Intermolecular Potential Energy Curves Research Articles

Peng: A program for transport properties of low-density binary gas mixtures

The fundamental properties of molecules bridge experiment and theory. Transport properties (diffusion, thermal diffusion, thermal conductivity and viscosity) of binary mixtures are measurable in experiments, and well-defined in theory, but difficult to compute with high accuracy. In addition to high-accuracy inter-molecular potential energy curves (PECs), a reliable and high-order solution program that compute the properties based on the PECs is required. In this work, we present a computer program called Peng that performs the collision integration numerically, and solves the Boltzmann equation in Chapman–Enskog fashion. The program has been devised to perform both parts of the solution procedure to arbitrary order, so that no hard-coded limitation will prevent a user from computing at higher precision, except the amount of RAM and the required computational time. Peng is well-designed in an Object-Oriented Programming (OOP) fashion, which make the program clear and easy to modify. In addition to the end-user oriented program, Peng is also compiled as a dynamic shared library that may readily be extended and embedded in users' programs. Program summaryProgram Title:PengCPC Library link to program files:https://doi.org/10.17632/n5tm9426jx.1Developer's repository link:https://github.com/zhaiyusci/pengCode Ocean capsule:https://codeocean.com/capsule/9951686Licensing provisions: LGPLProgramming language: C++Nature of problem: Nowadays, quantum chemistry provides high-accuracy intermolecular interactions potential energy curves (PECs), and more and more accurate thermophysical properties of dilute gases can be measured experimentally. It is meaningful to build a bridge between thermophysical properties and PECs, so that people can refine the PECs and learn more about the nature of dynamics of gases. For a dilute binary gas mixture, the theory, the Boltzmann equation, and its solution has been available for a long time, but fewer numerical solution packages are available for the public. An easy-to-use and easy-to-extend software package is required.Solution method: To complete the work, we have created a program that computes the collision integrals (Ω(ℓ,s)) for a set of temperatures, following which the thermophysical properties are computed using the Chapman–Enskog solutions of the Boltzmann equation. Both parts of the program are written in C++. The program is easy to use, and a well-designed framework is provided thanks to the Object-oriented design. Users with programming experience can readily extend the present work.Additional comments including restrictions and unusual features: In this version, the program is limited to the computation of the properties of mixtures of structureless atoms. For polyatomic molecules, additional work need to be done.

New Approach for Correcting Noncovalent Interactions in Semiempirical Quantum Mechanical Methods: The Importance of Multiple-Orientation Sampling.

A new approach is presented to improve the performance of semiempirical quantum mechanical (SQM) methods in the description of noncovalent interactions. To show the strategy, the PM6 Hamiltonian was selected, although, in general, the procedure can be applied to other semiempirical Hamiltonians and to different methodologies. A set of small molecules were selected as representative of various functional groups, and intermolecular potential energy curves (IPECs) were evaluated for the most relevant orientations of interacting molecular pairs. Then, analytical corrections to PM6 were derived from fits to B3LYP-D3/def2-TZVP reference–PM6 interaction energy differences. IPECs provided by the B3LYP-D3/def2-TZVP combination of the electronic structure method and basis set were chosen as the reference because they are in excellent agreement with CCSD(T)/aug-cc-pVTZ curves for the studied systems. The resulting method, called PM6-FGC (from functional group corrections), significantly improves the performance of PM6 and shows the importance of including a sufficient number of orientations of the interacting molecules in the reference data set in order to obtain well-balanced descriptions.

PSO Method for Fitting Analytic Potential Energy Functions. Application to I-(H2O).

In this work a particle swarm optimization (PSO) algorithm was used to fit an analytic potential energy function to I-(H2O) intermolecular potential energy curves calculated with DFT/B97-1 theory. The analytic function is a sum of two-body terms, each written as a generalized sum of Buckingham and Lennard-Jones terms with only six parameters. Two models were used to describe the two-body terms between I- and H2O: a three-site model H2O and a four-site model including a ghost atom. The fits are compared with those obtained with a genetic/nonlinear least-squares algorithm. The ghost atom model significantly improves the fitting accuracy for both algorithms. The PSO fits are significantly more accurate and much less time-consuming than those obtained with the genetic/nonlinear least-squares algorithm. Eight I----H2O potential energy curves, fit with the PSO algorithm for the three- and four-site models, have RMSE of 1.37 and 0.22 kcal/mol and compute times of ∼20 and ∼68 min, respectively. The PSO fit for the four-site model is quite adequate for determining densities of states and partition functions for I-(H2O) n clusters at high energies and temperatures, respectively. The PSO algorithm was also applied to the eight potential energy curves, with the four-site model, for a short time ∼8 min fitting. The RMSE was small, only 0.37 kcal/mol, showing the high efficiency of the PSO algorithm with retention of a good fitting accuracy. The PSO algorithm is a good choice for fitting analytic potential energy functions, and for the work presented here was able to find an adequate fit to an I-(H2O) analytic intermolecular potential with a small number of parameters.

