Orbital Basis Sets Research Articles

A full-potential and multiscale computational scheme for interactions between ultrafast intense laser pulses and condensed medium

We have presented a multiscale computational scheme for the simulation of interactions between ultrafast intense laser pulses and condensed medium. This approach solves the coupled time-dependent Kohn-Sham (TDKS) and Maxwell equations in real time and provides a unified description of microscopic electron dynamics and macroscopic light propagation from first principles and applicable to wide ultrafast phenomena. Especially, as the TDKS equation was solved within the framework of all-electron full-potential and the augmented plane wave with local orbitals basis sets were adopted, this approach overcomes the drawbacks of real space grids and pseudopotential approximations and works well for some extreme conditions that the information near the nucleus is important. We demonstrated the approach by calculating the microscopic electron dynamics of crystalline silicon (Si) excited with an intense laser pulse and the macroscopic propagation of a laser pulse in a ∼3.5 μm free standing Si film with the feedback of microscopic electron dynamics coupled together. We also verified the availability of this approach under extreme condition with hundreds TPa (1 TPa = 1012 Pa) pressure in a metallic solid neon, and reasonable results were obtained. Our approach provides a new paradigm for multiscale simulations of ultrafast phenomena that induced by intense laser pulses in condensed medium.

Synthesis, characterization, and quantum chemical study of cobalt(II) chelates with N-phenethyl-iminodiacetate(2-)-like ligands. Influence of p-(R)-phenethyl group on crystal pattern

From the reaction of Co(II) hydroxy-carbonates and N-p-(R)-phenethyliminodiacetic acids (H2pheida, R = H and H2MOpheida, R = CH3O) two binary complexes have been obtained in aqueous media. The crystal pattern of [Co(pheida)(H2O)3]·1.5H2O (1) (monoclinic, space group C2/c) differs from the related non-hydrated crystal of [Co(MOpheida)(H2O)3] (2) (monoclinic, space group P21/c). Both Co(II) complexes display distorted octahedral geometry imposed by 3d 7 electronic configuration. Our crystallographic results reveal that the metal chelates have a molecular structure and the used methoxy-substituent on the pheida skeleton yield different structural features. The iminodiacetic acid-arms [IDA] of pheida-like ligands adopt fac-NO2 conformation. For both chelators 1 and 2, single-point energy was calculated using restricted and/or unrestricted Hartree–Fock/BP/B3LYP functional. The analytical frequency, electronic absorption, and HOMO–LUMO energy gap were calculated using B3LYP functional with orbital basis set def2-SVP or def2-TZVP (for 2) along with the auxiliary basis set def2/J. The quantum chemical calculated geometry parameters are compared with their corresponding X-ray crystallographic data. The optical band gap (E g) arises due to the electronic transitions. The direct and indirect band gap energy measured 3.26, 3.19 eV for 1 and 3.39, 3.35 eV for 2, respectively, reflecting their semi-conducting nature. Crystal structure for H2MOpheida acid also reported herein.

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database.

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

New Theoretical Infrared Line List for the Methyl Radical with Accurate Vibrational Band Origins from High-Level Ab Initio Calculations.

In the present work, high-level ab initio calculations were carried out for the ground electronic state of the methyl radical (CH3). Dunning's augmented correlation-consistent orbital basis sets were employed up to the quintuple-ζ valence quality with the core-valence electron correlation [aug-cc-pCV5Z] combined with the single- and double-excitation unrestricted coupled-cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. The explicitly correlated version of the coupled-cluster approach [RHF-UCCSD(T)-F12x{x = a, b}] was additionally applied with the core-valence cc-pCVQZ-F12 basis set in order to study convergence with respect to the basis set size. The contributions beyond the coupled-cluster level of the theory like Douglas-Kroll-Hess scalar relativistic Hamiltonian, diabatic Born-Oppenheimer corrections, and high-order electronic correlations have been included into the ab initio potential energy surfaces (PESs). It is shown that the theoretical band origins of CH3 converge gradually to the experimental values when applying the ab initio PESs using the aug-cc-pCVXZ [X = T, Q, and 5] basis sets. For the first time, all available experimental band origins of the gaseous CH3 are reproduced within an accuracy of 0.2 cm-1 using a newly developed PES extrapolated to the complete basis set limit [CBS(TQ5Z)]. The reached accuracy is one order of magnitude better than that of the best available calculations. A new theoretical infrared line list was generated for astrophysical applications using an ab initio dipole moment surface computed at the RHF-UCCSD(T)/aug-cc-pCVQZ level of the theory. The manifestation of a large-amplitude motion in CH3 is also discussed.

