Analytical Potential Energy Function Research Articles

The ground electronic state of ClF: Updated molecular constants and potential curves for 35ClF and 37ClF

A comprehensive assessment of available literature spectroscopic data and molecular constants for the X 1Σ+ ground electronic states of isotopologues 35ClF and 37ClF is undertaken. Three different approaches are employed in the analysis of the available information. The first approach involves merging molecular constants from various studies to yield an optimized set of Dunham coefficients {Y01, Y02, Y03, Y10, Y11, Y21, Y02 and Y12}. Utilizing these updated constants, vibrational energies (Gυ) and rotational constants (Bυ) for υ = 0–9 are calculated, and RKR potentials are determined for both isotopologues. The second approach involves calculating synthetic spectroscopic line positions using literature molecular constants, with normally distributed random errors added on, and subjecting these to a modern direct-potential-fit analysis. This analysis produces a precise analytical potential energy function for 35ClF, and Born-Oppenheimer breakdown functions that characterize adiabatic and non-adiabatic corrections. The third approach involves fitting the synthetic spectroscopic data directly to Dunham coefficients. The results of the three approaches are compared and discussed.

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

A variationally improved Hulburt-Hirschfelder analytical potential energy function for diatomic molecules

In this paper, a variationally improved Hulburt-Hirschfelder (VIHH) analytical potential energy function (APEF) is presented and tested. The VIHH potential is composed of the remedy function and the improved Hulburt-Hirschfelder (IHH) APEF which possesses the same explicit parameters () with VIHH potential. Potential energy curves (PECs) for the ground electronic states of HI, HBr and KLi molecules have been modeled by the VIHH analytical potential, and it suggests that the VIHH potential is in good agreement of Rydberg-Klein-Rees (RKR) potential points and is superior to the original Hulburt-Hirschfelder (HH) potential, IHH potential and Morse potential, especially in the dissociation and the long-range region. The vibrational energy levels for the ground electronic state of the HI, HBr, and KLi molecules are obtained by numerically solving the radial Schrödinger equation using the LEVEL program for the case of the Morse potential, HH potential, IHH potential and the VIHH potential functions. The comparison for both vibrational energy levels and VIHH potential functions shows better agreement with the experimental data than the other potential functions. Comparing with IHH potential, the VIHH potential which included the remedy function has better physical behavior in the long-range region and the is effective for vanishing the invalid barrier.

Collision integrals for N(4S)–N(4S), N(4S)–N(2D), and N(4S)–N(2P) interactions

Collision integrals for the scattering of nitrogen (N) atoms are essential to model transport properties of air plasmas, which can be highly dependent on the species involved. At high temperatures, N atoms may exist in their excited states. Therefore, collision integrals for N atoms are computed at the temperature range of 500–50 000 K, in which the interactions between the excited [N(2D) and N(2P)] atoms and ground N(4S) atom are considered. The interaction between the excited N(2P) atom and ground N(4S) atom is considered for the first time. A comparison of the collision integrals from our combined-hyperbolic-inverse-power-representation (CHIPR) potential energy function with those obtained using other analytical potential energy functions in the literature is given. The results show that the trend of potential energy curves (PECs) in dissociated asymptotic and short-range regions has an important effect on the collision integrals. These regions are difficult to cover in experiments. Here we seek the state-of-the-art ab initio methods for a theoretical guideline to compute the PECs of N2, which are then modeled by the CHIPR function. PECs of some low-lying states are also refined by available experimental spectroscopic data. Overall, our collision integrals are reliable.

