Gaussian Basis Sets Research Articles

Assessing density functional theory in real-time and real-space as a tool for studying bacteriochlorophylls and the light-harvesting complex 2

We use real-time density functional theory on a real-space grid to calculate electronic excitations of bacteriochlorophyll chromophores of the light-harvesting complex 2 (LH2). Comparison with Gaussian basis set calculations allows us to assess the numerical trust range for computing electron dynamics in coupled chromophores with both types of techniques. Tuned range-separated hybrid calculations for one bacteriochlorophyll as well as two coupled ones are used as a reference against which we compare results from the adiabatic time-dependent local density approximation (TDLDA). The tuned range-separated hybrid calculations lead to a qualitatively correct description of the electronic excitations and couplings. They allow us to identify spurious charge-transfer excitations that are obtained with the TDLDA. When we take into account the environment that the LH2 protein complex forms for the bacteriochlorophylls, we find that it substantially shifts the energy of the spurious charge-transfer excitations, restoring a qualitatively correct electronic coupling of the dominant excitations also for TDLDA.

Finite element density functional calculations for light molecules using a cusp factor to mitigate the Coulomb potential

Finite element calculations have been performed in Cartesian coordinates using the density functional approach for a number of small molecules. In order to aid convergence of the orbitals and total energies a suitable cusp factor was employed, such that the resulting effective potential is non-singular at all nuclei. The resulting total energies and densities were compared with those obtained using the Gaussian basis set package NWChem [M. Valiev et al., Comput. Phys. Commun. 181, 1477 (2010)] and excellent agreement was found.

Geometry, and Normal Modes of Vibration (3N-6) for Di and Tetra-Rings Layer (6, 0) Linear (Zigzag) SWCNTs; A DFT Treatment

Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single wall carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequencies (symmetric and asymmetric modes) based on the image modes applied by the Gaussian 09 display. The whole relations for the vibration modes were also done including nCH stretching, nC--C stretching, δCH, δring (δC--C--C) deformation in plane of the molecule) and gCH, gring (gC--C--C) deformation out of plane of the molecule. The assignment also included modes of puckering, breathing and clock-anticlockwise bending vibrations.

Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model

We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi-linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication.

Nitrogen interstitial defects in silicon. A quantum mechanical investigation of the structural, electronic and vibrational properties

The vibrational features of eight interstitial nitrogen related defects in silicon have been investigated at the first principles quantum mechanical level by using a periodic supercell approach, a hybrid functionals, an all electron Gaussian type basis set and the Crystal code. The list includes defects that will be indicated as Ni (one N atom forming a bridge between two Si atoms), Ni-Ns (one interstitial and one substitutional N atom linked to the same Si atom), Ni-Ni (two Ni defects linked to the same couple of silicon atoms) and Ni-Sii-Ni (two Ni defects linked to the same interstitial silicon atom). Four 〈0 0 1〉 split interstitial (dumbbell) defects have also been considered, in which one lattice atom splits in two, and as a result the two interstitial atoms are three fold coordinated: they are two N (indicated as IN-N), one N and one Si (IN-Si), one N and one C (IC-N). For comparison, also the case with two Si atoms (ISi-Si) has been included. Four of these eight defects have unpaired electrons, and have been described through the UHF (Unrestricted Hartree-Fock like) computational scheme. The local defect geometry and the charge and spin density distributions have been analyzed. For the first time, intensities of IR and Raman spectra were calculated along with the frequencies, and this is crucial for the comparison of theoretical simulations with experiments. All these defects present very characteristic features in their IR spectrum, dominated by one or two very intense peaks. It has been possible to find a simulated counterpart to each one of the five peaks reported by Stein in 1985 (Applied Physics Letters, 47, 1339), and then to establish a correspondence between the microscopic structure of the defects and the IR intense peaks. The Raman spectra are in all cases dominated by the perfect silicon peak at about 530 cm−1, and are then not very useful for the characterization of the defects.

Hydrogen molecule-antihydrogen atom potential energy surface and scattering calculations

We have calculated ground state interaction energies for an antihydrogen atom and a hydrogen molecule within the Born–Oppenheimer approximation. Leptonic energies were calculated using a large basis set of explicitly correlated Gaussian functions. Energies were calculated at over 2800 geometries including different proton–proton distances. The energies have been fit to functional forms using a neural network for the short-range interaction which is combined with asymptotic formulas at long range. A two-dimensional rigid rotor and a three-dimensional atom–molecule potential energy surface (PES) have been determined. Rigid-rotor scattering calculations on these surfaces have been carried out using the S-matrix Kohn variational method with a two-dimensional Gaussian basis set. We have calculated cross sections for elastic, rotationally inelastic and annihilation collisions on the two-dimensional PES. This includes the first calculation of leptonic annihilation for this system.

Cluster Formation in Two-Component Fermi Gases.

Two-component fermions are known to behave like a gas of molecules in the limit of Bose-Einstein condensation of diatomic pairs tightly bound with zero-range interactions. We discover that the formation of cluster states occurs when the effective range of two-body interaction exceeds roughly 0.46 times the scattering length, regardless of the details of the short-range interaction. Using an explicitly correlated Gaussian basis set expansion approach, we calculate the binding energy of cluster states in trapped few-body systems and show the difference of structural properties between cluster states and gaslike states. We identify the condition for cluster formation and discuss the potential observation of cluster states in experiments.