Density Functional Theory Plus Dynamical Mean Field Theory within the Framework of Linear Combination of Numerical Atomic Orbitals: Formulation and Benchmarks.

The combination of density functional theory with dynamical mean-field theory (DFT+DMFT) has become a powerful first-principles approach to tackle strongly correlated materials in condensed matter physics. The wide use of this approach relies on robust and easy-to-use implementations, and its implementation in various numerical frameworks will increase its applicability on the one hand and help crosscheck the validity of the obtained results on the other. In this work, we develop a formalism within the linear combination of numerical atomic orbital (NAO) basis set framework, which allows for merging of NAO-based DFT codes with DMFT quantum impurity solvers. The formalism is implemented by interfacing two NAO-based DFT codes with three DMFT impurity solvers, and its validity is testified by benchmark calculations for a wide range of strongly correlated materials, including 3d transition metal compounds, lanthanides, and actinides. Our work not only enables DFT+DMFT calculations using popular and rapidly developing NAO-based DFT code packages but also facilitates the combination of more advanced beyond-DFT methodologies available in these codes with the DMFT machinery.

ADVANCED STUDY OF SPECTRAL AND HYPERFINE STRUCTURE PARAMETERS FOR Li-LIKE MULTICHARGED IONS WITHIN Relativistic Theory

The relativistic many-body perturbation theory with the optimized Dirac zeroth approximation is applied to calculation of some fundamental characteristics of the hyperfine structure of middle and heavy Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with performance of the gauge invariance principle. There are listed the calculated values of derivatives of the one-electron characteristics, including the hyperfine structure parameters, on nuclear radius for the Li-like multicharged ions with the corresponding analysis.

Localized Resolution of Identity Approach to the Analytical Gradients of Random-Phase Approximation Ground-State Energy: Algorithm and Benchmarks.

We develop and implement a formalism which enables calculating the analytical gradients of particle-hole random-phase approximation (RPA) ground-state energy with respect to the atomic positions within the atomic orbital basis set framework. Our approach is based on a localized resolution of identity (LRI) approximation for evaluating the two-electron Coulomb integrals and their derivatives, and the density functional perturbation theory for computing the first-order derivatives of the Kohn-Sham (KS) orbitals and orbital energies. Our implementation allows one to relax molecular structures at the RPA level using both Gaussian-type orbitals (GTOs) and numerical atomic orbitals (NAOs). Benchmark calculations against previous implementations show that our approach delivers adequate numerical precision, highlighting the usefulness of LRI in the context of RPA gradient evaluations. A careful assessment of the quality of RPA geometries for small molecules reveals that post-KS RPA systematically overestimates the bond lengths. We furthermore optimized the geometries of the four low-lying water hexamers-cage, prism, cyclic, and book isomers, and determined the energy hierarchy of these four isomers using RPA. The obtained RPA energy ordering is in good agreement with that yielded by the coupled cluster method with single, double and perturbative triple excitations, despite that the dissociation energies themselves are appreciably underestimated. The underestimation of the dissociation energies by RPA is well corrected by the renormalized single excitation correction.

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.

Automatic generation of complementary auxiliary basis sets for explicitly correlated methods.

Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: Coulomb‐exchange fitting (JK), resolution of the identity MP2 (RI‐MP2), and complementary auxiliary basis set (CABS). If unavailable for the orbital basis set and chemical elements of interest, the first two can be auto‐generated on the fly using existing algorithms, but not the third. In this paper, we present a quite simple algorithm named autoCABS; a Python implementation under a free software license is offered at Github. For the cc‐pVnZ‐F12 (n = D,T,Q,5), the W4‐08 thermochemical benchmark, and the HFREQ2014 set of harmonic frequencies, we demonstrate that autoCABS‐generated CABS basis sets are comparable in quality to purpose‐optimized OptRI basis sets from the literature, and that the quality difference becomes entirely negligible as n increases.

