Effective Core Potential Method Research Articles

Fermionic neural network with effective core potential

Deep learning techniques have opened a new venue for electronic structure theory in recent years. In contrast to traditional methods, deep neural networks provide much more expressive and flexible wave function Ans\"atze, resulting in better accuracy and timescale behavior. In order to study larger systems while retaining sufficient accuracy, we integrate a powerful neural-network-based model (FermiNet) with the effective core potential method, which helps to reduce the complexity of the problem by replacing inner core electrons with additional semilocal potential terms in the Hamiltonian. In this work, we calculate the ground-state energy of $3d$ transition metal atoms and their monoxides, which is quite challenging for the original FermiNet work, and the results are consistent with both experimental data and other state-of-the-art computational methods. Our work is an important step for a broader application of deep learning in the electronic structure calculation of molecules and materials.

Density functionalized [RuII(NO)(Salen)(Cl)] complex: Computational photodynamics and in vitro anticancer facets

Photodynamic therapy (PDT) is a treatment that uses photosensitizing agents to kill cancer cells. Scientific community has been eager for decades to design an efficient PDT drug. Under such purview, the current report deals with the computational photodynamic behavior of ruthenium(II) nitrosyl complex containing N, N'-salicyldehyde-ethylenediimine (SalenH2), the synthesis and X-ray crystallography of which is already known [Ref. 38,39]. Gaussian 09W software package was employed to carry out the density functional (DFT) studies. DFT calculations with Becke-3–Lee–Yang–Parr (B3LYP)/Los Alamos National Laboratory 2 Double Z (LanL2DZ) specified for Ru atom and B3LYP/6-31G(d,p) combination for all other atoms were used using effective core potential method. Both, the ground and excited states of the complex were evolved. Some known photosensitizers were compared with the target complex. Pthalocyanine and porphyrin derivatives were the compounds selected for the respective comparative study. It is suggested that effective photoactivity was found due to the presence of ruthenium core in the model complex. In addition to the evaluation of theoretical aspects in vitro anticancer aspects against COLO-205 human cancer cells have also been carried out with regard to the complex. More emphasis was laid to extrapolate DFT to depict the chemical power of the target compound to release nitric oxide. A promising visible light triggered nitric oxide releasing power of the compound has been inferred. In vitro antiproliferative studies of [RuCl3(PPh3)3] and [Ru(NO)(Salen)(Cl)] have revealed the model complex as an excellent anticancer agent. From IC50 values of 40.031mg/mL in former and of 9.74mg/mL in latter, it is established that latter bears more anticancer potentiality. From overall study the DFT based structural elucidation and the efficiency of NO, Ru and Salen co-ligands has shown promising drug delivery property and a good candidacy for both chemotherapy as well as light therapy.

Generalized relativistic effective core potential calculations of the adiabatic potential curve and spectroscopic constants for the ground electronic state of the Ca2molecule

The potential curve, dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ground state of the Ca2 molecule are calculated with the help of the generalized relativistic effective core potential method, which allows one to exclude the inner core electrons from the calculations and to take the relativistic effects into account effectively. Extensive generalized correlation basis sets were constructed and used. The scalar relativistic coupled cluster method with corrections for high-order cluster amplitudes is used for the correlation treatment. The results are analyzed and compared with the experimental data and corresponding all-electron results. © 2013 Wiley Periodicals, Inc.

Two-Component Spin-orbit Effective Core Potential Calculations with an All-electron Relativistic Program DIRAC

E-mail: yslee@kaist.eduReceived November 15, 2011, Accepted December 13, 2011We have implemented two-component spin-orbit relativistic effective core potential (SOREP) methods in anall-electron relativistic program DIRAC. This extends the capacity of the two-component SOREP method tomany ground and excited state calculations in a single program. As the test cases, geometries and energies ofthe small halogen molecules were studied. Several two-component methods are compared by using spin-orbitand scalar relativistic effective core potentials. For the I