Theoretical study on macroscopic thermodynamic properties of NO<sup>+</sup> ion system

<sec>NO<sup>+</sup> is one of the most important ions in the atmospheric ionosphere and ionospheric phenomena such as auroras, and is one of the most stable diatomic cations existing in interstellar clouds. It is crucial to understand the thermodynamic properties of NO<sup>+</sup> ion for exploring the composition of interstellar gas. To obtain macroscopic thermodynamic properties of diatomic molecules and ions, a practical theoretical method is to determine the partition function associated with a potential model. This approach can be used to calculate various thermodynamic properties of the system based on the microscopic information.</sec><sec>In this work, the improved Hulbert-Hirschfelder (IHH) based potential energy model is used to simulate the potential energy curve of NO<sup>+</sup> in the ground electronic state. Then, the rovibrational energy levels for the ground electronic state of the NO<sup>+</sup> are obtained by numerically solving the radial Schrödinger equation through using the LEVEL program for the IHH potential function. Finally, the total partition function and the thermodynamic properties such as the molar heat capacity, entropy, enthalpy and reduced molar Gibbs free energy of NO<sup>+</sup> in a temperature range of 100–6000 K are calculated in the frame of the quantum statistical ensemble theory. The comparison indicates that the potential energy curve calculated based on IHH potential energy function is in better agreement with the experimental data. The root mean square error of IHH potential and experimental Rydberg-Klein-Rees (RKR) potential is 96.9 cm<sup>–1</sup>, the root mean square error of Hulbert-Hirschfelder (HH) potential is 112.7 cm<sup>–1</sup>, and the root mean square error of MRCI/aug-cc-pV6Z potential is 133 cm<sup>–1</sup>. And the macroscopic thermodynamic properties of NO<sup>+</sup> predicted by IHH are closer to the experimental values, which shows that the IHH potential model is also applicable to the ion system.</sec><sec>A feasible method is presented to obtain the thermodynamic properties of gaseous diatomic ions based on microscopic information by constructing reliable analytical potential energy function associated with quantum statistical ensemble theory.</sec>

High-resolution photoelectron spectroscopy of the ground and first excited electronic states of MgKr+

We report on the characterisation of the lowest three electronic states of MgKr, the X ground state associated with the Mg(3s) + Kr(4p) dissociation limit and the A and B excited states associated with the Mg(3p) + Kr(4p) dissociation limits. The vibrational structure of the X ground state was measured by pulsed-field-ionisation zero-kinetic-energy photoelectron spectroscopy starting from the a metastable state of MgKr generated by laser ablation of a Mg rod in a Kr supersonic beam. The vibrational assignment was derived from the isotopic structure of the spectra and the adiabatic ionisation energy of the ionising transition was determined to be 38182.4(2.0) cm. Partially rotationally resolved spectra of the A X and B X transitions were recorded by monitoring the yield of Mg ions produced by dissociation of MgKr using the technique of isolated-core Rydberg-dissociation spectroscopy. Analytical potential-energy functions of the X, A, and B states were derived using a global model of these states that includes the spin-orbit interaction. The observation of the highest vibrational levels of the B state and the onset of the Kr + Mg(3p) dissociation continuum enabled the precise determination of the dissociation energies of the X, A and B states of MgKr and of the a state of MgKr. The X, A and B states of MgKr are important stepping stones to access the Rydberg states of MgKr and the ground state of MgKr by resonant multiphoton excitation.

Collision Integrals for Nitrogen and Hydrogen Ionized Gas: The Exact Values and Assessment of Approximations

Collision integrals are calculated for the H–N^{+}, N–H^{+}, N^{2+}–H, and N^{+}–H^{+} interactions in the temperature range of 1000–60,000 K. The resulting collision integrals were fitted to simple functional forms. The applicability of commonly used approximations for calculation of the collision integrals is verified. Those approximations are simplification of exact potentials (especially the repulsive ones), use of polarizability potential for atom–ion interaction, and use of Coulomb screened potential for ion–ion interaction. The reported collision integrals are based on the ab initio calculated points of the potential energy curves, so that the error of fitting the points with analytical potential energy function is not present.

