Gaussian Orbital Basis Sets Research Articles

Structural properties of group-III nitrides

We present first-principles calculations of structural and electronic properties of group-III nitrides in wurtzite and zinc-blende structure. For a most accurate treatment of these wide-band-gap semiconductors within local density approximation we employ our self-interaction- and relaxation-corrected pseudopotentials together with Gaussian-orbital basis sets. The results for BN, AlN, GaN, and InN are in good agreement with a host of experimental data yielding a consistent theoretical description of this class of technologically important semi- conductor compounds. [S0163-1829(97)05119-9]

Quantum simulations of molecular systems with intrinsic atomic orbitals

Quantum simulations of molecular systems on quantum computers often employ minimal basis sets of Gaussian orbitals. In comparison with more realistic basis sets, quantum simulations employing minimal basis sets require fewer qubits and quantum gates but yield results of lower accuracy. A natural strategy to achieve more accurate results is to increase the basis set size, which, in turn, requires increasing the number of qubits and quantum gates. Here we explore the use of intrinsic atomic orbitals in quantum simulations of molecules to improve the accuracy of energies and properties at the same computational cost required by a minimal basis. We investigate ground-state energies and one- and two-body density operators in the framework of the variational quantum eigensolver employing and comparing different Ans\"atze. We also demonstrate the use of this approach in the calculation of ground- and excited-state energies of small molecules by a combination of quantum algorithms using IBM quantum computers.

Structural properties of group-III nitrides

We present first-principles calculations of structural and electronic properties of group-III nitrides in wurtzite and zinc-blende structure. For a most accurate treatment of these wide-band-gap semiconductors within local density approximation we employ our self-interaction- and relaxation-corrected pseudopotentials together with Gaussian-orbital basis sets. The results for BN, AlN, GaN, and InN are in good agreement with a host of experimental data yielding a consistent theoretical description of this class of technologically important semi- conductor compounds. [S0163-1829(97)05119-9]

Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields.

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field.

Electronic and optical properties of hexathiapentacene in the gas and crystal phases

Using density functional theory (DFT) and its time-dependent (TD) extension, the electronic and optical properties of the hexathiapentacene (HTP) molecule, a derivative of pentacene (PNT) obtained by symmetric substitution of the six central H atoms with S atoms, are investigated for its gas and solid phases. For the molecular structure, all-electron calculations are performed using a Gaussian localized orbital basis set in conjunction with the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid exchange-correlation functional. Electron affinities, ionization energies, quasiparticle energy gaps, optical absorption spectra, and exciton binding energies are calculated and compared with the corresponding results for PNT, as well as with the available experimental data. The DFT and TDDFT results are also validated by performing many-body perturbation theory calculations within the $GW$ and Bethe-Salpeter equation formalisms. The functionalization with S atoms induces an increase of both ionization energies and electron affinities, a sizable reduction of the fundamental electronic gap, and a redshift of the optical absorption onset. Notably, the intensity of the first absorption peak of HTP falling in the visible region is found to be nearly tripled with respect to the pure PNT molecule. For the crystal structures, pseudopotential calculations are adopted using a plane-wave basis set together with the Perdew-Burke-Ernzerhof exchange-correlation functional empirically corrected in order to take dispersive interactions into account. The electronic excitations are also obtained within a perturbative B3LYP scheme. A comparative analysis is carried out between the ground-state and excited-state properties of crystalline HTP and PNT linking to the findings obtained for the isolated molecules.

Implementation of density functional embedding theory within the projector-augmented-wave method and applications to semiconductor defect states

We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.

Peptide bond formation via glycine condensation in the gas phase.