Precision calculation of the low-lying excited states of the Rf atom

Precision calculations of the ground and low-lying excited electronic states of the Rf atom (Z = 104) were performed. The relativistic effects were taken into account with the Dirac-Coulomb-Breit Hamiltonian. The finite nucleus size was taken into account in the Fermi model (A = 267). The correlation effects were described by the combined scheme that we suggested previously, which proved to be efficient: The relativistic coupled clusters method with one- and two-particle cluster amplitudes in the Fock space was used for describing the correlations of 44 outer electrons of the Rf atoms in a fairly large atomic basis set, and for the four valence electrons occupying the 7s, 7p, and 6d states, the contributions from three- and four-particle cluster amplitudes were taken into account using the complete configuration interaction method, but in a relatively small basis set. The relativistic configuration and term for the ground state of the Rf atom were refined, and the energies of its excitation to low-lying states were calculated. The accuracy of the calculation by the generalized relativistic effective core potential method was evaluated by comparing the results with those obtained similarly using the Dirac-Coulomb-Breit Hamiltonian.

A Quasirelativistic Two-component Density Functional and Hartree-Fock Program

Abstract This work describes the implementation of an efficient two-component quasirelativistic density functional and Hartree-Fock program. The fact that the basis functions are real can be exploited if a special internal representation of operators and density matrices is used. This also leads to a considerable reduction of the effort in the closed shell case. While in most applications to open shell molecules, the noncollinear approach to define a relativistic spin density is preferable, the collinear approach finds its application in the calculation of magnetic anisotropy energies. Linear algebra steps in the SCF procedure have a higher relative weight compared to the nonrelativistic case, therefore some care was necessary to make them fast when parallelizing the code. The quasirelativistic Hamiltonians that have been implemented are the ´zeroth-order regular approximation´ (ZORA) Hamiltonian, the Douglas-Kroll-Hess Hamiltonian up to the sixth order, together with an accurate approximation to treat the picture change effect of the electron interaction, and effective core potential (ECP) matrix elements. Geometry gradients are available for the ZORA and ECP methods.

Linear response formalism for the Douglas–Kroll–Hess approach to the Dirac–Kohn–Sham problem: First‐ and second‐order nuclear displacement derivatives of the energy

AbstractStarting from a matrix representation of the modified Dirac equation, we offer an alternative approach to the Douglas–Kroll–Hess (DKH) protocol, specifically for the popular decoupling of electronic and positronic degrees of freedom to second‐order in the potential. Then we use that approach for a convenient analysis of response properties. We discuss details of the linear and quadratic response of the DKH Hamiltonian to a geometric distortion encountered in calculations of first‐ and second‐order derivatives of the energy. We present an implementation of analytic force constants in a quasi‐relativistic (scalar) model constructed by the commonly used DKH transformation of second order in the nuclear potential only. We demonstrate the performance of the method by a comparison to the effective core potential method, using two isomers of the cluster Ir4 and aqua complexes of the uranyl dication, UO(H2O)n (n = 3,…6) as examples. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Two-component relativistic density-functional calculations of the dimers of the halogens from bromine through element 117 using effective core potential and all-electron methods

A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations--for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results--demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.

Accounting for correlations with core electrons by means of the generalized relativistic effective core potentials: Atoms Hg and Pb and their compounds

A way to account for correlations between the chemically active (valence) and innermore (core) electrons in the framework of the generalized relativistic effective core potential (GRECP) method is suggested. The "correlated" GRECP's (CGRECP's) are generated for the Hg and Pb atoms. Only correlations for the external 12 and 4 electrons of them, correspondingly, should be treated explicitly in the subsequent calculations with these CGRECP's whereas the innermore electrons are excluded from the calculations. Results of atomic calculations with the correlated and earlier GRECP versions are compared with the corresponding all-electron Dirac-Coulomb values. Calculations with the above GRECP's and CGRECP's are also carried out for the lowest-lying states of the HgH molecule and its cation and for the ground state of the PbO molecule, as compared to earlier calculations and experimental data. The accuracy for the vibrational frequencies is increased up to an order of magnitude and the errors for the bond lengths (rotational constants) are decreased in about two times when the correlated GRECP's are applied instead of earlier GRECP versions employing the same innercore-outercore-valence partitioning.

