A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.     

Basis-set quality and basis-set bias in molecular property calculations

Quality measures for Gaussian basis sets are proposed that are based on principal angles between the basis set and reference molecular orbitals. The principal angles are obtained from the cosine-sine (CS) decomposition of orthogonal matrices and yield detailed information about basis-set convergence with respect to different regions of space. Principal angles for occupied orbitals show excellent correlation with basis-set errors in ground-state energies. Furthermore, ground-state bias in finite basis sets can be estimated from the relation between principal angles for occupied and Rydberg orbitals. Ground-state bias is observed in basis sets including extensive diffuse augmentation and affects the quality of computed molecular response properties. Principal angles and ground-state bias are investigated for the H-Ne atoms and a series of diatomics using numerical Hartree-Fock calculations as a reference. Convergence of ground-state energies and static polarizabilities is studied for the hierarchies of correlation-consistent and Karlsruhe segmented def2 basis sets including different levels of diffuse augmentation.     

Cytochrome P450 compound I in the plane wave pseudopotential framework: GGA electronic and geometric structure of thiolate‐ligated iron(IV)–oxo porphyrin

The cytochromes P450 constitute a ubiquitous family of metalloenzymes, catalyzing manifold reactions of biological and synthetic importance via a thiolate‐ligated iron‐oxo (IV) porphyrin radical species denoted compound I (Cpd I). Experimental investigations have implicated this intermediate in a broad spectrum of biophysically interesting phenomena, further augmenting the importance of a Cpd I model system. Ab initio molecular dynamics, including Car–Parrinello and path integral methods, conjoin electronic structure theory with finite temperature simulation, affording tools most valuable to approach such enzymes. These methods are typically driven by density functional theory (DFT) in a plane‐wave pseudopotential framework; however, existing studies of Cpd I have been restricted to localized Gaussian basis sets. The appropriate choice of density functional and pseudopotential for such simulations is accordingly not obvious. To remedy this situation, a systematic benchmarking of thiolate‐ligated Cpd I is performed using several generalized‐gradient approximation (GGA) functionals in the Martins–Troullier and Vanderbilt ultrasoft pseudopotential schemes. The resultant electronic and structural parameters are compared to localized–basis DFT calculations using GGA and hybrid density functionals. The merits and demerits of each scheme are presented in the context of reproducing existing experimental and theoretical results for Cpd I. © 2013 Wiley Periodicals, Inc.     

Reaction energy benchmarks of hydrocarbon combustion by Gaussian basis and plane wave basis approaches

The reaction energies of 275 elementary reactions from the hydrocarbon combustion model GRI-Mech 3.0 were evaluated by electronic structure calculations using both localized Gaussian basis and plane wave basis sets. In the Gaussian basis calculations, the d-polarization function on C, N, and O elements reduces the mean absolute deviation (MAD) from the experimental value by 53%, a significant improvement in computational accuracy. In the plane wave basis calculation using different exchange-correlation (XC) functionals, the MAD values were 0.316–0.426 eV when non-hybrid type XC functionals such as RPBE, PBE, PW91, revPBE, and PBEsol were used. On the other hand, hybrid functionals like B3LYP and HSE06 reduced the MAD values significantly down to 0.182 and 0.233 eV, respectively. The B3LYP results have 49% less MAD compared to the PBE results. These demonstrated the strong advantage of the hybrid functional for calculating gas-phase reaction energies. The present comprehensive benchmarks will be crucial for future microkinetics as well as machine learning studies on the catalytic reactions. © 2019 Wiley Periodicals, Inc.     

Ultrasoft pseudopotentials in time-dependent density-functional theory

We describe an efficient formulation allowing the use of ultrasoft pseudopotentials (USPPs) in plane wave based time-dependent density-functional theory. The practical steps required to implement USPP functionality within real time propagation schemes and linear-response schemes based on Lanczos algorithms are provided. The functioning of the methodology is demonstrated by calculations of the optical absorption spectra of the fullerene C(60), using both real time propagation and the Lanczos/linear-response approaches. Comparisons between the rates of convergence of the optical spectra with the number of applications of the Hamiltonian required in calculations with ultrasoft pseudopotentials and norm-conserving pseudopotentials show clearly the benefits provided by the use of USPP.     

Gaussian basis sets for calculation of spin densities in first-row atoms

Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.     

