Atomic Orbital Basis Research Articles

Atomic Orbital Implementation of Extended Symmetry-Adapted Perturbation Theory (XSAPT) and Benchmark Calculations for Large Supramolecular Complexes.

We report an implementation of extended symmetry-adapted perturbation theory (XSAPT) in the atomic orbital basis, extending this method to systems where the monomers are large. In our "XSAPT(KS)" approach, monomers are described using range-separated Kohn-Sham (KS) density functional theory (DFT), with correct asymptotic behavior set by tuning the range-separation parameter ω in a monomer-specific way. This is accomplished either by conventional ionization potential (IP)-based tuning, in which ω is adjusted to satisfy the condition εHOMO(ω) = -IP(ω), or else using a "global density-dependent" (GDD) condition, in which ω is fixed based on the size of the exchange hole. The latter procedure affords better results for both total interaction energies and energy components, when used in conjunction with our third-generation pairwise atom-atom dispersion potential (+ aiD3). Three-body (triatomic) dispersion terms are found to be important when the monomers are large, and we incorporate these by means of an Axilrod-Teller-Muto term, Edisp,3BATM, which reduces errors in supramolecular interaction energies by about a factor of 2. The XSAPT(KS) + aiD3 + Edisp,3BATM(ωGDD) approach affords mean absolute errors as low as 1.2 and 4.2 kcal/mol, respectively, for the L7 and S12L benchmark test sets of large dimers. Such errors are comparable to those afforded by far more expensive methods, such as DFT-SAPT, and the closely related second-order perturbation theory with coupled dispersion (MP2C). We also survey the performance of various other quantum-chemical methods for these data sets and identify several semiempirical and DFT-based approaches whose accuracy approaches that of MP2C, at dramatically reduced cost.

First-principles calculations of LiNbO3 optical properties: From far-infrared to ultraviolet

We perform first-principles calculations of optical properties for ferroelectric phase of LiNbO3 crystal using density functional theory (DFT) for wide range of wavelengths, from far-infrared (IR) to ultraviolet. We study frequency dependence of complex dielectric tensor and related quantities, such as refractive and reflection indices, absorption coefficients, etc. Our calculation incorporates advantages of numerical approaches based on atomic-orbital all-electron Gaussian-type basis sets, as it is realized in CRYSTAL14 program. We compared predictions obtained in general-gradient approach with PBESOL exchange-correlation functional and in hybrid approach with PBESOL0 functional, and we have found that hybrid PBESOL0 functional is more applicable to describe the wide set of the experimental data.

Off‐center Gaussian functions: Applications toward larger basis sets, post‐second‐order correlation treatment, and truncated virtual orbital space in investigations of noncovalent interactions

AbstractThis work is a continuation of our pilot study on the use of off‐center s‐type Gaussian functions in noncovalent interaction calculations. A grid of s‐type Gaussians surrounding the molecule is intended to substitute for the presence of diffuse basis functions, which are important for accurate description of noncovalent interactions. The advantage over the use of diffuse functions is reduction or elimination of linear dependency issues in the atomic orbital basis set, which often causes convergence problems. Placement of a grid of s‐functions on the surface of the molecule allows more favorable scaling of the total number of basis functions with the molecular size to be achieved. In this article, we present several innovations on the concept, namely the parametrization and assessment of grids with triple‐ζ quality basis set; use in post‐second‐order correlation treatment (methods such as Møller–Plesset third‐order or coupled‐cluster); and combination with modified virtual orbital approaches, namely the frozen natural orbitals and optimized virtual orbital space methods.

Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set

The interaction of laser fields with solid-state systems can be modeled efficiently within the velocity-gauge formalism of real-time time dependent density functional theory (RT-TDDFT). In this article, we discuss the implementation of the velocity-gauge RT-TDDFT equations for electron dynamics within a linear combination of atomic orbitals (LCAO) basis set framework. Numerical results obtained from our LCAO implementation, for the electronic response of periodic systems to both weak and intense laser fields, are compared to those obtained from established real-space grid and Full-Potential Linearized Augmented Planewave approaches. Potential applications of the LCAO based scheme in the context of extreme ultra-violet and soft X-ray spectroscopies involving core-electronic excitations are discussed.

Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets.

We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

Reliable and computationally affordable prediction of the energy gap of (TiO2)n (10 ≤ n ≤ 563) nanoparticles from density functional theory.

The optical gap (Ogap) of a set of (TiO2)n nanoclusters and nanoparticles with n = 10-563 and different morphologies such as spherical, octahedral, lamellar, or tubular finite structures is investigated based on a relativistic all-electron description along with a numerical atomic centered orbital basis set. Two different functionals are used, PBE and PBEx, the former corresponds to a standard implementation of the generalized gradient approximation (GGA) and the latter to a hybrid functional with 12.5% of Fock exchange which reproduces the band gap of bulk TiO2 anatase and rutile. It is shown that the inclusion of exchange Fock in the PBE functional promotes a systematic energy gap opening of 1.25 eV relative to the PBE values. Remarkably, a linear correlation is found between PBEx and PBE Ogap calculated values with concomitant similar correlations for the HOMO and LUMO orbital energies. However, it appears that PBEx induces a larger downshift on the HOMO orbital than the upshift observed on the LUMO one. The fact that the PBEx hybrid functional was shown to reproduce the experimental energy gaps of stoichiometric and reduced TiO2 bulk phases leads to a suitable and practical way to successfully estimate Ogap of TiO2 nanoparticles containing up to thousands of atoms with PBEx precision from computationally affordable PBE calculations.

Real-time time dependent density functional theory with numerical atomic orbital basis set: methodology and applications

Real-time time dependent density functional theory (rt-TDDFT) approach directly provides the time domain evolution of electronic wave functions together with ionic movements, presenting a versatile way of real time tracking ultrafast dynamics and phenomena either in perturbative regime or in non-perturbative regime. Thus, rt-TDDFT is a unique ab initio quantum method applicable for the exploration of strong field physics that is beyond the linear response theory. Numerical implementations of the rt-TDDFT based on planewaves and real-space grids have been demonstrated in recent years. However, the above two methods are suitable for the efficient treatment of low energy excitation on the scale of a few electron volts in a small size system. In this paper, we present a state-of-the-art real-time TDDFT approach as implemented in the time dependent ab initio package (TDAP). By employing atomic orbital basis sets, which are small in size and fast in performance, we are able to simulate a large-size system for long electronic propagation time with less computational cost while maintaining relatively high accuracy. The length and velocity-gauge of electromagnetic field are both implemented, showing the flexibility and credibility in applying our methods to various laser induced phenomena in diverse systems including solids, interfaces and two-dimensional materials. Furthermore, recently developed k-resolved algorithm ensures the possibility of handling the problems with a unit cell approach, which significantly reduces the formidable computational costs of traditional rt-TDDFT simulations. Detailed flow and implementation of this method are discussed in this paper, and several quintessential examples for applications are introduced. First, we use the present method to calculate the photoabsorption properties of armchair graphene nanoribbons and monitor the excitation details with momentum resolution. Then, we simulate laser melting of silicon, which captures the most important features of nonthermal melting observed in experiment, and further reveals that it can be attributed to drastic laser-induced change in bonding electron density and subsequent decrease in the melting barrier. After that, a model MoS2/WS2 bilayer system is used as an example to show how our method can be used to monitor the electronic dynamics in such a van der Waals heterostructure. Finally, we show the possibility of controlling the electron dynamic process to enhance high harmonic generation intensity and generate isolated attosecond pulse in monolayer MoS2 via two-color field. Most of the above examples present new ideas in their respective areas and demonstrate that our method has a great potential application in studying interesting ultrafast dynamics phenomena in a wide range of quantum systems.