Detecting the minimum in argon high-harmonic generation spectrum using Gaussian basis sets

Coupling the real-time description of the ultrafast electron dynamics in strong laser fields with quantum chemistry techniques still represents an open challenge for theoreticians. In this work, high-harmonic generation (HHG) spectrum of the argon atom has been computed by means of the time-dependent configuration with singly excited configurations approach (TDCIS), using Gaussian basis sets. We show that adding a number of continuum-optimal Gaussian functions to basis sets routinely used in quantum chemistry calculations provides the expected position of the intensity minimum in the HHG spectrum, for a given selection of laser intensities and ionisation parameters. Advantages and weaknesses of the proposed computational strategy are discussed. We give evidence here that Gaussian-based TDCIS simulations are accurate enough to correctly reproduce the features of ultrafast and highly nonlinear optical processes, as HHG.

Exchange Rules for Diradical π-Conjugated Hydrocarbons.

A variety of planar π-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open- or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations.

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451-459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements HBr. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.

Hyperfine excitation of NS+ due to para-H2(j = 0) impact

ABSTRACT Sulphur bearing nitrogenous compounds have been observed in space over this last decade. Modelling their abundances has been done using rate coefficients of isoelectronic molecules. In order to satisfy the astrophysical precision required, we report the actual rate coefficients of NS+ induced by collision with the most abundant interstellar species (para-H2). Considering the 23 low-lying rotational levels of NS+, we were able to compute the (hyperfine) rate coefficients up to 100 K. These latter were carried out by averaging cross-sections over the Maxwell–Boltzmann velocity distribution. The state-to-state inelastic cross-sections were determined in the quantum mechanical close coupling approach for total energies ranging up to 1400 cm−1. These dynamic data result from a four dimensional potential energy surface (4D-PES) which was spherically averaged over the H2 orientations. The 4D-PES was calculated using the explicitly correlated coupled cluster method with simple, double, and non-iterative triple excitation (CCSD(T)–F12) connected to the augmented–correlation consistent–polarized valence triple zeta Gaussian basis set (aug–cc–pVTZ). The so-averaged PES presents a very deep well of 596.72 cm−1 at R = 5.94 a0 and θ1 = 123.20°. Discussions on the propensity rules for the (hyperfine) rate coefficients were made and they are in favour of (Δj = ΔF) Δj = 1 transitions. The results presented here may be crucially needed in order to accurately model the NS+ abundance in space. In addition, we expect that this paper will encourage investigations on the sulphur bearing nitrogenous compounds.

A Density-Based Basis-Set Correction for Wave Function Theory.

We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. This correction, which appropriately vanishes in the complete basis-set (CBS) limit, relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. Contrary to conventional RS-DFT schemes that require an ad hoc range-separation parameter μ, the key ingredient here is a range-separation function μ(r) that automatically adapts to the spatial nonhomogeneity of the basis-set incompleteness error. As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets.

A computational investigation on the electronic and optical properties of Coronene and its Boron-Nitride and perfluorinated counterparts

We present a computational study on the electronic and optical properties of a representative C-made and Boron-Nitride-made (BN) planar molecule of interest for potential applications in the solid state domain. In particular, we analyzed the case of Coronene (C24H12) in its BN and perfluorinated analogues. We performed all electrons Density Functional Theory (DFT) and Time Dependent-DFT (TD-DFT) calculations using a localized Gaussian basis-set in combination with a hybrid exchange-correlation functional. For all the systems we have calculated different electronic properties and the optical absorption spectra. A discussion on the possible implications of the general trends, observed for the BN-made clusters properties as compared to their C-based parents, will be given.

Fully numerical Hartree‐Fock and density functional calculations. I. Atoms

AbstractAlthough many programs have been published for fully numerical Hartree‐Fock (HF) or density functional (DF) calculations on atoms, we are not aware of any programs that support hybrid DFs, which are popular within the quantum chemistry community due to their better accuracy for many applications, or that can be used to calculate electric properties. Here, we present a variational atomic finite element solver in the HelFEM program suite that overcomes these limitations. A basis set of the type is used, where B n(r) are finite element shape functions and are spherical harmonics, which allows for an arbitrary level of accuracy. HelFEM supports nonrelativistic HF and DF calculations even with hybrid functionals, which are not available in other commonly available program packages. Hundreds of functionals at the local spin‐density approximation (LDA), generalized‐gradient approximation (GGA), as well as the meta‐GGA levels of theory are included through an interface with the Libxc library. Electric response properties are achievable via finite field calculations. We introduce an alternative grid that yields faster convergence to the complete basis set limit than commonly used alternatives. We also show that high‐order Lagrange interpolating polynomials yield the best convergence, and that excellent agreement with literature HF limit values for electric properties, such as static dipole polarizabilities, can be achieved with the present approach. Dipole moments and dipole polarizabilities at finite field are also reported with the PBE, PBEh, TPSS, and TPSSh functionals. Finally, we show that a recently published Gaussian basis set is able to reproduce absolute HF and DF energies of neutral atoms, cations, as well as anions within a few dozen microhartrees.

