A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations

Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localised orbitals in real-space, rather than the delocalised eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from \textsc{onetep}, our linear scaling method based on localised orbitals in real-space. The use of psinc functions for the underlying basis set and on-the-fly optimisation of the localised orbitals results in smooth potential energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimisation to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimisation algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.

Noncommutative Biology: Sequential Regulation of Complex Networks and Connected Matter

Motivated by the energetic and environmental relevance of methane clathrates, highly accurate ab initio potential energy surfaces (PESs) have been developed for the three possible dimers of the methane and water molecules: (H2O)2, CH4·H2O, and (CH4)2. While only a single monomer geometry was used for each monomer in the ab initio calculations, the PES parameterization makes it possible to produce distinct surfaces for all isotopologues within the rigid-monomer approximation. The PESs were fitted to computations at the frozen-core coupled-cluster level with single, double, and non-iterative triple excitations, employing basis sets of augmented triple- and quadruple-zeta quality plus bond functions, followed by extrapolations to the complete basis set limit. The long-range parts of the PESs are computed using the asymptotic version of symmetry-adapted perturbation theory based on a density-functional description of the monomers. All PESs are polarizable, i.e., in cluster or condensed-phase applications they approximate many-body effects by the induced dipole polarization model. The PESs were developed in a fully automated procedure applying the autoPES method, which is used for the first time to generate near-spectroscopic quality surfaces. The stationary points (SPs) on the PESs have been determined and compared with literature data. For CH4·H2O, previously unknown SPs have been identified and the first detailed study of the (CH4)2 potential energy landscape has been carried out. The PESs were used in variational quantum nuclear motion computations. For the water dimer, the resulting vibrational transitions are in excellent agreement with available high-resolution spectroscopic data. For (CH4)2, the intermonomer vibrational states are reported for the first time.

The geometry dependence of excitation domains in local correlation methods can lead to noncontinuous potential energy surfaces. We propose a simple domain merging procedure which eliminates this problem in many situations. The method is applied to heterolytic bond dissociations of ketene and propadienone, to SN2 reactions of Cl(-) with alkylchlorides, and in a quantum mechanical/molecular mechanical study of the chorismate mutase enzyme. It is demonstrated that smooth potentials are obtained in all cases. Furthermore, basis set superposition error effects are reduced in local calculations, and it is found that this leads to better basis set convergence when computing barrier heights or weak interactions. When the electronic structure strongly changes between reactants or products and the transition state, the domain merging procedure leads to a balanced description of all structures and accurate barrier heights.

A full-dimensional global potential energy surface (PES) for the H2 + N2 system is constructed using the permutation invariant polynomial-neural network method, based on high-level abinitio energy points computed at the CCSD(T)-F12a/AVQZ level. To accurately describe the long-range interactions, a multipole expansion parameterized by abinitio data is incorporated into the PES. Quantum close-coupling scattering calculations are reported for rotationally inelastic transitions in H2 + N2 collisions using the full-dimensional PES. Cross sections for rotational excitation of N2 within a rigid rotor model are found to be in excellent agreement with those obtained using a four-dimensional (4D) PES reported by Gomez etal. [Chem. Phys. Lett. 445, 99 (2007)]. Cross sections for pure rotational quenching of H2, as well as quenching of H2 accompanied by rotational excitation of N2, exhibit dense resonance structures. For collision energies above 2.0cm-1, the results are in close agreement with those obtained using the 4D PES of Gomez etal., including the positions of the sharp resonances. At lower collision energies, however, noticeable differences appear, indicating a strong sensitivity of the resonance features to the PES in this regime. An accurate simulation of energy transfer in collisions between rovibrationally excited H2 and D2 with N2 can now be addressed using the full-dimensional PES reported in this study.

Owing to its large dipole, astrophysicists use carbon monosulfide (CS) as a tracer of molecular gas in the interstellar medium, often in regions where H(2) is the most abundant collider. Predictions of the rovibrational energy levels of the weakly bound complex CS-H(2) (not yet observed) and also of rate coefficients for rotational transitions of CS in collision with H(2) should help to interpret the observed spectra. This paper deals with the first goal, i.e., the calculation of the rovibrational energy levels. A new four-dimensional intermolecular potential energy surface for the H(2)-CS complex is presented. Ab initio potential energy calculations were carried out at the coupled-cluster level with single and double excitations and a perturbative treatment of triple excitations, using a quadruple-zeta basis set and midbond functions. The potential energy surface was obtained by an analytic fit of the ab initio data. The equilibrium structure of the H(2)-CS complex is found to be linear with the carbon pointing toward H(2) at the intermolecular separation of 8.6 a(o). The corresponding well depth is -173 cm(-1). The potential was used to calculate the rovibrational energy levels of the para-H(2)-CS and ortho-H(2)-CS complexes. The present work provides the first theoretical predictions of these levels. The calculated dissociation energies are found to be 35.9 cm(-1) and 49.9 cm(-1), respectively, for the para and ortho complexes. The second virial coefficient for the H(2)-CS pair has also been calculated for a large range of temperature. These results could be used to assign future experimental spectra and to check the accuracy of the potential energy surface.