New Effective Core Method (Effective Core Potential and Valence Basis Set) for Al Clusters and Nanoparticles and Heteronuclear Al-Containing Molecules.

In previous work we have shown that the PBE0 hybrid density functional method with the MG3 all-electron basis set is an accurate method for calculating the atomization energies of small aluminum clusters (Al2-Al7). However, the MG3 basis set is very expensive for molecules much larger than Al13; therefore, we have developed a new effective core potential (ECP) method for aluminum to reduce the cost of obtaining accurate results for nanoparticles. Our method involves a hybrid of the Stuttgart semiempirical effective core potential and the compact effective potential (CEP) potential, and it uses a newly optimized polarized valence triple-ζ basis set. The combination of the new ECP and the new polarized valence triple-ζ basis set for Al is called the Minnesota effective core (MEC) method for Al. The method was optimized with a training set of atomization energies and geometries for AlH, AlC, AlO, AlCCH, Al2H, Al2C, Al2O, and Al3 and atomization energies of three Al13 structures, and we tested it on six test sets composed of 20 atomization energies for systems as large as Al13. We also present an improved all-electron polarized triple split basis set for oxygen, called 6-311+G(d*,p). For the test sets, the mean unsigned error (MUE) of the new method with respect to PBE0/MG3 is 0.06 eV for atomization energies and 0.007 Å for bond lengths, which constitutes a very significant improvement over the quality of the results that can be obtained with effective core potentials and valence basis sets in the literature (of the eight methods in the literature, the best previous method had average errors of 0.63 eV and 0.036 Å). We have also tested the MEC method with a variety of hybrid density functional theory, hybrid meta density functional theory, and pure GGA and meta GGA functionals and found that the average MUE, relative to each functional with all-electron basis sets, is 0.04 eV for atomization energies and 0.009 Å for bond lengths for the new effective core method and 0.16-0.20 eV and 0.013-0.033 Å for effective core potential and valence basis sets in the literature.

GRECP/MRD‐CI calculations on the Hg atom and HgH molecule

AbstractMultireference single‐ and double‐excitation configuration interaction (MRD‐CI) calculations of transition energies for the Hg atom and spectroscopic constants for the HgH molecule are carried out with the generalized relativistic effective core potential (GRECP) method. A new selection criterium for the reference configurations is discussed. The calculated spectroscopic constants are compared with experimental data and results of calculations of other groups. Improvement of accuracy is mainly observed for bond lengths from the GRECP/MRD‐CI calculations (without applying the T = 0 correction) with respect to the results of other groups. Analysis of the quality of the approximations employed is carried out. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Spin−Orbit Splittings in the Third-Row Transition Elements: Comparison of Effective Nuclear Charge and Full Breit−Pauli Calculations

The spin−orbit splittings of low-lying states in third-row transition elements were calculated using both an effective core potential (ECP) method within the one-electron (Zeff) approximation and all-electron (AE) methods using three different approaches. The wave functions were obtained using the multiconfiguration self consistent field (MCSCF) method followed by second-order configuration interaction (SOCI) calculations. All calculated results, except for the ones on atomic Ir, are in reasonable agreement with the corresponding experimental observations. The unsatisfactory results for atomic Ir are attributed to the poor theoretical prediction of the adiabatic energy gap between the lowest two 4F states. This gap has an incorrect sign in AE calculations without scalar relativistic corrections, but the gap can be reproduced qualitatively if these corrections are added using the newly developed RESC (relativistic elimination of small components) scheme. As a result, the AE calculations with the RESC appro...

Calculation of the Structures, Stabilities, and Properties of Mercury Sulfide Species in Aqueous Solution

Quantum mechanical methods are used to determine the structures, stabilities, and properties of a number of different mercury(II) sulfide, bisulfide, and hydroxide species in aqueous solution. Relativistic effective core potential bases and methods ranging in rigor from Hartree−Fock to quadratic configuration interaction with single and double substitutions are used for the gas-phase calculations while explicit solvation with small numbers of water molecules, SCRF, and IPCM methods are used to describe hydration. We find that the species with molecular composition HgS is unstable in water solution and that it probably exists as Hg(SH)(OH), hydrated strongly by four waters. Its isomer HgS(H2O) is unstable, spontaneously rearranging to Hg(SH)(OH). By comparing the dissociation energetics of Hg(SH)(OH) with that of other compounds containing a −SH group, we have determined that Hg(SH)(OH) has a pKa of 7 or larger, so that it is not significantly deprotonated near neutral pH. The HgS and HgS(H2O) species are ...