First-principles study on transport property of molecular} device with non-collinear electrodes

Molecular device is the ultimate electronic devices in the view point sense of scale size.Electron transport in molecular device shows obvious quantum effect,and the transport property of molecular device will be strongly affected by the chemical and structural details,including the contact position and method between the molecule and electrodes,the angle between two electrodes connecting to the molecule.However,we notice that in the existing reports on device simulations from first principles the two electrodes are always in a collinear case.Even for multi-electrode simulations,one usually used to adopt orthogonal electrodes,namely,each pair of the electrodes is in a collinear case.As the electrode configuration will clearly affect the transport property of a device on a nanometer scale,the first principles quantum transport studies with non-collinear electrodes are of great importance,but have not been reported yet.In this paper,we demonstrate the calculations of a transport system with non-collinear electrodes based on the state-of-the-art theoretical approach where the density functional theory (DFT) is combined with the Keldysh non-equilibrium Green's function (NEGF) formalism. Technically,to model a quantum transport system with non-collinear electrodes,the center scattering region of the transport system is placed into an orthogonal simulation box in all the other quantum transport simulations,while one or two electrodes are simulated within a non-orthogonal box.This small change in the shape of the simulation box of the electrode provides flexibility to calculate transport system with non-collinear electrodes,but also increases the complexity of the background coding.To date,the simulation of transport system with non-collinear electrodes has been realized only in the Nanodcal software package. Here,we take the Au-benzene (mercaptan)-Au molecular devices for example,and systematically calculate the quantum transport properties of the molecular devices with various contact positions and methods,and specifically,we first demonstrate the effect of the angle between the two electrodes on the transport property of molecular device from first principles.In our NEGF-DFT calculations performed by Nanodcal software package,the double- polarized atomic orbital basis is used to expand the physical quantities,and the exchange-correlation is treated in the local density approximation,and atomic core is determined by the standard norm conserving nonlocal pseudo-potential.Simulation results show that the chemical and structural details not only quantitatively affect the current value of the molecular device,but also bring new transport features to a device,such as negative differential resistance.From these results,we can conclude that the physics of a transport system having been investigated in more detail and a larger parameter space such as the effect of the contact model having been assessed by a comparison with ideal contacts,further understanding of the transport system can be made and more interesting physical property of the device can be obtained,which will be useful in designing of emerging electronics.

Density-functional theory based molecular dynamics simulation of tetrahedrite thermoelectrics: Effect of cell size and basis sets

In this work we investigated the effect of cell size and basis sets on the structural and dynamic properties from density-functional theory based molecular dynamics simulations. Three simulations, 1 × 1 × 1 cell with plane wave (PW) basis set, 1 × 1 × 1 cell with atomic orbital (AO) basis, and 2 × 2 × 2 cell with AO basis, were performed at 300 K on a model material: tetrahedrite thermoelectric Cu10Zn2Sb4S13. It was found that lattice parameters, vibrational spectra, heat capacity, and EXAFS spectra are comparable for three simulations. In addition, the 2 × 2 × 2 cell can provide access to length scales closer to the hydrodynamic limit, which allow us to identify the sound/acoustic modes in momentum/velocity correlation, as well as quasi-localized modes that are possibly responsible for its low lattice thermal conductivity.

PAOFLOW: A utility to construct and operate on ab initio Hamiltonians from the projections of electronic wavefunctions on atomic orbital bases, including characterization of topological materials

PAOFLOW is a utility for the analysis and characterization of materials properties from the output of electronic structure calculations. By exploiting an efficient procedure to project the full plane-wave solution on a reduced space of atomic orbitals, PAOFLOW facilitates the calculation of a plethora of quantities such as diffusive, anomalous and spin Hall conductivities, magnetic and spin circular dichroism, and Z2 topological invariants and more. The computational cost associated with post-processing first principles calculations is negligible. This code, written entirely in Python under GPL 3.0 or later, opens the way to the high-throughput computational characterization of materials at an unprecedented scale.

Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation.

Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc.