We compute four-dimensional diabatic potential energy surfaces and transition dipole moment surfaces of O2-O2, relevant for the theoretical description of collision-induced absorption in the forbidden X3Σg- → a1Δg and X3Σg- → b1Σg+ bands at 7883 cm-1 and 13 122 cm-1, respectively. We compute potentials at the multi-reference configuration interaction (MRCI) level and dipole surfaces at the MRCI and complete active space self-consistent field (CASSCF) levels of theory. Potentials and dipole surfaces are transformed to a diabatic basis using a recent multiple-property-based diabatization algorithm. We discuss the angular expansion of these surfaces, derive the symmetry constraints on the expansion coefficients, and present working equations for determining the expansion coefficients by numerical integration over the angles. We also present an interpolation scheme with exponential extrapolation to both short and large separations, which is used for representing the O2-O2 distance dependence of the angular expansion coefficients. For the triplet ground state of the complex, the potential energy surface is in reasonable agreement with previous calculations, whereas global excited state potentials are reported here for the first time. The transition dipole moment surfaces are strongly dependent on the level of theory at which they are calculated, as is also shown here by benchmark calculations at high symmetry geometries. Therefore, ab initio calculations of the collision-induced absorption spectra cannot become quantitatively predictive unless more accurate transition dipole surfaces can be computed. This is left as an open question for method development in electronic structure theory. The calculated potential energy and transition dipole moment surfaces are employed in quantum dynamical calculations of collision-induced absorption spectra reported in Paper II [T. Karman et al., J. Chem. Phys. 147, 084307 (2017)].

The treatment of the solvation charges using Gaussian functions in the polarizable continuum model results in a smooth potential energy surface. These charges are placed on top of the surface of the solute cavity. In this article, we study the effect of the solute cavity (van der Waals-type or solvent-excluded surface-type) using the Gaussian charge scheme within the framework of the conductor-like polarizable continuum model on (a) the accuracy and computational cost of the self-consistent field (SCF) energy and its gradient and on (b) the calculation of free energies of solvation. For that purpose, we have considered a large set of systems ranging from few atoms to more than 200 atoms in different solvents. Our results at the DFT level using the B3LYP functional and the def2-TZVP basis set show that the choice of the solute cavity does neither affect the accuracy nor the cost of calculations for small systems (< 100 atoms). For larger systems, the use of a vdW-type cavity is recommended, as it prevents small oscillations in the gradient (present when using a SES-type cavity), which affect the convergence of the SCF energy gradient. Regarding the free energies of solvation, we consider a solvent-dependent probe sphere to construct the solvent-accessible surface area required to calculate the nonelectrostatic contribution to the free energy of solvation. For this part, our results for a large set of organic molecules in different solvents agree with available experimental data with an accuracy lower than 1 kcal/mol for both polar and nonpolar solvents.

A heterogeneous conductorlike solvation model (conductorlike screening model/conductorlike polarizable continuum model) that uses different local effective dielectrics for different portions of the solute cavity surface is implemented for quantum chemical Hartree-Fock and Kohn-Sham methods. A variational treatment is used to form the heterogeneous solvation operator, so a simple analytic expression of the energy gradients, which are vital for geometry optimization and molecular dynamics simulation, is derived and implemented. Using the new Fixed Points with Variable Areas surface tessellation scheme, continuous and smooth potential energy surfaces as well as analytic gradients are obtained for this heterogeneous model. Application of the heterogeneous solvation model to a realistic quantum model consisting of 101 atoms for the type-1 Cu center in rusticyanin shows that the desolvation due to protein burial can likely raise the reduction potential by approximately 200 mV and, including the heterogeneity in geometry optimization, can likely affect the results by approximately 2 kcal/mol or approximately 70 mV.

Al dimer dynamics on Al(111) at equilibrium and under compression is studied using first-principles density-functional theory calculations. A smooth potential energy surface provides a long-range attraction between the dimer atoms and leads to a substantial temperature window in which dissociation is frozen and exotic dimer dynamics is observed. Surface relaxations play a prominent role in the uncovering of an unexpected ground state and a new diffusion path. A way of affecting growth by compression is illustrated. The possibility of a metal quantum rotor is addressed and further examined using effective-medium theory calculations.