Relativistic pseudopotentional incorporating core/valence polarization and nonlocal effects.

A relativistic pseudopotentional (RPP) for use in ab initio molecular electronic structure calculations is derived in the context of the relativistic effective core potential (REP) method of Lee et al. The resulting atom-specific RPP has salient features of the REP imbedded within it while retaining the form of a functional that is dynamically defined at runtime when used in calculations on molecules. The RPP is determined from Dirac-Fock wave functions for the isolated atom. Outer core two-electron interactions are incorporated into the RPP by means of variable coefficients that are defined in the context of the final molecular wave function. This form permits polarization of the outer core shells analogous to that occurring in all-electron molecular Hartree-Fock calculations while retaining these shells as part of the atomic pseudopotentional. Use of the RPP in post-Hartree-Fock molecular calculations permits the incorporation of core/valence correlation effects.

Formal analysis of effective core potential methods.

Effective core potentials are analyzed from the standpoint of the underlying frozen core approximation. The content of the pseudoorbital, the content of the potential, and the properties of both are elaborated, showing the points at which they differ from the frozen core approximation and where possible deficiencies might lie.

On the Transition Metal Complexation (Fischer-Type) of Phosphanylcarbenes

The formation of a Fischer-type transition metal complex with a W(CO)5 fragment is evaluated for the phosphanylcarbenes, Arduengo-type carbenes, and Bertrand-type carbenes by means of quantum chemical investigations at a density functional level with effective core potential methods. Accordingly, the stabilities of the complexes depend strongly on the substitution pattern of the carbenic unit. Amino-substituted carbenes as well as the Arduengo-type carbene form stable transition metal complexes. The stabilities of the complexes decrease for the phosphanylcarbenes and are at a minimum for the hitherto unknown transition metal complexes of the push−pull-type carbene of Bertrand. The matter is analyzed in terms of distortion energies required to bring the carbene units into the geometrical standard state for complexation with the transition metal fragment. The arguments evaluated for the phosphanylcarbenes should hold equally well for other carbenes substituted with electropositive ligands. For the mono-phos...

Molecular Design for Organic Nonlinear Optics: Polarizability and Hyperpolarizabilities of Furan Homologues Investigated by Ab Initio Molecular Orbital Method

Static polarizabilities and hyperpolarizabilities have been calculated for the furan homologues including furan (C4H4O), thiophene (C4H4S), selenophene (C4H4Se), and tellurophene (C4H4Te), at the Hartree−Fock and various correlation levels by ab initio molecular orbital methods. The influence of substitution with heavy atoms on the molecular properties of the homologues was examined theoretically. In the calculations for molecules with Se and Te atoms, the contribution of core electrons in the atoms was estimated using effective core potential (ECP) methods. With the calculation for the thiophene molecule, effectiveness of the use of the ECP method was examined, and the ECP method was found to give the (hyper)polarizability values similar to those obtained considering all electrons for the molecule. The calculated results show that substitution of the heteroatom with heavy atoms systematically increases the individual components of the polarizability, α, and second hyperpolarizability, γ. On the other hand, this does not give systematic variations on the first hyperpolarizability, β. The variation of these values depending on the homologues was examined in terms of the perturbation expansion formula and was explained by the energy levels of the electronic excited states in the valence states. The second hyperpolarizability values calculated, including electron correlation effect, are well correlated with the observed electronic components of nonlinear optical susceptibilities, χ(3), obtained using optical Kerr effect experiments, which have been done in our laboratory. However, some discrepancy is observed between the theoretical and the experimental values for the homologues with heavier heteroatoms. Possible causes for the discrepancy are discussed in detail.