Theoretical study on the vibrational spectra and potential energy curves for SiC ([formula omitted]) and SiS ([formula omitted]) molecules

In this work, the vibrational constants (ωe,ωexe) calculated by the variational algebraic method (VAM) and some other molecular constants (De,re,Be,αe) were used to construct the improved Hulburt–Hirschfelder (IHH) analytical potential energy function (APEF). Not only that, but the calculated VAM potential points are used as the ’true’ energies to determine the value of the variational parameter λ which is the pivotal fitting parameter in the IHH potential. With limited experimental data, high-precision IHH potential can be achieved by combining the VAM and the IHH APEF. This combination of the VAM and the IHH APEF is referred to be VAIHH APEF, which is employed to study the vibrational energies and potential energy curves (PECs) of SiC (X3Π) and SiS (X1Σ+) molecules, yielding full vibrational spectra and spectroscopic constants. The calculational results indicate that the VAIHH APEFs of SiC (X3Π) and SiS (X1Σ+) molecules are in good agreement with the experimental RKR potential points. Accurate PECs of SiC (X3Π) and SiS (X1Σ+) molecules imply that the VAIHH APEF is of high quality.

Ab initio calculation of the ground and first excited states of the lithium dimer

Based on a high level ab initio calculation which is carried out with the multireference configuration interaction method under the aug-cc-pVXZ (AVXZ) basis sets, X = T, Q, 5, the accurate potential energy curves (PECs) of the ground state and the first excited state of Li2 are constructed. By fitting the ab initio potential energy points with the Murrell–Sorbie potential function, the analytic potential energy functions (APEFs) are obtained. The molecular bond length at the equilibrium (R e ), the potential well depth (D e ), and the spectroscopic constants (B e , ω e , α e , and ω e χ e ) for the state and the state are deduced from the APEFs. The vibrational energy levels of the two electronic states are obtained by solving the time-independent Schrödinger equation with the Fourier grid Hamiltonian method. All the spectroscopic constants and the vibrational levels agree well with the experimental results. The Franck–Condon factors (FCFs) corresponding to the transitions from the vibrational level (v′ = 0) of the ground state to the vibrational levels (v″ = 0–74) of the first excited state have been calculated. The FCF for the vibronic transition of (v″ = 0) ←(v′ = 0) is the strongest. These PECs and corresponding spectroscopic constants provide reliable theoretical references to both the spectroscopic and the molecular dynamic studies of the Li2 dimer.

Accurate theoretical study of potential energy curves, spectroscopic parameters, vibrational energy levels and spin-orbit coupling interaction on SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) ion

<sec>The analytical potential energy function (APEF) of SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) is fitted by Aguado-Paniagua function with 112 <i>ab initio</i> energy points, which are calculated by Molpro 2012 Package with the multi-reference configuration interaction including the Davidson correction method using AV<i>X</i> Z and AV<i>X</i> dZ (<i>X</i> = Q, 5, 6) basis sets. Moreover, the calculated <i>ab initio</i> energy points are subsequently extrapolated to complete basis set (CBS) limit to avoid the basis set superposition error. All the fitting parameters of APEFs for AV6Z, CBS(Q, 5), AV6dZ, CBS(Qd, 5d), SA-AV6dZ and SOC-AV6dZ methods are gathered. The potential energy curves (PEC) and the corresponding <i>ab initio</i> points are also shown. As can be seen, the PECs show excellent agreement with the <i>ab initio</i> points and a smooth behavior both in short range and long range, which ensures the high quality of fitting process for the current APEFs. </sec><sec> Based on these APEFs of different basis sets and methods including AVQZ, AV5Z, AV6Z, CBS(Q, 5), AVQdZ, AV5dZ, AV6dZ and CBS(Qd, 5d), the spectral constants <i>D</i><sub>e</sub>, <i>R</i><sub>e</sub>, <i>ω</i><sub>e</sub>, <i>B</i><sub>e</sub>, <i>α</i><sub>e</sub> and <i>ω</i><sub>e</sub><i>χ</i><sub>e</sub> are obtained. In addition, the effects of spin-orbit coupling interaction (SOC) on the system are also investigated. By comparing the spectral constants of SA-AV6dZ with the ones of SOC-AV6dZ, it is found that the effect of SOC on SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) is small and can be ignored. We also compare the spectral constants in this work with the experimental values and other theoretical results. The results of this work accord well with the corresponding experimental and other theoretical results. It is worth noting that the deviation of dissociation energy between the theoretical calculations and experimental values is relatively large. Based on this conclusion, we suggest that the spectral constants including the dissociation energy for SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) should be remeasured. </sec><sec> Based on the APEF of SOC-AV6dZ which should be more accurate than others in theory, the top 23 vibrational states (<i>j</i> = 0) of SiH<sup>+</sup>(X<sup>1</sup>Σ<sup>+</sup>) are calculated first by solving the radial Schrödinger equation. All the vibrational energy levels, classical turning points, rotation constants and six centrifugal distortion constants are also provided. The results of this work can provide significant references for the experimental and other theoretical work.</sec>