Optimization of the r2SCAN-3c Composite Electronic-Structure Method for Use with Slater-Type Orbital Basis Sets.

The “Swiss army knife” composite density functional electronic-structure method r2SCAN-3c (J. Chem. Phys.2021, 154, 064103) is extended and optimized for the use with Slater-type orbital basis sets. The meta generalized-gradient approximation (meta-GGA) functional r2SCAN by Furness et al. is combined with a tailor-made polarized triple-ζ Slater-type atomic orbital (STO) basis set (mTZ2P), the semiclassical London dispersion correction (D4), and a geometrical counterpoise (gCP) correction. Relativistic effects are treated explicitly with the scalar-relativistic zeroth-order regular approximation (SR-ZORA). The performance of the new implementation is assessed on eight geometry and 74 energy benchmark sets, including the extensive GMTKN55 database as well as recent sets such as ROST61 and IONPI19. In geometry optimizations, the STO-based r2SCAN-3c is either on par with or more accurate than the hybrid density functional approximation M06-2X-D3(0)/TZP. In energy calculations, the overall accuracy is similar to the original implementation of r2SCAN-3c with Gaussian-type atomic orbitals (GTO), but basic properties, intermolecular noncovalent interactions, and barrier heights are better described with the STO approach, resulting in a lower weighted mean absolute deviation (WTMAD-2(STO) = 7.15 vs 7.50 kcal mol–1 with the original method) for the GMTKN55 database. The STO-optimized r2SCAN-3c outperforms many conventional hybrid/QZ approaches in most common applications at a fraction of their cost. The reliable, robust, and accurate r2SCAN-3c implementation with STOs is a promising alternative to the original implementation with GTOs and can be generally used for a broad field of quantum chemical problems.

Analysis of Information Entropies for He-Like Ions

The electronic structure, a special quality of an atomic or molecular system, is the major factor for further realization of physical results. However, in this paper, we present the topical issue of normalized electron density in position and momentum spaces, Shannon, Rényi, and Tsallis entropies to quantify the reach of electron delocalization for several atomic systems. Hartree-Fock-Roothaan (HFR) wave function is performed and considered for He-like ions using single-Zeta 𝛽-type orbital (βTOs) basis set to investigate the affecting of electron density and information entropies. The electron density maxima in position space are raised, and their positions move toward the nucleus as Z increases, in accordance with the increasing attractive force of the nucleus, and vice versa in momentum space. Shannon’s entropy has impacted the delocalization of the electron in different atomic systems. In the limit γ→1, both Rényi and Tsallis entropy results recover Shannon’s entropy value. Rényi and Tsallis entropies decrease by increasing γ. Indeed, the estimated results have been calculated via the Wolfram Mathematica program and have good agreement with the literature results. The obtained results may be a useful reference for future studies on theoretical information quantities. Doi: 10.28991/ESJ-2022-06-04-08 Full Text: PDF

Superhalogen Anions Supported by the Systems Comprising Alternately Aligned Boron and Nitrogen Central Atoms.

Using DFT/(B3LYP/wB97XD/B2PLYPD) and OVGF electronic structure methods with flexible atomic orbital basis sets, we examined the series of polynuclear superhalogen anions matching the (BF3(BN) n F4n+1)– formula (for n = 1-10,13,18-20) containing alternately aligned boron and nitrogen central atoms decorated with fluorine ligands. It was found that the equilibrium structures of these anions correspond to fully extended chains (with each B and N central atom surrounded by four substituents arranged in a tetrahedral manner) and thus mimic the globally stable fully extended (all-trans) conformations of higher n-alkanes. The vertical electron detachment energies of the (BF3(BN) n F4n+1)– anions were found to exceed 8 eV in all cases and gradually increase with the increasing number of n. The approximate limiting value of vertical electron binding energy that could be achieved for such polynuclear superhalogen anions was estimated as equal to ca. 10.7 eV.

