functions. The bond function basis sets, which were optimized in the preceding paper to obtain accurate dissociation energies, also gave the most accurate parameters. The potential curves were then corrected for basis set superposition error using the counterpoise correction, and the spectroscopic parameters were computed again. The BSSE-corrected curves showed worse agreement with experiment for all properties than the original (uncorrected) curves. The reasons for this finding are discussed. In addition to the numerical results, some problems in the application of the BSSE correction to basis sets containing bond functions are shown. In particular, there is an overcounting of the lowering due to the bond functions, regardless of which type of correction is applied. Also, genuine BSSE affects cannot be separated from energy-lowering effects due to basis set incompleteness, and we postulate that it is the latter which is strongly dominant in the calculation of covalent potential curves. Based on these arguments, two conclusions follow: (1) application of BSSE corrections to potential curves should not be routinely applied in situations where the bonding is strong, and (2) appropriate use of bond functions can lead to systematic improvement in the quality of potential curves.     

A simple model for the calculation of HOMO and LUMO energy levels of benzocatafusenes

A simple model for the calculation of HOMO and LUMO energy levels of benzocatafusenes (i.e., molecules that are only constituted by mutually condensed benzene rings and without interior carbon atoms, which belong to three benzene rings) is presented. Using semiempirical AM1 method, 615 benzocatafusenes were studied (29 normal and 586 branched). The relation between energy and molecular structure was coded by the three Hückel parameters: Coulomb integral, bond integral, and secular x eigenvalue. Analytical functions for HOMO and LUMO energy levels in terms of x parameter were obtained for normal benzocatafusenes, and energies for branched benzocatafusenes were satisfactorily modelled by the introduction of a simple correction function into the analytical functions describing normal benzocatafusenes. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The electronic structure of tetrahedral III–V compounds: The ground state of boron nitride

The bond-orbital theory of III–V compounds, previously described by Coulson, Redei and Stocker, is used to calculate the effective atomic charges and the binding energy per bond in boron nitride. The theory is reformulated in a manner which is convenient for performing both ab initio and semiempirical calculations. Two different choices for the atomic-orbital exponents are considered and, in both cases, the results obtained from the ab initio method are at variance with the earlier calculations in predicting an electronic charge displacement from nitrogen to boron. The magnitude of the effective charges is found to vary according to the method of partitioning the overlap charge between the nitrogen and boron atoms. The use of orthogonalized Slater 2s functions is also examined. The semiempirical calculations are performed with an explicit inclusion of the Madelung energy from the outset. The ionicity in the bond is shown to be determined by the competition between the difference in orbital electronegativities and the difference in Madelung potential across the ends of the bond. Unfortunately, the semiempirical theory breaks down because the energy per bond passes through a maximum at the optimum value of the polarity parameter. The reasons for this behaviour are examined and discussed.     

On the calculation of the structure of tris-(tert-butyl)-methane

A simple potential energy function developed on unstrained molecules and containing only 16 parameters can account for the unusually long C-C bonds and high C-H stretchings in highly strained tris-(tert-butyl)methane. On average, the structural deviations from experimental data are smaller than for some recently reported potential energy functions with 20–29 parameters. The success is thought to be due to fortunate handling of nonbonded interactions which include Coulomb terms.     

Filled and empty states of carbon nanotubes in water: Dependence on nanotube diameter, wall thickness and dispersion interactions

We have carried out a series of molecular dynamics simulations of water containing a narrow carbon nanotube as a solute to investigate the filling and emptying of the nanotube and also the modifications of the density and hydrogen bond distributions of water inside and also in the vicinity of the outer surfaces of the nanotube. Our primary goal is to look at the effects of varying nanotube diameter, wall thickness and also solute-solvent interactions on the solvent structure in the confined region also near the outer surfaces of the solute. The thickness of the walls is varied by considering single and multi-walled nanotubes and the interaction potential is varied by tuning the attractive strength of the 12–6 pair interaction potential between a carbon atom of the nanotubes and a water molecule. The calculations are done for many different values of the tuning parameter ranging from fully Lennard-Jones to pure repulsive pair interactions. It is found that both the solvation characteristics and hydrogen bond distributions can depend rather strongly on the strength of the attractive part of the solute-water interaction potential. The thickness of the nanotube wall, however, is found to have only minor effects on the density profiles, hydrogen bond network and the wetting characteristics. This indicates that the long range electrostatic interactions between water molecules inside and on the outer side of the nanotube do not make any significant contribution to the overall solvation structure of these hydrophobic solutes. The solvation characteristics are primarily determined by the balance between the loss of energy due to hydrogen bond network disruption, cavity repulsion potential and offset of the same by attractive component of the solute-water interactions. Our studies with different system sizes show that the essential features of wetting and dewetting characteristics of narrow nanotubes for different diameter and interaction potentials are also present in relatively smaller systems consisting of about five hundred molecules. We dedicate this work to Professor Debashis Mukherjee on his 60th Birthday.     

A potential function for computer simulation studies of proton transfer in acetylacetone

A potential energy model is developed to study the intramolecular proton transfer in the enol form of acetylacetone. It makes use of the empirical valence bond approach developed by Warshel to combine standard molecular mechanics potentials for the reactant and product states to reproduce the interconversion between these two states. Most parameters have been fitted to reproduce the key features of an ab initio potential surface obtained from 4-31G^* Hartree-Fock calculations. The partial charges have been fitted to reproduce the electrostatic potential surface of 6-31G^* Hartree-Fock wave functions, subject to total charge and symmetry constraints, using a fitting procedure based on generalized inverses. The resulting potential energy function reproduces the features most important for proton transfer simulations, while being several orders of magnitude faster in evaluation time than ab initio energy calculations. © 1997 by John Wiley & Sons, Inc.     