Analytical potential energy function study for the 41∏ electronic state of Na85Rb molecule

In this paper, a new spectroscopic and analytical potential energy function (APEF) investigation on the electronic state of the Na85Rb molecule is reported. This research is conducted by using the 4-terms variation algebraic energy consistent method (VAECM(4)) with a variable parameter λ. The calculated full vibrational energies of 78 levels are used in a global linear reduction to molecular vibrational constants. With these new and improved vibrational constants, the potential energy curve and the vibrational force constants have been calculated. Precise values for the long-range parameters and the dissociation energy have been derived. The results obtained in this study also provide valuable reference data for other areas of researches on Na85Rb.

Potential energy curves, spectroscopic constants, and vibrational energy levels of CS+(X 2Σ+/A 2Π)

ABSTRACT The accurate potential energy curves (PECs) of the are obtained based on the ab initio energies which are calculated via the multi-reference configuration interaction including the Davidson correction method (MRCI(Q)), together with aug-cc-pVXZ (X = T, Q, 5, 6) basis sets. The ab initio energy points calculated by the MRCI(Q)/aug-cc-pVXZ (X = Q, 5) are subsequently extrapolated to the complete basis set (CBS) limit. For the ground state of , it is found that there is a lower barrier in the long range, and the Gaussian function can be used to fit it. Then the root mean square derivations, spectroscopic constants, vibrational energy levels and classical turning points are obtained based on such obtained analytical potential energy functions (APEFs). The present results are in agreement well with other theoretical and experimental works, which prove that such APEFs including Gaussian function are reliable and highly accurate in both short and long ranges.

Global Potential Energy Surface for HO2+ Using the CHIPR Method.

An analytical potential energy function for the title ion based on the combined hyperbolic inverse power representation (CHIPR) method and its characteristics are discussed at length in the present work. The curves of two diatomic ions, O2+ and OH+, are also obtained within the same approach. The model PES so obtained exhibits extraordinary flexibility in describing with subchemical accuracy even the weak topological features near the higher energy regions. Thus, structural properties predicted by the model may help spectroscopists who want to compare their experimental values with the ones from theory. The relaxed PESs in various coordinates have been calculated by relaxing the O2 bond distance using the present model, thus throwing light on all the possible isomers and their interconversions. The latest estimates of IR frequencies for three vibrational modes have been compared with the computed frequencies using the present model, and the agreement seems encouraging.

Spectroscopic properties and analytical potential energy function of ground and low-lying excited states of BeC moleule