Intermolecular potential for binding of protonated peptide ions with perfluorinated hydrocarbon surfaces.

An analytic potential energy function was developed to model both short-range and long-range interactions between protonated peptide ions and perfluorinated hydrocarbon chains. The potential function is defined as a sum of two-body potentials of the Buckingham form. The parameters of the two-body potentials were obtained by fits to intermolecular potential energy curves (IPECs) calculated for CF4, which represents the F and C atoms of a perfluoroalkane chain, interacting with small molecules chosen as representatives of the main functional groups and atoms present in protonated peptide ions: specifically, CH4, NH3, NH4(+), and HCOOH. The IPECs were calculated at the MP2/aug-cc-pVTZ level of theory, with basis set superposition error (BSSE) corrections. Good fits were obtained for an energy range extending up to about 400 kcal/mol. It is shown that the pair potentials derived from the NH3/CF4 and HCOOH/CF4 fits reproduce acceptably well the intermolecular interactions in HCONH2/CF4, which indicates that the parameters obtained for the amine and carbonyl atoms may be transferable to the corresponding atoms of the amide group. The derived potential energy function may be used in chemical dynamics simulations of collisions of peptide-H(+) ions with perfluorinated hydrocarbon surfaces.

Intermolecular potentials for simulations of collisions of SiNCS+ and (CH3)2SiNCS+ ions with fluorinated self-assembled monolayers

Analytical potential energy functions were developed for interactions of SiNCS+ and (CH3)2SiNCS+ ions with perfluorinated self-assembled monolayer (F-SAM) surfaces. Two model compounds were used to represent an F-SAM: CF4 and nine chains of perfluorobutane forming a miniSAM structure. Density functional theory plus dispersion (DFT-D) calculations were carried out to compute intermolecular potential energy curves (IPECs) for these systems. The applied DFT-D method (specifically, B97-D) was successfully tested against high-level wavefunction calculations performed on the smallest system investigated. The IPECs calculated at the B97-D level were fitted to analytical potentials of the Buckingham type. The calculations show that the parameters obtained from the fits involving CF4 are transferable to the miniSAM system, provided the fittings are conducted with caution, thus corroborating that CF4 is a good model for parameterizing intermolecular potentials for interactions of gases with F-SAM surfaces.

Determination of a potential energy function for nitrogen trifluoride by inversion of the new reduced viscosity collision integrals at zero density

A new correlation equation for the low-density viscosity collision integrals of nitrogen trifluoride (NF 3) was developed. The correlation equation spans the temperature range of Hurly’s data [J.J. Hurly, Int. J. Thermophys. 25 (2004) 625]. The acquired equation was inverted directly to give an effective isotropic reduced intermolecular potential energy curve corresponding to the viscosity collision integrals. This correlation provides a practical tool for further calculations. The potential energy function of NF 3 was determined at zero pressure and was fitted to the exponential-spline-Morse-spline-van der Waals (ESMSV) in order to obtain the analytical potential forms. It was concluded that the pair interaction potential energy function obtained from the inversion procedure reproduces viscosity coefficients within −1% up to 0.2% moderate density regime and could be used as input for calculating of the other thermophysical properties of NF 3 from molecular-based standpoint.

Potential energy calculations for various water dimer configurations

Intermolecular potential energy curves are presented and analyzed for three different water dimer structures: the normal hydrogen-bonded structure (Cs); a weakly hydrogen-bonded structure (C1) thought to be important in encounters of hydrated ions in aqueous solution; and a repulsive configuration (C2h) characterized by a head-on approach of hydrogen atoms (OH … HO). Results are based on ab initio calculations [SCF and CI (at the MP2 level), with and without counterpoise (CP) correction for basis set superposition error (BSSE)] and also a recent semiempirical effective pair potential (RWK2). The CP corrections have a significant effect on the location and depth of the potential wells for the hydrogen-bonded structures, even when CI and extended basis sets are employed.