Optimized gaussian bond functions for CO

Optimum bond function parameters of ξ_1s = 1.12 and ξ_2p = 0.70 placed at 0.44 of the bond distance from the oxygen atom are reported for the CO molecule. Using these parameters, the total ground-state energy is lower than that obtained by Neumann and Moskowitz using two sets of 3d type polarization functions on each atomic center with exponents of 0.5 and 1.5. The one-electron properties, however, are slightly inferior to those calculated using the 3d functions.     

Empirical valence bond models for reactive potential energy surfaces: a parallel multilevel genetic program approach

We describe a new method for constructing empirical valence bond potential energy surfaces using a parallel multilevel genetic program (PMLGP). Genetic programs can be used to perform an efficient search through function space and parameter space to find the best functions and sets of parameters that fit energies obtained by ab initio electronic structure calculations. Building on the traditional genetic program approach, the PMLGP utilizes a hierarchy of genetic programming on two different levels. The lower level genetic programs are used to optimize coevolving populations in parallel while the higher level genetic program (HLGP) is used to optimize the genetic operator probabilities of the lower level genetic programs. The HLGP allows the algorithm to dynamically learn the mutation or combination of mutations that most effectively increase the fitness of the populations, causing a significant increase in the algorithm's accuracy and efficiency. The algorithm's accuracy and efficiency is tested against a standard parallel genetic program with a variety of one-dimensional test cases. Subsequently, the PMLGP is utilized to obtain an accurate empirical valence bond model for proton transfer in 3-hydroxy-gamma-pyrone in gas phase and protic solvent.     

THEORY OF INTRAMOLECULAR ORIENTATIONAL ORDER OF MESOGENIC UNITS IN MC-LCPS AND ITS APPLICATION

New concepts such as intramolecular orientational order parameter and corresponding model as well as theory were proposed to describe the intramolecular orientation of mesogenic units in the liquid crystalline polymer chains. The relationship between the intramolecular orientational order parameter and the molecular geometrical parameters such as the bond angle, the bond rotational angle and the rotational potential energy of chemical bonds was deduced. A significant even-odd oscillation of the intramolecular orientational order parameter of LCPs with different length of flexible spacer was found and rationally related to even-odd zig-zag manner of transition properties The verification and application of the theory are also discussed. The isotropic transition temperature predicted by the theory is shown to be in favourable agreement with the experiments.     

Bond dissocation and conformational energetics of tetrasulfur: a quantum Monte Carlo study

Variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) calculations are performed for S4. The effect of single- and multireference trial functions, as well as choice of orbitals, is investigated for its effect on the quality of the Monte Carlo estimates. Estimates of symmetric (two S2 molecules) and asymmetric (S atom and S3 molecule) bond dissociation are reported. The conformational change of S4 from C2v to D2h defines a double-well potential and is also estimated. Multireference DMC with natural orbitals (DMC/NO) estimates the energy of the conformational change as 1.20(20) kcal/mol; the dissociation of the long S-S single bond is estimated at 21.1(1.3) kcal/mol, and the asymmetric bond energy is estimated as 53.2(2.4) kcal/mol. An estimate of the total atomization energy using multireference DMC/NO gives a value of 219.5(2.2) kcal/mol. The relative quality of result and implications for simplified trial function design are discussed.     

On low‐lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the C C bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values. © 2017 Wiley Periodicals, Inc.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

Prediction of the thermodynamic properties of {ammonia + water} using cubic equations of state with the SOF cohesion function

The SOF cohesion function for cubic equations of state is based on the behavior of the residual energy of pure fluids. It contains two adjustable parameters for each component, which have been obtained for over 800 substances by regression of pure-fluid saturation pressures, and correlated in terms of a four-parameter corresponding states principle. In the present work, we compare the performance of this function and of the original Soave cohesion function with the Redlich-Kwong and Peng-Robinson equations of state in the prediction of vapor-liquid equilibria and enthalpy-composition diagrams for the polar system {ammonia + water}. We use simple van der Waals one-fluid mixing rules, linear for the covolume and quadratic for the cohesion parameter with one (symmetric) and two (asymmetric) binary interaction parameters. The non-linear least squares minimization algorithm lsqnonlin, in Matlab^®, is used to adjust the interaction parameters to phase equilibrium and enthalpy data taken from the IAPWS fundamental formulation. Upper and lower bounds of the optimized interaction parameters are obtained using Matlab^®bootstrap with 95% confidence of a normal distribution sampling. The validity of the parameters as functions of temperature is between the triple point of water and the critical point of ammonia. At lower temperatures, a rapid increase of statistical uncertainties is observed that can be attributed to the scarcity of phase equilibrium data.The two-parameter SOF cohesion function and the cubic equations of state are shown to give accurate predictions of the VLE and enthalpies of {ammonia + water}. Both equations of state give very similar results. Statistical analysis of the interaction parameters shows that their values (within the range of validity mentioned above) are effectively the same for both cohesion functions. At higher temperatures, however, extrapolation of the two cohesion functions gives different results, and correspondingly requires different interaction parameters.     

Determination of vibrational level spacings of van der waals molecules from the Lennard-Jones potential

An approximate expression for the eigenvalues for van der Waals molecules by use of the Lennard-Jones (12-6) potential in the WKB approximation is presented. The expression is applied to the rare gas molecules. Ar₂, Kr₂, and Xe₂ by fitting the potential function to the observed potential parameters. Calculated results of vibrational energy spacings for these molecules agree well with the experiment and other calculations which are based on numerical integration of the Schrödinger equation. For Xe₂, the energy spacing expression is used to determine the thermodynamic functions of the van der Waals bond.