Heavy-hole bilayer trions of transition metal dichalcogenides by analytical treatment to model He-isoelectronic ions upto dipole factor of Green’s function expansion of Coulomb interaction

Electronic structures of heavy-hole trions and He-isoelectronic ions show dependence on transitions among two-electron bound states constituted of hydrogenic orbitals for which Coulomb (exchange) interaction causes nontrivial secular divergence to Schrödinger equation (SE). Coulomb interaction between a pair of electrons triggers nonadiabatic transitions due conical intersections and larger vibrational amplitudes of nuclei. Therefore, existing state-of-art theories ubiquitously urge analytical integrals for multipoles of electrostatic Green’s function expansion. Born–Oppenheimer (BO) approximation separates the hamiltonian into electronic and nuclear coordinates at adiabatic limit. Employing associated Laguerre polynomial and Whittaker-M function basis sets of hydrogenic orbitals for the pair of electrons (electronic coordinate) furnishes analytical, terminable, simple and finitely summed integrals in terms of Lauricella functions. The exact integrals also remedy the difficulty arisen from different scaling factors of bound states for higher order perturbation calculations. Analytical perturbation calculations for monopole and dipole factors using singly and doubly excited states (|n2sn4s〉, |n2pn4p〉) with spherical and dumbbell symmetries show sufficient convergence of ground-state energy correction of He-isoelectronic series within 0.20–6.89% of reported results. Calculation of current-density with ground-state upto first order perturbation correction clearly shows that singly and doubly excited spherically symmetric states do not contribute to local current of He-isoelectronic series for monopole factor. Binding energies of heavy-hole trions of transition metal dichalcogenides (TMDCs) are found to be in good agreement with experimentally observed values.

Bonding character of intermediates in on-surface Ullmann reactions revealed with energy decomposition analysis.

On-surface synthesis has become a thriving topic in surface science. The Ullmann coupling reaction is the most applied synthetic route today, but the nature of the organometallic intermediate is still under discussion. We investigate the bonding nature of prototypical intermediate species (phenyl, naphthyl, anthracenyl, phenanthryl, and triphenylenyl) on the Cu(111) surface with a combination of plane wave and atomic orbital basis set methods using density functional theory calculations with periodic boundary conditions. The surface bonding is shown to be of covalent nature with a polarized shared-electron bond supported by π-back donation effects using energy decomposition analysis for extended systems (pEDA). The bond angle of the intermediates is determined by balancing dispersion attraction and Pauli repulsion between adsorbate and surface. The latter can be significantly reduced by adatoms on the surface. We furthermore investigate how to choose computational parameters for pEDA of organic adsorbates on metal surfaces efficiently and show that bonding interpretation requires consistent choice of the density functional.

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

All-Electron BSE@GW Method for K-Edge Core Electron Excitation Energies.

We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G0W0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.

Configuration-interaction calculations on the 3s23pn configuration of neutral phosphorus and two of its ions

We perform valence, core-core, and core-valence nonrelativistic configuration-interaction (CI) calculations on the states belonging to the $3{s}^{2}3{p}^{n}$ configuration with $n=2$, 3, and 4, for ${\mathrm{P}}^{+}(^{3}P,^{1}D, ^{1}S$), $\mathrm{P}{(}^{4}{S}^{\ensuremath{\circ}},^{2}D^{\ensuremath{\circ}}, ^{2}P^{\ensuremath{\circ}}$), and ${\mathrm{P}}^{\ensuremath{-}}(^{3}P,^{1}D, ^{1}S$) species, respectively. Excitation energies, ionization potential, and electron affinities related to these states were calculated using orbital basis sets up to $\ensuremath{\ell}=12$ and corrected with relativistic contributions. We also carry out relativistic CI calculations for the fine structure splitting of the sublevels ${}^{3}{P}_{0,1,2}$ and ${}^{3}{P}_{2,1,0}$ in ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{\ensuremath{-}}$, respectively, and both ${}^{2}{D}_{3/2,5/2}^{\ensuremath{\circ}}$ and ${}^{2}{P}_{1/2,3/2}^{\ensuremath{\circ}}$ in P, using orbital basis sets up to $\ensuremath{\ell}=3$. Systematic studies on the convergence of both nonrelativistic and relativistic CI calculations for each electronic state show the energy contributions corresponding to each CI excitation level. Our results for the excitation energies, ionization potential, and electron affinity of the ${(3{s}^{2}3{p}^{3})}^{4}{S}^{\ensuremath{\circ}}$ ground state, as well as fine structure splittings, are in very good agreement with the experiment and give reliability to the predicted electron affinities of the ${(3{s}^{2}3{p}^{3})}^{2}{D}^{\ensuremath{\circ}}$ and $^{2}P^{\ensuremath{\circ}}$ excited states of 1135(1) meV and 1040(1) meV, respectively.