Calculation of transport properties and intermolecular potential energy function of the binary mixtures of H 2 with Ne, Ar, Kr and Xe by a semi-empirical inversion method

The present paper contains inspection of the improved corresponding states principle for transport properties of hydrogen and the binary mixtures of hydrogen with Ne, Ar, Kr and Xe. The set of corresponding states parameters has been defined by a complex numerical analysis of a carefully selected body of experimental data. The obtained correlations for the reduced orientation-averaged diffusion and viscosity collision integrals are restricted to low densities in a temperature range from T = ɛ/ k to the onset of ionization. These equations have been inverted directly to give the isotropic and effective intermolecular potential energy curve for binary mixtures of H 2 with Ne, Ar, Kr and Xe corresponding to the viscosity collision integrals. The results are then used to obtain the best Morse-Spline-Van der Waals (MSV) potential parameters. Our inverted potential energies have been compared with experimental intermolecular potentials that were obtained by molecular beam scattering and infrared spectroscopic measurements. In this research, the Chapman–Enskog and Wang Chang-Uhlenbeck-de Boer (WCUB) version of kinetic theory have been used in conjunction with our inverted potential energies to reproduce viscosity, diffusion, thermal conductivity and thermal diffusion factor of binary mixtures of H 2 with Ne, Ar, Kr and Xe in a wide temperature range for equimolar composition. As the deviation plots illustrate, our obtained intermolecular potential energies (on the basis of the algorithm presented in the inversion process) represent the low-density transport properties of binary mixtures of H 2 with Ne, Ar, Kr and Xe within their expected experimental uncertainties. Close agreement between the predicted values and the literature results of transport properties demonstrates the predictive power of the inversion scheme.

Intermolecular Potential To Represent Collisions of Protonated Peptide Ions with Fluorinated Alkane Surfaces

The MP2/6-311++G(2df,2pd) level of theory was used to calculate intermolecular potential curves between CF(4), as a model for the C and F atoms of a fluorinated alkane surface, and CH(4), NH(3), NH(4)(+), H(2)CO, and H(2)O as models for different types of atoms and functional groups comprising protonated peptide ions. This level of theory was tested by comparisons with the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ theories. Explicit-atom (EA) analytic potential energy functions were then derived by fitting these potential energy curves with two-body potentials between the atoms of the two interacting molecules. An intermolecular potential for the interaction of a protonated peptide ion with a fluorinated alkane surface may be constructed from these two-body potentials. Intermolecular potentials, for which CF(4) is treated as a united atom (UA), were developed by isotropically averaging the CF(4) orientation for each of the EA potential energy curves. The intermolecular potential energy curves calculated for CF(4) are compared with curves calculated previously for CH(4) interacting with the same molecules, to consider the relative efficiency of energy transfer for protonated peptide ion collisions with hydrogenated and fluorinated alkane surfaces.

Direct determination of pair potential energy function from extended law of corresponding states and calculation of thermophysical properties for H2–He

Abstract A new correlation equation for the low-density binary diffusion and viscosity collision integrals of hydrogen–helium over a very large reduced temperature range from 1 to the onset of ionization is obtained. These equations has been inverted directly to give the isotropic reduced intermolecular potential energy curve for H 2 –He, corresponding to the viscosity collision integrals and we used these data in conjunction with the second virial coefficient to calculate outer branch of the potential well. Comparison is made between the present MSV interaction potential energy function and the independently known H 2 –He potential energy function. The present potential function provides the best overall agreement for the available low-density gas phase thermophysical data, i.e., transport properties in a wide composition and temperature range.

Br − - H 2 and I−-H2 anion complexes: Infrared spectra and radial intermolecular potential energy curves

Midinfrared spectra of the Br−81-H2 and I−-H2 anion complexes are measured in the H-H stretch region by monitoring the production of halide anion photofragments. The spectra, which are assigned to complexes containing ortho H2, exhibit rotationally resolved ∑-∑ bands whose origins are redshifted from the molecular hydrogen Q1(1) transition by 110.8 cm−1 (Br−-H2) and 74.1 cm−1 (I−-H2). The complexes are deduced to possess linear equilibrium structures, with vibrationally averaged intermolecular separations between the halide anion and H2 center of mass of 3.461 Å (Br−-H2) and 3.851 Å (I−-H2). Vibrational excitation of the H2 subunit causes the intermolecular bond to stiffen and contract by 0.115 Å (Br−-H2) and 0.112 Å (I−-H2). Rydberg–Klein–Rees inversion of the spectroscopic data is used to generate effective radial potential energy curves near the potential minimum that are joined to long-range potential energy curves describing the interaction between an H2 molecule and a point negative charge. From these curves the dissociation energies of Br−-H2 and I−-H2 with respect to isolated H2 (j=1) and halide fragments are estimated as 365 and 253 cm−1, respectively.