An exchange-Coulomb (XC) potential energy model is developed for the Ne-N2 interaction. The construction of this new potential energy surface is based on recent results for the Heitler-London interaction energy, the long range dispersion energies, and the microwave spectra of the dimer. The adjustable parameters in the final XC1 potential energy surface have been determined by fitting the frequencies of three representative lines of the microwave spectrum for the two isotopomers 20Ne-14N2 and 20Ne-15N2 while simultaneously maintaining agreement with the experimental second virial coefficient data obtained with the initial (unadjusted XC0 potential. With no further adjustment of parameters, the final XC potential reproduces, within 0.005%, the frequencies of the 34 microwave transitions studied experimentally for four isotopomers of Ne-N2. Excellent agreement with experiment is obtained also for the binary diffusion, the interaction viscosity, and the mixture viscosity (for all compositions) coefficients for all temperatures. Agreement with experiment for the relaxation cross-sections associated with viscomagnetic effects, and with the pressure broadening of depolarized Rayleigh light scattering, is very good given the level of computation used for the calculations and the accuracy with which some of these cross-sections currently can be determined from experimental data. Comparisons are made with predictions calculated from the three best literature potential energy surfaces or Ne-N2. The final XC1 potential energy surface is overall the most reliable potential energy for this van der Waals complex to date. The flexibility still inherent in this potential can be exploited, if required, in future studies of the Ne-N2 system.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTA model analytic potential energy function for formyl radical decompositionSeon Woog. Cho, William L. Hase, and Kandadai N. SwamyCite this: J. Phys. Chem. 1990, 94, 19, 7371–7377Publication Date (Print):September 1, 1990Publication History Published online1 May 2002Published inissue 1 September 1990https://pubs.acs.org/doi/10.1021/j100382a012https://doi.org/10.1021/j100382a012research-articleACS PublicationsRequest reuse permissionsArticle Views67Altmetric-Citations14LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

Quantum Chemical Study of Coupled Molecular Photoswitches

We present high-level ab initio calculations for the global adiabatic potential energy surfaces of the ground state (X̃ 2A′) and several excited states (Ã 2A′, B̃ 2A″, C̃ 2A′, D̃ 2A′, and Ẽ 2A″) of LiFH, including the valleys leading to Li+HF and LiF+H. The ab initio calculations were carried out using the multireference singles and doubles configuration interaction method with 99 reference configuration state functions (CSFs) for the A′2 states and 39 reference CSFs for the A″2 states. The basis set consisted of 140 contracted Gaussian functions, including specifically optimized diffuse functions, and calculations were performed on a dense grid of ∼3500 nuclear geometries which allowed us to construct an accurate analytic representation of the two lowest-energy LiFH potential energy surfaces. An analytic 2×2 quasidiabatic potential energy matrix was obtained by fitting physically motivated functional forms to the ab initio data for the two lowest-energy adiabatic states and explicitly including long-range interactions. The newly presented LiFH fit is compared to several ground-state LiFH fits and one excited-state LiFH fit that have appeared in the literature.

The reliability of five N2-Ar potential-energy surfaces in representing the N2-Ar interaction has been investigated by comparing their abilities to reproduce a variety of experimental results, including interaction second viral coefficients, bulk transport properties, relaxation phenomena, differential scattering cross sections, and the microwave and infrared spectra of the van der Waals complexes. Four of the surfaces are the result of high-level ab initio quantal calculations; one of them utilized fine tuning by fitting to microwave data. To date, these four potential-energy surfaces have only been tested against experimental microwave data. The fifth potential-energy surface, based upon the exchange-Coulomb potential-energy model for the interaction of closed-shell species, is developed herein: it is a combination of a damped dispersion energy series and ab initio calculations of the Heitler-London interaction energy, and has adjustable parameters determined by requiring essentially simultaneous agreement with selected quality interaction second viral coefficient and microwave data. Comparisons are also made with the predictions of three other very good literature potential-energy surfaces, including the precursor of the new exchange-Coulomb potential-energy surface developed here. Based upon an analysis of a large body of information, the new exchange-Coulomb and microwave-tuned ab initio potential-energy surfaces provide the best representations of the N2-Ar interaction; nevertheless, the other potential-energy surfaces examined still have considerable merit with respect to the prediction of specific properties of the N2-Ar van der Waals complex. Of the two recommended surfaces, the new exchange-Coulomb surface is preferred on balance due to its superior predictions of the effective cross sections related to various relaxation phenomena, and to its reliable, and relatively simple, representation of the long-range part of the potential-energy surface. Moreover, the flexibility still inherent in the exchange-Coulomb potential form can be further exploited, if required, in future studies of the N2-Ar interaction.