Supplementary d and f functions in molecular wave functions at large and small internuclear separations

The CO, CO₂, CS, CIF, and SO₂ molecules were used to test the dependence of supplementary d and f function exponents to changes in bond lengths and bond angles in MO calculations utilizing Gaussian basis sets in Hartree–Fock and Moller–Plesset calculations. Using Dunning–Hay double zeta basis sets, optimizations were performed at internuclear separations from 100–200 pm and beyond. The energy cost of not reoptimizing d function exponents when bonds are stretched or compressed is much smaller for correlated calculations than for those at the Hartree–Fock level and is greatest at the lower end of the range of internuclear distances. The problem is much less serious at all levels when multiple sets of d functions are used. © 1993 John Wiley & Sons, Inc.     

Theoretical study of ketenimine: Geometry,electronic properties,force constants and barriers to inversion and rotation

Non-empirical calculations of the structure and properties of ketenimine have been performed using nine Gaussian basis sets. Values for the bond lengths and angles, HOMO and LUMO energies, atomic charges, overlap populations, dipole moments, bond energies, force constants and barriers to nitrogen inversion and internal rotation are predicted.     

Ground- and excited-state properties of DNA base molecules from plane-wave calculations using ultrasoft pseudopotentials

We present equilibrium geometries, vibrational modes, dipole moments, ionization energies, electron affinities, and optical absorption spectra of the DNA base molecules adenine, thymine, guanine, and cytosine calculated from first principles. The comparison of our results with experimental data and results obtained by using quantum chemistry methods show that in specific cases gradient-corrected density-functional theory (DFT-GGA) calculations using ultrasoft pseudopotentials and a plane-wave basis may be a numerically efficient and accurate alternative to methods employing localized orbitals for the expansion of the electron wave functions.     

Neon L-shell photoabsorption cross sections from moment theory and finite basis pseudospectra

Pseudospectra from Gaussian basis set calculations within a frozen-core approximation have been used in a moment analysis to obtain Tchebychev profiles for the photoabsorption process in the valence shell of Ne. The profiles show good agreement with cross sections obtained in equivalent calculations using numerical atomic wave functions and continuum orbitals, particularly when the dipole-velocity form is employed. Variation of the basis sets shows that it is possible to obtain meaningful photoabsorption profiles using 13–15 virtual orbitals to describe the outgoing electron.     

A study of the performance of numerical basis sets in DFT calculations on sulfur-containing molecules

The performance of numerical basis sets in relation to Gaussian basis sets is examined, by studying 20 small sulfur-containing molecules. The results of geometry optimization calculations are reported for each molecule using both density functional and Hartee-Fock methods. In comparison with experimental data, it is shown that the use of numerical bases tend to overestimate structural parameters, particularly bond lengths, and, in most cases, more than Gaussian basis sets. It is also shown that the use of a larger Gaussian basis set in DFT calculations has the effect of reducing bond lengths. © 1996 John Wiley & Sons, Inc.     

Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics

We have implemented the use of mixed basis sets of Gaussian one- and two-electron (geminal) functions for the calculation of second-order M?ller-Plesset (MP2) correlation energies. In this paper, we describe some aspects of this implementation, including different forms chosen for the pair functions. Computational results are presented for some closed-shell atoms and diatomics. Our calculations indicate that the method presented is capable of yielding highly accurate second-order correlation energies with rather modest Gaussian orbital basis sets, providing an alternative route to highly accurate wave functions. For the neon atom, the hydrogen molecule, and the hydrogen fluoride molecule, our calculations yield the most accurate MP2 energies published so far. A critical comparison is made with established MP2-R12 methods, revealing an erratic behaviour of some of these methods, even in large basis sets.     

Accurate calculations of dynamic first hyperpolarizability: Construction of physically justified slater‐type basis sets

An efficient procedure for construction of physically rationalized Slater‐type basis sets for calculations of dynamic hyperpolarizability is proposed. Their performance is evaluated for the DFT level calculations for model molecules, carried out with a series of functionals. Advantages of new basis sets over standard d‐aug‐cc‐pVTZ and recently developed LPOL‐(FL,FS) Gaussian‐type basis sets are discussed. © 2014 Wiley Periodicals, Inc.     

Cyanoacetylene adsorption on amorphous and crystalline water ice films: investigation through matrix isolation and quantum study.

