Ab Initio Potential Energy Functions Research Articles

Ab initio potential energy functions, spectroscopy and thermal physics for krypton-contained rare gas dimers

Three state-of-the-art ab initio interatomic potential energy functions (PEFs) for the Kr-Ne, Kr-Ar, Kr-Xe rare gas dimers are presented. These PEFs are based upon extrapolation to complete basis set (CBS) limit results of supermolecular computations at the coupled-cluster level with single, double, and perturbative triple excitations (CCSD(T)) and correlation-consistent basis sets up to sextuple-zeta quality, augmented with mid-bond functions. Core-core and core-valence electron correlation, higher-order coupled-cluster excitations up to perturbative quadruple excitations, CCSDT(Q), and scalar relativistic corrections have also been taken into account. We have employed Morse/Long Range (MLR) potential energy functions (PEFs) to fit the total interaction energies as a function of the internuclear separation, followed by the calculation of spectroscopic parameters, vibrational and rotational energy levels, absorption spectra, and thermophysical properties over an extensive temperature range. Good agreement with experimental data and an empirical potential energy function shows that our ab initio MLR PEFs are superior not only to previous PEFs, but also to most empirical PEFs.

Transport properties of two-component radium – halogen dilute gas media

Based on state-of-the-art ab initio potential energy functions and classical kinetic theory, some transport properties (diffusion, viscosity and thermal conductivity coefficients) of two-component dilute gas media of radium and halogen (F, Cl, Br, I) atoms were predicted as functions of the translation temperature up to 3000 K. Calculations were performed by sequential analytical and (or) numerical computations of deflection angle, cross-section and collision integrals. A detailed methodology for the calculation of the transport properties using the Morse potential was developed. Some numerical difficulties arising due to the singularity of the integrands and discontinuous character of the variable of integration are considered. The dependence of transport properties on isotope mass is also shown. Possible errors introduced by using the model Morse potential function instead of the real potential for the interaction between atoms are estimated. These data can be useful for the planning of the experiments on the direct laser cooling of the monohalides of alkaline earth metals.

Ab Initio Partition Functions and Thermodynamic Quantities for the Molecular Hydrogen Isotopologues.

In this work, we calculate the partition functions and thermodynamic quantities of molecular hydrogen isotopologues using the rovibrational energy levels provided by the highly accurate ab initio adiabatic potential energy functions recently determined by Pachucki and Komasa (Pachucki, K.; Komasa, J. J. Chem. Phys.2014, 141, 224103). The partition functions are calculated by including all bound energy levels of the isotopologues, up to their dissociation limits, plus the quasi-bound levels lying below the centrifugal potential barriers. For the homonuclear isotopologues, H2, D2, and T2, we also determine the partition functions and thermodynamic quantities of the normal mixtures using the statistical treatment recently proposed by Colonna et al. (Colonna, G.; D’Angola, A.; Capitelli, M. Int. J. Hydrogen Energy2012, 37, 9656) based on the definition of the partition function of the mixture, which avoids inconsistencies in the values of the thermodynamic quantities depending directly on the internal partition function, in the high-temperature limit.

Size and Structure Dependence of the Anomalous Bulk Modulus for FCC Metallic Nanoparticles

The purpose of this work is to develop a theoretical model to calculate the bulk moduli of FCC nanoparticles that account for their size and structure. The bulk modulus for spherical nanoparticles has been derived from the cohesive energy which had been calculated by summing up the potential energy function of every pair of atoms of these metallic nanoparticles. The ab initio pair potential energy function has been formed by inverting the cohesive energy function proposed by (Rose et al., 1981), using the Chen-Mobius method. The results show that, as the size decreases, the bulk modulus decreases for spherical nanoparticles, which agrees with previous experimental and theoretical predictions. The results also predicted an “amorphous” structure for ultra-small nanoparticles and were consistent with previous experimental work.

Estimating vibrational and thermodynamic properties of adsorbates with uncertainty using data driven surrogates

AbstractIn this work, we propose a strategy to develop data driven local surrogate models of ab initio potential energy functions describing the interaction of adsorbates on heterogeneous catalytic materials. We show that these multivariable surrogate models, based on orthogonal polynomial expansion and trained on sampled ab‐initio energies/forces, can be used to compute harmonic vibrational frequencies and the entropy of adsorbates. Further, we show that the errors in our surrogate model can be estimated and propagated to calculate the uncertainty in the computed properties. We show proof‐of‐concept illustrations of our method to calculate the vibrational frequencies of ethene on 1D edges of molybdenum sulfide (MoS2), (b) 2D surfaces of Pt(111), and (c) 3D micropores of a HZSM‐5 zeolite; the entropy of ethane adsorbed on Pt(111); and the associated uncertainties in all the cases.