Diatomic molecule BeC has a complex electronic structure with a large number of low-lying excited states that are all strongly bound electronic states. Thus, the BeC molecule has the abundant spectral information. In this work, the potential energy curves and wavefunctions of <inline-formula><tex-math id="M4445">\begin{document}$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M4445.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M4445.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M78777">\begin{document}${\rm{A}}^3 {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M78777.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M78777.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M88881">\begin{document}$ {{\rm{b}}^1} {{\text{Δ}} } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M88881.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M88881.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M55555">\begin{document}${{\rm{c}}^1} {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M55555.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M55555.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M666766">\begin{document}$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M666766.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M666766.png"/></alternatives></inline-formula> states of the BeC molecule are calculated by using the internally contracted multi-reference configuration interaction (MRCI) approach, which is based on the use of a dynamically weighted complete active space self-consistent field (DW-CASSCF) procedure. To improve the reliability and accuracy of calculation, the scalar relativistic corrections and the extrapolation of potential energy to the complete basis set limit are taken into account. On the basis of the calculated potential energy curves and wavefunctions, the spectroscopic constants (<i>T</i><sub>e</sub>, <i>R</i><sub>e</sub>, <inline-formula><tex-math id="M999999">\begin{document}${\omega _{\rm{e}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M999999.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M999999.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M99998779">\begin{document}${\omega _{\rm{e}}}{x_{\rm{e}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M99998779.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M99998779.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M99779">\begin{document}${\omega _{\rm{e}}}{y_{\rm{e}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M99779.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M99779.png"/></alternatives></inline-formula>, <i>B</i><sub>e</sub>, <inline-formula><tex-math id="M99999">\begin{document}${\alpha _{\rm{e}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M99999.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M99999.png"/></alternatives></inline-formula>, and <i>D</i><sub>e</sub>) and permanent dipole moments of those states are determined, the results of which are in good agreement with the existing available experimental and theoretical values. The obtained permanent dipole moments indicate that the electrons transfer from Be to C and the polarity for molecule is <inline-formula><tex-math id="M666654">\begin{document}$ {\rm{B}}{{\rm{e}}^{{\text{δ}} + }}{{\rm{C}}^{{\text{δ}} - }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M666654.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M666654.png"/></alternatives></inline-formula>. The transition properties of the spin-allowed <inline-formula><tex-math id="M76777">\begin{document}${\rm{A}}^3 {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M76777.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M76777.png"/></alternatives></inline-formula>−<inline-formula><tex-math id="M4446">\begin{document}$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M4446.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M4446.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M5522252582">\begin{document}${{\rm{c}}^1} {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M5522252582.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M5522252582.png"/></alternatives></inline-formula>−<inline-formula><tex-math id="M88882">\begin{document}$ {{\rm{b}}^1} {{\text{Δ}} } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M88882.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M88882.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M55555582">\begin{document}${{\rm{c}}^1} {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M55555582.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M55555582.png"/></alternatives></inline-formula>−<inline-formula><tex-math id="M666566">\begin{document}$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M666566.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M666566.png"/></alternatives></inline-formula> transitions are predicted, including the transition dipole moments, Franck-Condon factors, and radiative lifetimes. The radiative lifetimes for the <inline-formula><tex-math id="M75777">\begin{document}${\rm{A}}^3 {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M75777.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M75777.png"/></alternatives></inline-formula>−<inline-formula><tex-math id="M4447">\begin{document}$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M4447.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M4447.png"/></alternatives></inline-formula> transitions are predicated to be at a <inline-formula><tex-math id="M55523">\begin{document}$ {{\text{µ}}\rm{ s}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M55523.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M55523.png"/></alternatives></inline-formula> level, and the good agreement with previous theoretical values is found. Radiative lifetimes for <inline-formula><tex-math id="M585582">\begin{document}${{\rm{c}}^1} {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M585582.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M585582.png"/></alternatives></inline-formula>−<inline-formula><tex-math id="M88883">\begin{document}$ {{\rm{b}}^1} {{\text{Δ}} } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M88883.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M88883.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M554582">\begin{document}${{\rm{c}}^1} {\text{Π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M554582.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M554582.png"/></alternatives></inline-formula>−<inline-formula><tex-math id="M66645766">\begin{document}$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M66645766.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M66645766.png"/></alternatives></inline-formula> transitions are also evaluated at the levels of <inline-formula><tex-math id="M554523">\begin{document}$ {{\text{µ}}\rm{ s}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M554523.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181695_M554523.png"/></alternatives></inline-formula> and ms, respectively. The PEC for the ground state is fitted into accurate analytical potential energy functions by using the extended-Rydberg potential function.