Four unique gas phase mechanisms for peptide bond formation between two glycine molecules have been mapped out with quantum mechanical electronic structure methods. Both concerted and stepwise mechanisms, each leading to a cis and trans glycylglycine product (four mechanisms total), were examined with the B3LYP and MP2 methods and Gaussian atomic orbital basis sets as large as aug-cc-pVTZ. Electronic energies of the stationary points along the reaction pathways were also computed with explicitly correlated MP2-F12 and CCSD(T)-F12 methods. The CCSD(T)-F12 computations indicate that the electronic barriers to peptide bond formation are similar for all four mechanisms (ca. 32-39 kcal mol(-1) relative to two isolated glycine fragments). The smallest barrier (32 kcal mol(-1)) is associated with the lone transition state for the concerted mechanism leading to the formation of a trans peptide bond, whereas the largest barrier (39 kcal mol(-1)) was encountered along the concerted pathway leading to the cis configuration of the glycylglycine dipeptide. Two significant barriers are encountered for the stepwise mechanisms. For both the cis and trans pathways, the early electronic barrier is 36 kcal mol(-1) and the subsequent barrier is approximately 1 kcal mol(-1) lower. A host of intermediates and transition states lie between these two barriers, but they all have very small relative electronic energies (ca. ± 4 kcal mol(-1)). The isolated cis products (glycylglycine + H2O) are virtually isoenergetic with the isolated reactants (within -1 kcal mol(-1)), whereas the trans products are about 5 kcal mol(-1) lower in energy. In both products, however, the water can hydrogen bond to the dipeptide and lower the energy by roughly 5-9 kcal mol(-1). This study indicates that the concerted process leading to a trans configuration about the peptide bond is marginally favored both thermodynamically (exothermic by ca. 5 kcal mol(-1)) and kinetically (barrier height ≈ 32 kcal mol(-1)) according to the CCSD(T)-F12/haTZ electronic energies. The other pathways have slightly larger barrier heights (by 4-8 kcal mol(-1)).

Basis set dependence of molecular information channels and their entropic bond descriptors

Information channels from SCF MO calculations using different basis sets and their entropic bond descriptors are compared within the orbital communication theory. In this information-theoretic (IT) treatment of communications between basis functions the overall covalency and ionicity bond components reflect the average communication noise and information flow, respectively, in the resolution level specified by the adopted set of basis functions. The basis-set dependence of the orbital conditional probabilities and their entropic descriptors of the information covalency/ionicity content is explored. Compared to the minimum set \({{\bf \chi}}\) of the occupied atomic orbitals of the separated constituent atoms, the extended basis sets of Gaussian orbitals and/or their formal contractions generally give rise to a higher IT-covalency and lower IT-ionicity descriptors of the system chemical bonds. In the augmented set case, \({{\bf \chi}^{aug.} = ({\bf \chi},{\bf \psi})}\) , containing the polarization function complement \({{\bf \psi}}\) of \({{\bf \chi}}\) , the use of only \({{\bf \chi} \rightarrow {\bf \chi}}\) communications is advocated in a semi-quantitative chemical interpretation of the IT bond indices. The maximum-overlap criterion is used to transform the general (orthonormal) extended basis \({{\bf \xi}}\) to its semi-augmented form \({\widetilde{\bf \chi}^{aug.} = \widetilde{\bf \xi}=(\widetilde{\bf \chi}, \widetilde{\bf \psi}),}\) in which \({\widetilde {\bf \chi} \approx {\bf \chi}}\) and \({\widetilde {\bf \psi} \approx{\bf \psi}}\), which facilitates the near minimum basis set interpretation of bond descriptors and extraction of communications involving the polarization functions \({{\widetilde {\mathbf \psi}}}\) . A similar transformation using the minimum information distance criterion can be also envisaged. The effect of the atomic reduction of the molecular channels, which misses the effect of the “internal” communications (bonds) on constituent atoms, is also examined. As intuitively expected, the IT descriptors of such reduced channels are found to be less sensitive to the basis set enlargement.

Magnetic anisotropy of thin Co and Ni films on diamond surfaces

We present results of ab initio investigations of magnetic properties of Co and Ni multilayers on diamond surfaces. The generalized gradient approximation is used within the framework of noncollinear density-functional theory, and fully relativistic pseudopotentials are employed together with a basis set of Gaussian orbitals. The validity of this approach is demonstrated for freestanding transition-metal (TM) monolayers and TM monolayers on the Cu(001) surface. Our results for these test systems are in good agreement with respective literature data. We employ the approach to study up to six Co or Ni adlayers on (111) and (001) surfaces of diamond. These systems are characterized by a very small lattice mismatch of the constituents. We analyze the influence of the strong covalent bonds forming in these hybrid systems on the magnetic properties, focusing on the magnetic anisotropy. For Co multilayers on C(111), the anisotropy energies are quite large and show a weak dependence on the number of adlayers. For Co or Ni multilayers on C(001), on the other hand, these energies are an order of magnitude smaller but their dependence on adlayer thickness is much more pronounced. For the hybrid systems considered, we find configurations with noncollinear magnetization within a given layer or on different layers to be unstable.