Challenging High-Level ab initio Rovibrational Spectroscopy: The Nitrous Oxide Molecule

Abstract The equilibrium structure and rovibrational energies of nitrous oxide (N2O) in its electronic ground state (X 1 Σ +) are derived from a high-level ab initio potential energy function (PEF). This PEF is based on a composite approach with the basic contribution given by explicitly correlated coupled-cluster (CC) calculations. Smaller contributions include corrections due to inner-shell correlation, scalar-relativistic effects and higher-order correlation up to iterative pentuple excitations (CCSDTQP in CC nomenclature). The high importance of higher-order correlation in order to reach the desired accuracy led to the use of an extrapolation scheme to approximately account for the effect of hextuple and some pentuple excitations. A reasoning for the soundness of the method is given in this work. The results of the rovibrational calculations are compared to those of two multi-reference (MR) based composite PEFs, where the basic contribution is given by MR configuration interaction and MR average coupled-pair functional calculations. A highly accurate electric dipole moment function is also computed by the three composite methods in excellent agreement with the experimental values available. Subtle irregularities in the intensity pattern are reproduced in great detail and several kinds of resonances are analyzed without the need to empirically adjust our best ab initio PEF. The equilibrium bond lengths were determined by a mixed experimental/theoretical approach yielding R e(NN) = 1.12695(10) Å and R e(NO) = 1.18539(5) Å.

Determination of the binding energies of the np Rydberg states of H2, HD, and D2 from high-resolution spectroscopic data by multichannel quantum-defect theory

Multichannel quantum-defect theory (MQDT) is used to calculate the electron binding energies of np Rydberg states of H2, HD, and D2 around n = 60 at an accuracy of better than 0.5 MHz. The theory includes the effects of rovibronic channel interactions and the hyperfine structure, and has been extended to the calculation of the asymmetric hyperfine structure of Rydberg states of a heteronuclear diatomic molecule (HD). Starting values for the eigenquantum-defect parameters of MQDT were extracted from ab initio potential-energy functions for the low-lying p Rydberg states of molecular hydrogen and subsequently refined in a global weighted fit to available experimental data on the singlet and triplet Rydberg states of H2 and D2. The electron binding energies of high-np Rydberg states derived in this work represent important quantities for future determinations of the adiabatic ionization energies of H2, HD, and D2 at sub-MHz accuracy.

Anharmonic Vibrational Frequency Calculations Are Not Worthwhile for Small Basis Sets.

Anharmonic calculations using vibrational perturbation theory are known to provide near-spectroscopic accuracy when combined with high-level ab initio potential energy functions. However, performance with economical, popular electronic structure methods is less well characterized. We compare the accuracy of harmonic and anharmonic predictions from Hartree-Fock, second-order perturbation, and density functional theories combined with 6-31G(d) and 6-31+G(d,p) basis sets. As expected, anharmonic frequencies are closer than harmonic frequencies to experimental fundamentals. However, common practice is to correct harmonic predictions using multiplicative scaling. The surprising conclusion is that scaled anharmonic calculations are no more accurate than scaled harmonic calculations for the basis sets we used. The data used are from the Computational Chemistry Comparison and Benchmark Database (CCCBDB), maintained by the National Institute of Standards and Technology, which includes more than 3939 independent vibrations for 358 molecules.

Accurate ab initio determination of the adiabatic potential energy function and the Born–Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues

High level ab initio potential energy functions have been constructed for LiH in order to predict vibrational levels up to dissociation. After careful tests of the parameters of the calculation, the final adiabatic potential energy function has been composed from: (a) an ab initio nonrelativistic potential obtained at the multireference configuration interaction with singles and doubles level including a size-extensivity correction and quintuple-sextuple ζ extrapolations of the basis, (b) a mass-velocity-Darwin relativistic correction, and (c) a diagonal Born-Oppenheimer (BO) correction. Finally, nonadiabatic effects have also been considered by including a nonadiabatic correction to the kinetic energy operator of the nuclei. This correction is calculated from nonadiabatic matrix elements between the ground and excited electronic states. The calculated vibrational levels have been compared with those obtained from the experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys. 134, 9378 (2004)]. It was found that the calculated BO potential results in vibrational levels which have root mean square (rms) deviations of about 6-7 cm(-1) for LiH and ∼3 cm(-1) for LiD. With all the above mentioned corrections accounted for, the rms deviation falls down to ∼1 cm(-1). These results represent a drastic improvement over previous theoretical predictions of vibrational levels for all isotopologues of LiH.