Geometry, Vibrational Frequencies, and Ionization Energies of BeX2 (X = F, Cl, Br, and I)

The equilibrium geometries and harmonic vibrational frequencies of BeF2, BeCl2, BeBr2, and BeI2 are calculated. For the lighter two molecules, only all-electron methods were used, whereas for the heavier two, all-electron and effective core potential (ECP) methods were used. MP2, QCISD, and B3LYP calculations were employed, and it was found that the combination of ECPs (with a suitable valence basis set) with the B3LYP density functional method is a relatively inexpensive means of obtaining reliable information on these species. All four molecules were found to be linear, in agreement with simple molecular orbital ideas. The lowest electronic states are calculated using the configuration interaction with single excitations approach. Finally the adiabatic and vertical ionization energies of the BeX2 species are calculated. For BeF2 and BeCl2, the first vertical ionization energy (VIE) was calculated at the CASSCF+MRCI level, and the lowest four VIEs were calculated at the CCSD(T) level using large basis sets: for BeCl2 comparison with the photoelectron spectrum is presented. For BeBr2 and BeI2, the lowest VIEs were calculated using a density functional approach, including spin−orbit effects. During the calculation of the adiabatic ionization energies, the equilibrium geometries of the BeX2+ species were calculated; it was found that BeF2+ and BeCl2+ had bent equilibrium geometries (corresponding to the X̃2B2 Renner−Teller component of the lowest 2Πg state, in a linear configuration), whereas BeBr2+ and BeI2+ have linear (X2Πg) equilibrium geometries. The calculated adiabatic ionization energies for BeF2 and BeCl2 are significantly higher than previously accepted values.

Structures and Stabilities for Halides and Oxides of Transactinide Elements Rf, Db, and Sg Calculated by Relativistic Effective Core Potential Methods

The ground states of the halides and oxides containing transactinide elements Rf (element 104), Db (element 105), and Sg (element 106) were calculated at the HF, MP2, QCISD, CCSD, and CCSD(T) levels of theory using one- and two-component relativistic effective core potentials. Spin−orbit effects are rather small for geometries, harmonic vibrational frequencies, charge distributions, overlap populations, and dipole moments, but considerable for atomization energies. Electron correlations are necessary for any accurate determination of the molecular properties, in particular for the evaluation of atomization energies. The bond lengths of Sg compounds are consistently longer than those of the corresponding W compounds by 0.04−0.06 Å. The atomization energies for Sg compounds are slightly smaller than those for the corresponding W compounds due to spin−orbit and correlation effects. The differences tend to increase with the number of oxygen atoms in the compounds. Metal charges and dipole moments are larger for the Sg compounds than for the W compounds, implying that Sg is more ionic than W. The D3h structures are calculated to be more stable by about 2 kcal/mol than the C4v ones for TaCl5, TaBr5, DbCl5, and DbBr5.

Generalized relativistic effective core potential: Theoretical grounds

The generalized relativistic effective core potential (GRECP) method is analyzed from theoretical and computational points of view. The Hamiltonian in the frozen-core approximation is compared with the Hamiltonian containing the GRECP operator. It is demonstrated that the GRECP operator can be derived from rather natural physical grounds and the procedure of the GRECP generation can be justified theoretically. The accuracy of the RECP approximations in the simulation of the interactions and densities in the valence and outer-core regions is analyzed. The reliability of the simulation of the interaction with the inner-core electrons removed from the calculations with the GRECP is also studied. The importance of additional nonlocal terms both with the potentials for the outer-core pseudospinors and with the potentials depending on the occupation numbers of the outermost core shells in the expression for the GRECP operator is demonstrated in calculations on the Ag, Ba, Hg, Tl, and U atoms. The difference between the outer core and valence potentials was investigated. It is shown that in the valence region the two-component pseudospinors coincide with the large components of four-component spinors in calculations for the same configuration states with a very high accuracy. Problems of Gaussian approximation caused by rather singular shapes of the potentials are considered. To attain a required high accuracy of approximation of the numerical potentials by Gaussians, serious additional efforts were undertaken. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 359–401, 1999