Analytical Hessian of electronic excited states in time-dependent density functional theory with Tamm-Dancoff approximation

We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values.

A parallel implementation of the analytic nuclear gradient for time-dependent density functional theory within the Tamm–Dancoff approximation

We derived the analytic gradient for the excitation energies from a time-dependent density functional theory calculation within the Tamm–Dancoff approximation (TDDFT/TDA) using Gaussian atomic orbital basis sets, and introduced an efficient serial and parallel implementation. Some timing results are shown from a B3LYP/6-31G**/SG-1-grid calculation on zincporphyrin. We also performed TDDFT/TDA geometry optimizations for low-lying excited states of 20 small molecules, and compared adiabatic excitation energies and optimized geometry parameters to experimental values using the B3LYP and ωB97 functionals. There are only minor differences between TDDFT and TDA optimized excited state geometries and adiabatic excitation energies. Optimized bond lengths are in better agreement with experiment for both functionals than either CC2 or SOS-CIS(D0), while adiabatic excitation energies are in similar or slightly poorer agreement. Optimized bond angles with both functionals are more accurate than CIS values, but less accurate than either CC2 or SOS-CIS(D0) ones.

Discrete Variable Representation Implementation of the One-Electron Polarization Model.

A discrete variable representation (DVR) implementation of an one-electron polarization model (OPEM) for characterizing (H2O)n− clusters is described. For the (H2O)90− cluster, evaluation of the energy and gradient using a suitable DVR basis sets is about a 2 orders of magnitude faster than corresponding calculations using a Gaussian orbital basis set. The DVR version of the code has been parallelized using OpenMP to enable molecular dynamics (MD) simulations of large (H2O)n− clusters.

Quasiparticle band structures and lifetimes in noble metals using Gaussian orbital basis sets

We present the calculations of quasiparticle bandstructures and lifetimes for noble metals Cu and Ag within the $GW$ approximation based on localized Gaussian orbital basis sets. For Cu, both the calculated positions of the $d$ bands and the width of the $d$ bands are within 0.1 eV compared to the experimental results. For Ag, partial core correction should be included in the pseudopotential to get reliable positions of the $d$ bands. The calculated lifetimes agree with the experiment in the energy region away from the Fermi level, but deviate from the experimental results near the Fermi level where short-range interactions which $GW$ approach fails to describe play an important role. For a better description of the lifetime near the Fermi level, terms beyond the $GW$ approximation in the many-body perturbation theory need to be considered.

Origin of electronic structure and time-dependent state averaging in the multi-configuration time-dependent Hartree–Fock approach to electron dynamics

In this Letter, we discuss problems that can arise in the interpretation of results obtained by quantum dynamical simulations with the multi-configuration time-dependent Hartree–Fock (MCTDHF) method. In particular, we show that an effect, which can be seen as the time-dependent version of the state averaging known from standard quantum chemistry, can modify the electronic structure as derived from such a simulation. We illustrate our findings with numerical calculations for the laser excitation of a water molecule, with a Gaussian Type Orbital basis set.

Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements

Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of \({\gamma = 1.4 a_{0}^{-1}}\) can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated.

Quantum Chemistry: Restricted Hartree-Fock SCF Calculations Using Microsoft Excel

Programs that facilitate ab initio calculations can relegate the underlying SCF procedure (usually coupled with contracted Gaussian atomic orbital basis sets) to a ‘black box.’ This paper attempts to rectify this situation with a spreadsheet that contains all the essential elements of far more complicated ab initio calculations, but on the simplest possible molecular system.

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 Møller-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.

Spin Symmetry Requirements in Density Functional Theory: The Proper Way to Predict Magnetic Coupling Constants in Molecules and Solids

In this paper it is argued that the use of density functional theory (DFT) to solve the exact, non-relativistic, many-electron problem, for magnetic systems requires impos- ing space and spin symmetry constraints exactly in the same way as it is currently done in ab initio wave function theory. This strong statement is supported on pertinent calculations for selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids. These calculations include several wave function methods of increasing accuracy and different forms of the exchange- correlation functional. The comparisons of numerical results carried out always within the same standard Gaussian Type Orbital atomic basis set show that imposing or not the spin and space constraints (restricted or unrestricted formalisms) leads to contradictory results. Therefore, it appears that, in the case of the Heisenberg magnetic constant, the present exchange-correlation functionals may provide reasonable numerical results although for the wrong physical reasons thus evidencing the failure of the current DFT methods to properly describe magnetic systems.