Are ab initio quantum chemistry methods able to predict vibrational states up to the dissociation limit for multi-electron molecules close to spectroscopic accuracy?

The aim of the study was to explore the limits of ab initio methods towards the description of excited vibrational levels up to the dissociation limit for molecules having more than two electrons. To this end a high level ab initio potential energy function was constructed for the four-electron LiH molecule in order to accurately predict a complete set of bound vibrational levels corresponding to the electronic ground state. It was composed from: (a) an ab initio non-relativistic potential obtained at the MR-CISD level including size-extensivity corrections and quintuple-sextuple ζ extrapolation of the basis, (b) MVD relativistic corrections obtained at icMR-CISD/cc-pwCV5Z level, and (c) DBOC obtained at the MR-CISD/cc-pwCVTZ level. Finally, the importance of non-adiabatic effects was also tested by using atomic masses in the vibrational kinetic energy operator. The calculated vibrational levels were compared with those obtained from experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys., 2004, 121, 9378]. Our best estimate of the potential curve results in vibrational energies with a RMS deviation of only ∼1 cm(-1) for the entire set of all empirically determined vibrational levels known so far. These results represent a drastic improvement over previous theoretical predictions of vibrational levels of (7)LiH up to dissociation, D(0), which was predicted to be 19,594 cm(-1).

Ab-initio potential energy functions for scattering from energy-partitioned Ab-initio SCF intermolecular energies plus dispersion

Ab-initio intermolecular potential energy functions for scattering derived from separately fitting each term from energy-partitioned ab-initio SCF intermolecular calculations (plus dispersion) hold promise of being more accurate and more reliable than intermolecular potential energy functions fitted solely to total calculated ab-initio SCF intermolecular energies (plus dispersion). This procedure also will permit the derivation of ab-initio potential functions between much larger molecules than are customarily possible at present.

An ab initio strategy for handling induction phenomena in metal ion complexes

A strategy that incorporates the macromolecular, non-polarisable CHARMM force field models of atomic charges and polarisabilities determined from high-level quantum mechanical calculations, is probed in the paradigmatic case of metal ion complexes. Although the ab initio polarisable potential energy function is capable of hierarchising correctly the affinity of a divalent calcium ion for three distinct electron–donor chelating agents, severe inaccuracies in the underlying contributions to the total binding energy, compared to a reference symmetry-adapted perturbation theory (SAPT) expansion, illuminate the incompleteness of the interaction model. The reported calculations suggest that mapping faithfully the signature electrostatic potential and induction energy of the isolated species is a necessary, albeit not sufficient condition to guarantee that intermolecular interactions be described accurately when key physical phenomena are evidently missing from a force field to which explicit induction effects have been introduced. They further suggest that in the present strategy, naive attempts to correct the flawed reproduction of the electrostatic and induction terms of the perturbative expansion–rooted, for instance, in an inappropriate representation of electron-cloud penetration–through de novo parametrisation of the mathematically questionable ‘6–12’ form of the van der Waals potential, common to many macromolecular force fields, are unavoidably bound to failure.

Interactions between anionic and neutral bromine and rare gas atoms

High-quality, ab initio potential energy functions are obtained for the interaction of bromine atoms and anions with atoms of the six rare gases (Rg) from He to Rn. The potentials of the nonrelativistic (2)Sigma(+) and (2)Pi electronic states arising from the ground-state Br((2)P)-Rg interactions are computed over a wide range of internuclear separations using a spin-restricted version of the coupled cluster method with single and double excitations and noniterative correction to triple excitations [RCCSD(T)] with an extrapolation to the complete basis set limit, from basis sets of d-aug-cc-pVQZ and d-aug-cc-pV5Z quality. These are compared with potentials derived previously from experimental measurements and ab initio calculations. The same approach is used also to refine the potentials of the Br(-)-Rg anions obtained previously [Buchachenko et al., J. Chem. Phys. 125, 064305 (2006)]. Spin-orbit coupling in the neutral species is included both ab initio and via an atomic approximation; deviations between two approaches that are large enough to affect the results significantly are observed only in the Br-Xe and Br-Rn systems. The resulting relativistic potentials are used to compute anion zero electron kinetic energy photoelectron spectra, differential scattering cross sections, and the transport coefficients of trace amounts of both anionic and neutral bromine in the rare gases. Comparison with available experimental data for all systems considered proves a very high precision of the present potentials.