Review of force fields and intermolecular potentials used in atomistic computational materials research

Molecular simulation is a powerful computational tool for a broad range of applications including the examination of materials properties and accelerating drug discovery. At the heart of molecular simulation is the analytic potential energy function. These functions span the range of complexity from very simple functions used to model generic phenomena to complex functions designed to model chemical reactions. The complexity of the mathematical function impacts the computational speed and is typically linked to the accuracy of the results obtained from simulations that utilize the function. One approach to improving accuracy is to simply add more parameters and additional complexity to the analytic function. This approach is typically used in non-reactive force fields where the functional form is not derived from quantum mechanical principles. The form of other types of potentials, such as the bond-order potentials, is based on quantum mechanics and has led to varying levels of accuracy and transferability. When selecting a potential energy function for use in molecular simulations, the accuracy, transferability, and computational speed must all be considered. In this focused review, some of the more commonly used potential energy functions for molecular simulations are reviewed with an eye toward presenting their general forms, strengths, and weaknesses.

Anharmonic Densities of States for Vibrationally Excited I-(H2O), (H2O)2, and I-(H2O)2.

Monte Carlo sampling calculations were performed to determine the anharmonic sum of states, Nanh( E), for I-(H2O), (H2O)2, and I-(H2O)2 versus internal energy up to their dissociation energies. The anharmonic density of states, ρanh( E), is found from the energy derivative of Nanh( E). Analytic potential energy functions are used for the calculations, consisting of TIP4P for H2O···H2O interactions and an accurate two-body potential for the I-···H2O fit to quantum chemical calculations. The extensive Monte Carlo samplings are computationally demanding, and the use of computationally efficient potentials was essential for the calculations. Particular emphasis is directed toward I-(H2O)2, and distributions of its structures versus internal energy are consistent with experimental studies of the temperature-dependent vibrational spectra. At their dissociation thresholds, the anharmonic to harmonic density of states ratio, ρanh( E)/ρh( E), is ∼2, ∼ 3, and ∼260 for I-(H2O), (H2O)2, and I-(H2O)2, respectively. The large ratio for I-(H2O)2 results from the I-(H2O)2 → I-(H2O) + H2O dissociation energy being more than 2 times larger than the (H2O)2 → 2H2O dissociation energy, giving rise to highly mobile H2O molecules near the I-(H2O)2 dissociation threshold. This work illustrates the importance of treating anharmonicity correctly in unimolecular rate constant calculations.

Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions.

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.

A new empirical potential energy function for Ar2

ABSTRACTA critical re-analysis of all available spectroscopic and virial coefficient data for Ar2 has been used to determine an improved empirical analytic potential energy function that has been ‘tuned’ to optimise its agreement with viscosity, diffusion and thermal diffusion data, and whose short-range behaviour is in reasonably good agreement with the most recent ab initio calculations for this system. The recommended Morse/long-range potential function is smooth and differentiable at all distances, and incorporates both the correct theoretically predicted long-range behaviour and the correct limiting short-range functional behaviour. The resulting value of the well depth is cm−1 and the associated equilibrium distance is re = 3.766 (±0.002) Å, while the 40Ar s-wave scattering length is −714 Å.

Assessing Many-Body Effects of Water Self-Ions. I: OH-(H2O) n Clusters.

The importance of many-body effects in the hydration of the hydroxide ion (OH-) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the CCSD(T) level of theory, extrapolated to the complete basis set limit, for the low-lying isomers of OH-(H2O) n clusters, with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of OH- and water molecules and the hydrogen bonding connectivity within each fragment. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) method, this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling OH- hydration. Furthermore, the rapid convergence of the many-body expansion of the interaction energy also suggests a rigorous path for the development of analytical potential energy functions capable of describing individual OH--water many-body terms, with chemical accuracy. Finally, a comparison between the reference CCSD(T) many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that range-separated, dispersion-corrected, hybrid functionals exhibit the highest accuracy, while GGA functionals, with or without dispersion corrections, are inadequate to describe OH--water interactions.

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.