Generalized reconstruction model ofSiC(001)−(n×2)surfaces and Si ad-dimer strings

We report ab initio calculations on the atomic and electronic structure of the $7\ifmmode\times\else\texttimes\fi{}2$ and $8\ifmmode\times\else\texttimes\fi{}2$ surfaces of cubic $\mathrm{SiC}(001)$ carried out within local density approximation of the density functional theory. Supercells, nonlocal norm-conserving pseudopotentials and Gaussian orbital basis sets are used to describe the surface systems. Our results for the surface structure are in good accord with a lot of experimental data. These investigations complement our previous ab initio studies on $c(4\ifmmode\times\else\texttimes\fi{}2)$, $3\ifmmode\times\else\texttimes\fi{}2$ and $5\ifmmode\times\else\texttimes\fi{}2$ reconstructions of the $\mathrm{SiC}(001)$ surface. On the basis of all our results, we suggest a general two adlayer asymmetric dimer model (TAADM) for $n\ifmmode\times\else\texttimes\fi{}2$ reconstructions of $\mathrm{SiC}(001)$. The model is based on two structural building blocks. The first contains an asymmetric dimer in one partial adlayer while the second contains an asymmetric dimer configuration of six Si adatoms in two partial adlayers. These are characteristic for the $c(4\ifmmode\times\else\texttimes\fi{}2)$ and $3\ifmmode\times\else\texttimes\fi{}2$ reconstructions, respectively. Employing the model for higher $n$ values allows us to suggest optimal structures for a large host of $n\ifmmode\times\else\texttimes\fi{}2$ reconstructions. Comparing the formation energies of the $c(4\ifmmode\times\else\texttimes\fi{}2)$ and all $n\ifmmode\times\else\texttimes\fi{}2$ structures considered, we find in agreement with experiment that the $3\ifmmode\times\else\texttimes\fi{}2$ and $c(4\ifmmode\times\else\texttimes\fi{}2)$ reconstructions are most favorable for silicon-rich and silicon-poor growth conditions, respectively. The formation energies of all other reconstructions fall in between these two limits. In particular, the general TAADM allows us to rationalize the occurrence of periodic and nonperiodic Si ad-dimer-string arrangements at Si-terminated $3\mathrm{C}\text{\ensuremath{-}}\mathrm{SiC}(001)$ surfaces in very good accord with experimental data.

Metallization of the3C−SiC(001)−(3×2)surface induced by hydrogen adsorption: A first-principles investigation

We report ab initio calculations on the atomic and electronic structure, formation energies and surface vibrational modes of a variety of hydrogenated $3C\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}(001)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}2)$ surfaces to shed more light on the recently discovered hydrogen-induced metallization of this semiconductor surface. The calculations are carried out employing the local density approximation of density functional theory. The adsorption systems are described using supercells, nonlocal norm-conserving pseudopotentials and Gaussian orbital basis sets. First, we show in agreement with other most recent ab initio calculations that Si dangling bonds at the third layer, originally suggested for explaining the experimentally observed surface metallization, are not stable. Instead, for low H exposure, we find H atoms to form monohydrides at the top layer and to become adsorbed in angular Si-H-Si bonds on the third layer. Due to these bonds the surface becomes metallic. We scrutinize further possibilities of surface metallization investigating numerous conceivable other H configurations on the first three layers of the $\mathrm{Si}\mathrm{C}(001)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}2)$ surface. It turns out that H atoms can also occupy bridge positions in angular Si-H-Si bonds on the second layer yielding a locally stable metallic surface. For larger H exposure, we find H atoms to form dihydrides at the top layer and to become adsorbed on the second and/or third layer in angular Si-H-Si bridge bonds. These structures are metallic, as well, and they are energetically even more favorable. In all cases considered, the angular Si-H-Si bonds are the origin of the surface metallization giving rise to partially occupied surface state bands which close the gap and overlap in parts with the lower projected conduction bands. Finally we address surface phonons. Some of the calculated frequencies are in very good accord with experiment. Others, particularly characteristic for the Si-H-Si bridge bonds, have not been resolved in experiment, to date.