First-Principle Calculation of Reduced Masses in Vibrational Analysis Using Generalized Internal Coordinates: Some Crucial Aspects and Examples

In this paper we present and analyze the most essential aspects of reduced masses along generalized internal coordinates. The definition of reduced masses in the internal coordinate formalism is established through the Wilson G-matrix concept and includes sophisticated relations between internal and Cartesian coordinates. Moreover, reduced masses in internal coordinates are, in general, no longer constant but coordinate-dependent. Based on the approach presented earlier [Stare, J.; Balint-Kurti, G. G. J. Phys. Chem. A 2003, 107, 7204-7214] and on our experience with reduced masses discussed in this paper, we have developed a robust program for the calculation of Wilson G-matrix elements and their functional coordinate dependence. The approach is based on the first principles and can be used in virtually any (internal) coordinate set. Since the program allows for projection of any kind of nuclear motion on the selected internal coordinates, the method is particularly suitable for ab initio or DFT potential energy functions calculated by partial geometry optimization. Moreover, reduced masses obtained by this program can be used as a decision tool for selecting the most appropriate internal coordinates for the considered vibrational problem and for the inclusion or omission of the kinetic coupling terms in the vibrational Hamiltonian.

Radiative transition probabilities of CO2+

AbstractRadiative transition probabilities (Einstein A coefficients), Franck‐Condon factors, and radiative lifetimes have been determined for the X3Π, 3Σ−, a1Σ+, 1Π, c1 Δ, and A3Σ+ states of the CO2+ dication using ab initio potential energy, spin‐orbit coupling, electric dipole and electronic transition moment functions, and the standard complex‐scaling method. The calculated radiative lifetimes of the upper electronic states of the spin‐allowed A3Σ+–X3Π and b1Π–a1Σ+ transitions are generally longer than their predissociating lifetimes, explaining thus the failure of the attempts made so far to observe CO2+ in the optical spectral region in a convincing fashion. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Franck-Condon simulation of the single vibronic level emission spectra of HSiF and DSiF including anharmonicity.

Potential energy functions (PEFs) of the X (1)A(') and A (1)A(") states of HSiF have been computed using the coupled-cluster single-double plus perturbative triple excitations and complete-active-space self-consistent-field multireference internally contracted configuration interaction methods, respectively, employing augmented correlation-consistent polarized-valence quadruple-zeta basis sets. For both electronic states of HSiF and DSiF, anharmonic vibrational wavefunctions and energies of all three modes have been calculated variationally with the ab initio PEFs and using Watson's Hamiltonian for nonlinear molecules. Franck-Condon factors between the two electronic states, allowing for Duschinsky rotation, were computed using the calculated anharmonic vibrational wavefunctions. These Franck-Condon factors were used to simulate the single vibronic level (SVL) emission spectra recently reported by Hostutler et al. in J. Chem. Phys. 114, 10728 (2001). Excellent agreement between the simulated and observed spectra was obtained for the A (1)A(")(1,0,0)-->X (1)A(') SVL emission of HSiF. Discrepancies between the simulated and observed spectra of the A (1)A(")(0,1,0) and (1,1,0) SVL emissions of HSiF have been found. These are most likely, partly due to experimental deficiencies and, partly to inadequacies in the ab initio levels of theory employed in the calculation of the PEFs. Based on the computed Franck-Condon factors, minor revisions of previous vibrational assignments are suggested. The calculated anharmonic wave functions of higher vibrational levels of the X (1)A(') state show strong mixings between the three vibrational modes of HSi stretching, bending, and SiF stretching.