Structural, electronic, and mechanical properties of cubic TiO2: A first-principles study

We present an analysis of structural, electronic, and mechanical properties of cubic titanium dioxide (TiO2) using an all electron orthogonalzed linear combinations of atomic orbitals (OLCAO) basis set under the framework of density functional theory (DFT). The structural property, especially the lattice constant a, and the electronic properties such as the band diagram and density of states (DOS) are studied and analyzed. The mechanical properties such as bulk moduli, shear moduli, Young’s Moduli, and Poison’s ratio are also investigated thoroughly. The calculations are carried out on shear moduli and anisotropy factor for cubic TiO2. The Vickers hardness is also tested for fluorite and pyrite cubic-structured TiO2. Furthermore, the results are compared with the previous theoretical and experimental results. It is found that DFTbased simulation produces results which are approximation to experimental results, whereas the calculated elastic constants are better than the previous theoretical and experimental values.

Calculations of nuclear magnetic shielding constants based on the exact two-component relativistic method.

From the matrix representation of the modified Dirac equation based on the restricted magnetically balanced gauge-including atomic orbital (RMB-GIAO) basis, previously one of the authors (Yoshizawa) and co-workers derived the two-component normalized elimination of the small component (2c-NESC) formulas for 2c relativistic calculations of nuclear magnetic resonance (NMR) shielding tensors. In the present study, at the Hartree-Fock (HF) level, we numerically confirm that for several molecules the RMB-GIAO-based 2c-NESC method provides gauge-origin independent NMR shielding values. Moreover, we investigate the accuracy of the 2c-NESC method by comparison with the 4c relativistic NMR calculations at the HF level. For noble gas dimers and Hg compounds, it is shown that the 2c-NESC method reproduces the 4c relativistic NMR shielding constants within errors of 0.12%-0.31% of the 4c relativistic values and yields chemical shifts sufficiently close to the 4c relativistic results. Also, we discuss the basis set convergence of NMR shielding constants calculated with the 2c-NESC and 4c relativistic methods.

Detailed Wave Function Analysis for Multireference Methods: Implementation in the Molcas Program Package and Applications to Tetracene.

High-level multireference computations on electronically excited and charged states of tetracene are performed, and the results are analyzed using an extensive wave function analysis toolbox that has been newly implemented in the Molcas program package. Aside from verifying the strong effect of dynamic correlation, this study reveals an unexpected critical influence of the atomic orbital basis set. It is shown that different polarized double-ζ basis sets produce significantly different results for energies, densities, and overall wave functions, with the best performance obtained for the atomic natural orbital (ANO) basis set by Pierloot et al. Strikingly, the ANO basis set not only reproduces the energies but also performs exceptionally well in terms of describing the diffuseness of the different states and of their attachment/detachment densities. This study, thus, not only underlines the fact that diffuse basis functions are needed for an accurate description of the electronic wave functions but also shows that, at least for the present example, it is enough to include them implicitly in the contraction scheme.

Density-Based Multilevel Hartree-Fock Model.

We introduce a density-based multilevel Hartree-Fock (HF) method where the electronic density is optimized in a given region of the molecule (the active region). Active molecular orbitals (MOs) are generated by a decomposition of a starting guess atomic orbital (AO) density, whereas the inactive MOs (which constitute the remainder of the density) are never generated or referenced. The MO formulation allows for a significant dimension reduction by transforming from the AO basis to the active MO basis. All interactions between the inactive and active regions of the molecule are retained, and an exponential parametrization of orbital rotations ensures that the active and inactive density matrices separately, and in sum, satisfy the symmetry, trace, and idempotency requirements. Thus, the orbital spaces stay orthogonal, and furthermore, the total density matrix represents a single Slater determinant. In each iteration, the (level-shifted) Newton equations in the active MO basis are solved to obtain the orbital transformation matrix. The approach is equivalent to variationally optimizing only a subset of the MOs of the total system. In this orbital space partitioning, no bonds are broken and no a priori orbital assignments are carried out. In the limit of including all orbitals in the active space, we obtain an MO density-based formulation of full HF.

Many-body expansion of the Fock matrix in the fragment molecular orbital method.

A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.

Quadrupolar NMR Relaxation from ab Initio Molecular Dynamics: Improved Sampling and Cluster Models versus Periodic Calculations.