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.

Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields

ABSTRACT We present fully numerical electronic structure calculations on diatomic molecules exposed to an external magnetic field at the unrestricted Hartree–Fock limit, using a modified version of a recently developed finite-element programme, HelFEM. We have performed benchmark calculations on a few low-lying states of H, HeH, LiH, BeH, BH and CH as a function of the strength of an external magnetic field parallel to the molecular axis. The employed magnetic fields are in the range of atomic units, where T. We have compared the results of the fully numerical calculations to ones obtained with the LONDON code using a large uncontracted gauge-including Cartesian Gaussian (GICG) basis set with exponents adopted from the Dunning aug-cc-pVTZ basis set. By comparison to the fully numerical results, we find that the basis set truncation error (BSTE) in the GICG basis is of the order of 1 kcal/mol at zero field, that the BSTE grows rapidly in increasing magnetic field strength, and that the largest BSTE at exceeds 1000 kcal/mol. Studies in larger Gaussian-basis sets suggest that reliable results can be obtained in GICG basis sets at fields stronger than , provided that enough higher-angular-momentum functions are included in the basis.

Non-relativistic and relativistic investigation of the low lying electronic states of Sr2+Xe, Sr+Xe and SrXe systems

The potential energy curves and permanent and transition dipole moments of the neutral SrXe and the ionic Sr+Xe systems are calculated with an ab initio approach using pseudopotential techniques, core polarization potentials, large Gaussian basis sets and full configuration interaction for two electron calculations. The spectroscopic constants of the ground state and lower excited states are in good agreement with the available experimental and theoretical works. The spin–orbit coupling is also included for the ionic system Sr+Xe and the neutral one SrXe. Its effect is significant on the potential energy curves, dipole moments and energy level spacing. For SrXe, the spin–orbit splitting has been considered for the states (2)3Σ0,1, (1,2)3Π0,1,2 and (1)3Δ0,1,2,3.

Substitutional boron and nitrogen pairs in diamond. A quantum mechanical vibrational analysis

The lattice structures, electronic characteristics and spectroscopic features of the three vicinal substitutional, spin zero defects, Ns-Ns (A-centre), Bs-Bs, and Bs-Ns in diamond are reported. They are derived from all-electron B3LYP calculations based on Gaussian basis sets, within a periodic supercell scheme, including both 64- and 216-atom cells. The local geometry reflects the differences between the strong C-C bond of the host lattice and the weaker impurity-impurity bonding in the defective systems. The band structures show two occupied bands 1.06 eV above the VBE for Ns-Ns, and empty bands 3.36 eV and 0.25 eV below the CBE for Bs-Bs and for Bs-Ns respectively. The IR spectra of Bs-Bs and Ns-Ns contain sharp peaks at 631 cm−1, 692 cm−1 and 1373 cm−1, and 451 cm−1, 571 cm−1 and 1276 cm−1, respectively, which might reasonably be considered as ‘finger prints’ for these systems. For Bs-Ns, a set of medium intensity absorptions are predicted at 890 cm−1, 945 cm−1, 1018 cm−1, 1078 cm−1 and 1281 cm−1. However, numerous peaks in this region have been predicted for other defective systems, so that the firm identification of Bs-Ns based on these frequencies is much less certain than Bs-Bs and Ns-Ns.

Multisliced gausslet basis sets for electronic structure

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal functions. We adapt the gausslets to particular systems using one dimensional coordinate transformations, putting more basis functions near nuclei, while maintaining orthogonality. Three dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate the new bases with both Hartree Fock and density matrix renormalization group (DMRG) calculations on hydrogen chain systems. With both methods, we can go to higher accuracy in the complete basis set limit than is practical for conventional Gaussian basis sets, with errors near 0.1 mH per atom.

Implementation of the Many-Pair Expansion for Systematically Improving Density Functional Calculations of Molecules.

Density functional theory (DFT) is the method of choice for predicting structures and reaction energies of molecular systems. However, it remains a daunting task to systematically improve the accuracy of an approximate density functional. The recently proposed many-pair expansion (MPE) [ Phys. Rev. B 2016, 93, 201108] is a density functional hierarchy that systematically corrects any deficiencies of an approximate functional to converge to the exact energy, and was shown to give accurate results for lattice models. In this work, we extend MPE to molecular systems and implement it using Gaussian basis sets. The self-attractive Hartree (SAH) decomposition [ J. Chem. Theory Comput. 2018, 14, 92-103] is employed to generate localized v-representable pair densities for performing MPE calculations. We demonstrate that MPE at the second order (MPE2) already predicts accurate molecular and reaction energies for a series of small molecules and hydrogen chains, with the EXX functional as its starting point. We also show that MPE correctly describes the symmetric bond breaking in hydrogen rings, indicating its ability to remove strong correlation errors. MPE thus provides a promising framework to systematically improve density functional calculations of molecules.