Tuning the quasi-harmonic treatment of crystalline ionic liquids within the density functional theory.

Five ionic liquids are selected for benchmarking the performance of quasi-harmonic density functional theory (DFT) calculations of structural, phonon, and thermodynamic properties of their crystals. Data predicted by individual computational setups are sorted, establishing a distinct hierarchy among the first-principles approaches. PBE-D3 and B3LYP-D3 functionals are coupled with various plane wave and Gaussian-type orbital (GTO) basis sets. Propagation of the basis set superposition error and of the imperfections of both functionals into finite-temperature properties is discussed in detail. PBE-D3 together with a triple-zeta GTO basis set often yields the most accurate predictions of predicted molar volume and heat capacity with errors at 1% and 8%, respectively, representing the state-of-the-art for quasi-harmonic DFT calculations for crystalline ionic liquids. Fortuitous error cancellation between the basis-set superposition (overbinding) and PBE imperfection (overexpanding) strongly affects the overall accuracy, unlike the case of B3LYP/GTO calculations, impeding systematic convergence of the methodology towards higher accuracy.

Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: The case of water on graphitic carbon nitride.

A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride is reported employing an embedding approach for many-electron correlation methods. To this end, a plane-wave based implementation to obtain intrinsic atomic orbitals and Wannier functions for arbitrary localization potentials is presented. In our embedding scheme, the localized occupied orbitals allow for a separate treatment of short-range and long-range correlation contributions to the adsorption energy by a fragmentation of the simulation cell. In combination with unoccupied natural orbitals, the coupled cluster ansatz with single, double, and perturbative triple particle-hole excitation operators is used to capture the correlation in local fragments centered around the adsorption process. For the long-range correlation, a seamless embedding into the random phase approximation yields rapidly convergent adsorption energies with respect to the local fragment size. Convergence of computed binding energies with respect to the virtual orbital basis set is achieved employing a number of recently developed techniques. Moreover, we discuss fragment size convergence for a range of approximate many-electron perturbation theories. The obtained benchmark results are compared to a number of density functional calculations.

New Ab Initio Potential Energy Surfaces for NH3 Constructed from Explicitly Correlated Coupled-Cluster Methods.

Accurate calculation of ab initio potential energy surfaces (PESs) for the NH3 molecule is a difficult task because of the poor convergence of the standard CCSD(T) method with respect to the basis size. Currently, the best available NH3 PESs contain empirically refined parameters. In this paper, we show that CCSD(T)/aug-cc-pCV6Z calculations are not sufficient to properly describe the PES over a large range of nuclear configurations. However, the PES obtained by the extrapolation of the CCSD(T)/aug-cc-pCVXZ (X = T, Q, 5, and 6) energies to the complete basis set limit is closer to that based on the explicitly correlated CCSD(T)-F12a method using the cc-pCVQZ-F12 orbital basis set. All of the ab initio PESs constructed in this work include the following corrections: one electron relativistic effects, diagonal Born-Oppenheimer correction, and high-order electronic correlations (CCSDT, CCSDTQ, and CCSDTQP). Finally, the root-mean-square deviation between the predicted band centers obtained from our final "pure" ab initio PES and the experimental ones in the spectral region [0-7000] cm-1 is divided by two compared to the most accurate ab initio PES available in the literature.