Direct Determination of the Intermolecular Potential for H2–H2from a Viscosity Correlation Equation

A correlation equation for the low-density viscosity collision integral of hydrogen molecules over a very large temperature range is obtained. This equation has been inverted directly to give the reduced intermolecular potential energy curve for H 2 –H 2 corresponding to the collision integral. The results are then used to obtain a best Morse-Spline-Van der Waals (MSV) potential model. Comparison is made between the present interaction potential energy function and two other previously published H 2 –H 2 potential energy functions. The present potential function provides the best overall agreement for the available low-density gas phase thermophysical data, i.e. second virial coefficient and transport properties, and can thus be recommended for calculation of all properties that depend upon the intermolecular interaction.

Comparative study of BSSE correction methods at DFT and MP2 levels of theory

A comparative study of intermolecular potential energy curves is performed on the complexes H2O(SINGLE BOND)HF, H2O(SINGLE BOND)H2O, H2O(SINGLE BOND)H2S, and H2S(SINGLE BOND)H2S using nine different basis sets at the MP2 and DFT (BLYP and B3LYP) levels of theory. The basis set superposition error is corrected by means of the counterpoise scheme and based on the “chemical Hamiltonian approach.” The counterpoise and CHA-corrected DFT curves are generally close to each other. Using small basis sets, the B3LYP functional cannot be favored against the BLYP one because the BLYP results sometimes get closer to the MP2 values than those of B3LYP. From the results—including the available literature data—we suggest that one has to use at least polarized-valence triple-zeta-quality basis sets (TZV, 6-311G) for the investigation of hydrogen-bonded complexes. Special attention must be paid to the physical nature of the binding. If the dispersion forces become significant DFT methods are not able to describe the interaction. Proper correction for the basis set superposition error is found to be mandatory in all cases. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 575–584, 1998

A pseudopotential study of the hydrogen bond in H2O·H2S, H2S·H2S and H2O·H2Se systems

Intermolecular potential energy curves for the hydrogen bonded systems H2O·H2S, H2O·H2Se and H2S·H2S were calculated with nonempirical pseudopotentials using optimized-in-molecules basis sets augmented by polarization functions. The H2O·H2O interaction energy curve has been also considered as a test case. The present results for H2O·H2S and H2S·H2S indicate much weaker intermolecular interactions than those found in previous ab initio calculations. The H2O·H2Se interaction was found to be quite similar to H2O·H2S.

Some problems est the calculation of ab initio potential energy curves

The non-adiabatic and adiabatic approaches to the calculation of molecular energy levels are presented. The concept of the potential energy curve, its accuracy and limitations are discussed. Simplified approaches to calculations of the intermolecular potential energy curves are also considered.

Curve Crossing for Low-Energy Elastic Scattering ofHe+by Ne

The perturbation seen in the experimental differential elastic-scattering cross section for the 40-eV He/+/ + Ne system has been attributed to a single crossing of two intermolecular potential-energy curves. A new theoretical treatment of the curve-crossing problem, namely, that of Delos and Thorson, is employed to obtain the crossing probabilities and phases associated with the crossing. These are determined by utilizing ab initio potentials involved in the crossing and are further used in a partial-wave calculation of the cross section, which is compared with our experiment. The origin of the oscillatory structure observed in the differential cross section is discussed in semiclassical terms by defining the problem in terms of two pseudo-deflection-functions. A rainbow effect is shown to be related to a particular feature (a maximum rather than a minimum) of these deflection functions.

Excess Volumes in Binary Liquid Mixtures of Simple Molecules

RECENT statistical theories of liquid mixtures have made it possible to calculate the excess thermodynamic functions of binary mixtures from the parameters characterizing the intermolecular potential-energy curves for the two pairs of like molecules. For small molecules, between which only dispersion forces are supposed to operate, these parameters may conveniently be taken to be e11, the minimum value of the potential energy, and r11 the molecular separation corresponding to this minimum (for a pair of like molecules of species 1). The theories are of two types. Those of the first type use a definite model for the liquid, and enable the excess functions to be calculated from the appropriate e and r values alone. This applies to the treatment of Prigogine and Mathot1 (and its extension by Prigogine and Bellemans2) and to that of Salsburg and Kirkwood3. In treatments of the second type4,5, based on the theory of corresponding states, the excess functions are expressed in terms of (a) the ratios e11/e22 and r11/r22 and (b) the macroscopic properties of one of the two pure components, chosen as reference substance. Thus, the excess volume, VE, depends on the molar volume of the reference liquid and the temperature variation of this volume.