The structure and energy properties of the 1:1 complexes formed between cyanoacetylene and H2O (D2O) are investigated using FT-IR matrix isolation spectroscopy and ab initio calculations at the MP2/ 6-31G(d,p) level. Cyanoacetylene adsorption and desorption on amorphous ice film are monitored by FT-IR using the temperature-programmed desorption method. In an argon matrix, two types of 1:1 complexes are observed. The first one corresponds to the NH structure, which involves a hydrogen bond with the terminal nitrogen of cyanoacetylene. The second corresponds to the HO form, which involves a hydrogen bond from the cyanoacetylene to the oxygen of water. This last complex is the more stable (DeltaE = -8.1 kJ/mol.). As obtained in argon matrixes, two kinds of adsorption site are observed between HC3N and ice. The first one, stable between 25 and 45 K is characterized by a nu(OH) shift similar to the one observed in matrix for the NH complex. The second, stable at higher temperatures (between 45 and 110 K), corresponds to an interaction with the dangling oxygen site of ice and is similar to the HO complex observed in matrix. From theoretical calculations (DFT method combined with a plane wave basis set and ultrasoft pseudopotentials), it is shown that, for this adsorption site, the HC3N moiety is flattened on the ice surface and stabilized by a long-distance interaction ( approximately 3 A) between one dangling OH and the pi system of the C triple bond C triple bond. The HC3N desorption occurs between 110 and 140 K, and the associated desorption energy is 39 kJ/mol. This value is in good agreement with the first principle calculation based on density functional theory and ultrasoft pseudopotentials (34 kJ/mol). These calculations confirm the electrostatic nature of the interaction forces. A small amount of cyanoacetylene is incorporated into the bulk and desorbs at the onset of the ice crystallization near 145 K. In these two kinds of experiments, HC3N acts as both an electrophilic and a nucleophilic molecule.     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

Evaluation of Gaussian basis sets in ab initio

Ab initio wave functions for NH₃ have been calculated using the STONG program, where N is 2 to 6, and with Gaussian 70, employing the 4–31 and 6–31 basis sets. Electric field gradients at the N atom were computed from the gaussian basis orbitals, and, with STONG, also from the equivalent STO's. Results from the two split valence shell Gaussian 70 calculations are in good agreement with values from extended SCF and SCFCI calculations. Because of adequate agreement with more extended calculations, the use of the 4–31 basis set is chosen to calculate field gradients in molecules consisting of five or more second row atoms. It should be adequate for the prediction of the region for searching for new ¹⁴N, ¹⁷O and ²H NQR spectra. An improved value of the electric quadrupole moment for the ¹⁴N nucleus is proposed.     

Extrapolation to the limit of a complete basis set for electronic structure calculations on the N2 molecule

Results obtained from nonrelativistic electronic structure calculations using finite Gaussian basis sets are extrapolated to the limit of a complete basis set, employing the results of explicitly correlated coupled-cluster calculations including singles and doubles substitutions (CCSD). For N₂, the basis-set limits for the electronic binding energy, equilibrium bond length and harmonic vibrational wave number are established for the CCSD model including a perturbative correction for triples substitutions and for the internally contracted multireference configuration interaction method. The resulting numbers are in good agreement with experimental values. Received: 2 December 1997 / Accepted: 3 February 1998 / Published online: 17 June 1998     

A comparison between plane wave and Gaussian-type orbital basis sets for hydrogen bonded systems: formic acid as a test case

The formic acid molecule, its dimers, and its molecular crystal are adopted as test systems to compare results obtained with plane wave (PW) basis sets and norm-conserving pseudopotentials to all-electron Gaussian-type orbital (GTO) calculations. The CPMD and CRYSTAL06 codes, respectively, are applied with the PBE, PW91, and BLYP density functionals. Hydrogen bonding is the leading interaction in the dimers and the crystal. In the latter, dispersive and weak C-H...O interactions are also relevant. Irrespective of the adopted functional, for all considered structures PW and GTO results converge smoothly as a function of the quality of the adopted basis sets to the same values for structures, energies of interaction, and harmonic vibrational features. To achieve a high level of mutual agreement the use of GTO basis sets of at least of triple-zeta quality including one set of polarization functions and PW basis sets with a kinetic energy cutoff higher than 110 Ry is recommended. Pros and cons of both approaches for studying molecular crystals are also discussed.