Equilibrium Structure and Internal Rotation in B2F4 from Electron Diffraction and Spectroscopic Data and Quantum Chemical Calculations

Electron diffraction (ED) data for B2F4 recorded by Hedberg et al. over the temperature range −80 to +150°C have been used to obtain equilibrium geometry of this molecule in the framework of a large-amplitude motion model. The torsional coordinate has been adiabatically separated from the rest of vibrations. Two types of constraints applied to obtain ab initio torsional potential energy function (PEF) and the parameters of the geometry relaxation are discussed. The relations between anharmonic interaction force constants and the parameters of the geometry relaxation are briefly considered. Ab initio force constant matrices for rigid vibrational coordinates as well as large-amplitude torsional PEF have been scaled in the procedure of simultaneous fitting to the ED data and experimental vibrational frequencies. The resulting equilibrium geometry and potential function provided good fit to both ED and spectroscopic data. As expected, the results for the equilibrium geometry obtained from separate ED patterns recorded at different temperatures did not show noticeable temperature trend. The determined equilibrium structural parameters for B2F4 are: r e (B–B) = 1.719(4) A, r e (B–F) = 1.309(2) A, ∠BBF = 121.1(1)°. Uncertainties given in parentheses include three times standard deviation and a systematic error. The rotational barrier height was evaluated as 160(50) cm−1.

A first-principle calculation of the binary diffusion coefficients pertinent to kinetic modeling of hydrogen/oxygen/helium flames

First-principle calculations were carrid out to determine the binary diffusion coefficients of H−He, H−Ar, H−H 2 , and He−H 2 . Potential energy functions of pair interactions were critically reviewed for H−He and H−Ar and verified against molecular beam scatering and low-temperature diffusion cross-section data. Complementary quantum chemistry calculations were carried out for the interactions of H−He and H−Ar and CCSD(T)/AUG-cc-PV * Z level of theory. The calculation of the H−He and H−Ar diffusion coefficients was performed by direct integration using literature potential functions. For H−H 2 and He−H 2 , the diffusion cross-sections were determined using the close-coupling method, again using ab initio potential energy functions in recent literature. The computed diffusion coefficients of all pairs were compared with experimental data at room temperature, which showed very good agreement for all pairs. With the exception of H−Ar, the diffusion coefficients of the current study of all other pairs differ notably from those predicted by the Sandia TRANFIT and DRFM compilations. The implication of the current result in kinetic modeling of hydrogen-oxygen-helium flames is discussed.

A new method of calculation of Franck–Condon factors which includes allowance for anharmonicity and the Duschinsky effect: Simulation of the He I photoelectron spectrum of ClO2

A new method of Franck–Condon (FC) factor calculation for nonlinear polyatomics, which includes anharmonicity and Duschinsky rotation, is reported. Watson’s Hamiltonian is employed in this method with multidimensional ab initio potential energy functions. The anharmonic vibrational wave functions are expressed as linear combinations of the products of harmonic oscillator functions. The Duschinsky effect, which arises from the rotation of the normal modes of the two electronic states involved in the electronic transition, is formulated in Cartesian coordinates, as was done previously in an earlier harmonic FC model. This new anharmonic FC method was applied to the simulation of the bands in the He I photoelectron (PE) spectrum of ClO2. For the first band, the harmonic FC model was shown to be inadequate but the anharmonic FC simulation gave a much-improved agreement with the observed spectrum. The experimentally derived geometry of the X̃ 1A1 state of ClO2+ was obtained, for the first time, via the iterative FC analysis procedure {R(Cl–O)=1.414±0.002 Å, ∠O–Cl–O=121.8±0.1°}. The heavily overlapped second PE band of ClO2, corresponding to ionization to five cationic states, was simulated using the anharmonic FC code. The main vibrational features observed in the experimental spectrum were adequately accounted for in the simulated spectrum. The spectral simulation reported here supports one of the two sets of published assignments for this band, which was based on multireference configuration interaction (MRCI) calculations. In addition, with the aid of the simulated envelopes, a set of adiabatic (and vertical) ionization energies to all five cationic states involved in this PE band, more reliable than previously reported, has been derived. This led also to a reanalysis of the photoabsorption spectrum of ClO2.

Accurate ab initio near-equilibrium potential energy and dipole moment functions of the ground electronic state of ozone

We report a highly correlated multireference configuration interaction calculation of the near-equilibrium potential energy surface of ozone using a large correlation consistent basis set. Three-dimensional analytical expressions are obtained for the potential energy and dipole moment functions using least-squares fits to ab initio points near the C2v equilibrium geometry. Low-lying vibrational band origins of O316 and some of its isotopic variants are calculated using the ab initio potential energy function. The calculated fundamental frequencies for the symmetric stretching and bending vibrations are within about 3 cm−1 of the observed values, while that for the antisymmetric stretch deviates from experiment by about 13 cm−1. The agreement with experiment can be significantly improved if the ab initio potential energy function is scaled in the antisymmetric stretching coordinate. Absolute infrared absorption intensities are also calculated using ab initio electric dipole moment functions and in good agreement with the available experimental data.