Quadrupolar NMR relaxation rates are computed for 17O and 2H nuclei of liquid water, and of 23Na+, and 35Cl- in aqueous solution via Kohn-Sham (KS) density functional theory ab initio molecular dynamics (aiMD) and subsequent KS electric field gradient (EFG) calculations along the trajectories. The calculated relaxation rates are within about a factor of 2 of experimental results and improved over previous aiMD simulations. The relaxation rates are assessed with regard to the lengths of the simulations as well as configurational sampling. The latter is found to be the more limiting factor in obtaining good statistical sampling and is improved by averaging over many equivalent nuclei of a system or over several independent trajectories. Further, full periodic plane-wave basis calculations of the EFGs are compared with molecular-cluster atomic-orbital basis calculations. The two methods deliver comparable results with nonhybrid functionals. With the molecular-cluster approach, a larger variety of electronic structure methods is available. For chloride, the EFG computations benefit from using a hybrid KS functional.

Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the density-fitting approximation.

An efficient implementation of analytic gradients for the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method with the density-fitting (DF) approximation, denoted as DF-CCSD(T), is reported. For the molecules considered, the DF approach substantially accelerates conventional CCSD(T) analytic gradients due to the reduced input/output time and the acceleration of the so-called "gradient terms": formation of particle density matrices (PDMs), computation of the generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the effective PDMs and GFM, back-transformation of the PDMs and GFM, from the molecular orbital to the atomic orbital (AO) basis, and computation of gradients in the AO basis. For the largest member of the molecular test set considered (C6H14), the computational times for analytic gradients (with the correlation-consistent polarized valence triple-ζ basis set in serial) are 106.2 [CCSD(T)] and 49.8 [DF-CCSD(T)] h, a speedup of more than 2-fold. In the evaluation of gradient terms, the DF approach completely avoids the use of four-index two-electron integrals. Similar to our previous studies on DF-second-order Møller-Plesset perturbation theory and DF-CCSD gradients, our formalism employs 2- and 3-index two-particle density matrices (TPDMs) instead of 4-index TPDMs. Errors introduced by the DF approximation are negligible for equilibrium geometries and harmonic vibrational frequencies.

Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis.

In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis functions are inherently localized and the number of active orbitals is comparatively small, our formulation is particularly suited for a linearly scaling NEVPT2 implementation. In our formulation, there are two kinds of NEVPT2 energy contributions, which differ in the number of active orbitals in the two-electron integrals involved. Those involving integrals with either no or a single active orbital can be formulated completely in the AO basis as single-reference second-order Møller-Plesset perturbation theory and benefit from sparse active pseudo-density matrices-particularly if the active molecular orbitals are localized only in parts of a molecule. Conversely, energy contributions involving integrals with either two or three active orbitals can be obtained from Coulomb and exchange matrices generalized for pairs of active orbitals. Moreover, we demonstrate that Laplace-transformed partially contracted NEVPT2 is nothing less than time-dependent NEVPT2 [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)] iff the all-active intermediates are computed with the internal-contraction approximation. Furthermore, we show that for multi-reference perturbation theories it is particularly challenging to find optimal parameters of the numerical Laplace transformation as the fit range may vary among the 8 different OEDs by many orders of magnitude. Selecting the number of quadrature points for each OED separately according to an accuracy-based criterion allows us to control the errors in the NEVPT2 energies reliably.

An ab initio study of the vibrational properties of alkaline-earth metal nitrates and their crystallohydrates

The vibrational frequencies and corresponding intensities have been calculated ab initio for the center of the Brillouin zone of crystalline magnesium, calcium, strontium, and barium nitrates; magnesium nitrate hexahydrate; and calcium nitrate tetrahydrate. The calculation has been performed within the electron- density functional theory using the PBE exchange-correlation functional in the basis of localized atomic orbitals with the aid of the CRYSTAL14 software. The calculated values and the experimental IR and Raman spectral data on strontium and barium nitrates are shown to be in satisfactory agreement. The frequencies of normal long-wavelength vibrations in the nitrates become red-shifted with an increase in the cation atomic mass. The occurrence of several peaks due to the vibrations of hydrogen atoms in water molecules with different dynamic charges is predicted in the IR spectrum of hexahydrate magnesium in the frequency range above 3430 cm–1.