Core Model Potential Research Articles

Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory

ContextAnalytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses.MethodAll calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.

Application of Model Core Potentials to Zn- and Mg-containing Metalloproteins in the Fragment Molecular Orbital Method

Application of Model Core Potentials to Zn- and Mg-containing Metalloproteins in the Fragment Molecular Orbital Method

On the equivalence of the hybrid particle-field and Gaussian core models.

Hybrid particle-field molecular dynamics is a molecular simulation strategy, wherein particles couple to a density field instead of through ordinary pair potentials. Traditionally considered a mean-field theory, a momentum and energy-conserving hybrid particle-field formalism has recently been introduced, which was demonstrated to approach the Gaussian Core model potential in the grid-converged limit. Here, we expand on and generalize the correspondence between the Hamiltonian hybrid particle-field method and particle-particle pair potentials. Using the spectral procedure suggested by Bore and Cascella, we establish compatibility to any local soft pair potential in the limit of infinitesimal grid spacing. Furthermore, we document how the mean-field regime often observed in hybrid particle-field simulations is due to the systems under consideration, and not an inherent property of the model. Considering the Gaussian filter form, in particular, we demonstrate the ability of the Hamiltonian hybrid particle-field model to recover all structural and dynamical properties of the Gaussian Core model, including solid phases, a first-order phase transition, and anomalous transport properties. We quantify the impact of the grid spacing on the correspondence, as well as the effect of the particle-field filtering length scale on the emergent particle-particle correlations.

Investigating the Heaviest Halogen: Lessons Learned from Modeling the Electronic Structure of Astatine’s Small Molecules

We present a systematic study of electron-correlation and relativistic effects in diatomic molecular species of the heaviest halogen astatine (At) within relativistic single- and multireference coupled-cluster approaches and relativistic density functional theory. We establish revised reference ab initio data for the ground states of At2, HAt, AtAu, and AtO+ using a highly accurate relativistic effective core potential model and in-house basis sets developed for accurate modeling of molecules with large spin-orbit effects. Spin-dependent relativistic effects on chemical bonding in the ground state are comparable to the binding energy or even exceed it in At2. Electron-correlation effects near the equilibrium internuclear separation are mostly dynamical and can be adequately captured using single-reference CCSD(T). However, bond elongation in At2 and, especially, AtO+ results in rapid manifestation of its multireference character. While useful for evaluating the spin-orbit effects on the ground-state bonding and properties, the two-component density functional theory lacks predictive power, especially in combination with popular empirically adjusted exchange-correlation functionals. This drawback supports the necessity to develop new functionals for reliable quantum-chemical models of heavy-element compounds with strong relativistic effects.

Structure, reactions, and electronic spectra of the rare gas cyanohydrides and isocyanohydrides, HRgCN and HRgNC (Rg = Xe or Rn)

The low-energy electronic excitations of HRgCN and HRgNC (Rg = Xe, Rn) were computed at the TDDFT level of theory, both in the gas phase and in xenon cluster. It was found that the most prominent peak in the spectra was due to the highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) transition (∼6 eV for HRgCN and ∼4.5 eV for HRgNC). Cluster confinement brought about bathochromic shifts in the spectra and better agreement with experiment for HXeCN. The effects of spin–orbit coupling (SOC) in the heavier Rn systems were investigated: for HRnCN, SOC red-shifted the HOMO–LUMO peak, while it blue-shifted the HOMO–LUMO peak for HRnNC. Geometry optimizations were carried out for the HRgCN and HRgNC systems to locate minima and transition states for dissociation and isomerization. Effects of isotopic substitution on reaction rates were predicted. A new model core potentials basis set was introduced and effectiveness of several pseudopotential basis sets was studied.

Tunneling matrix element and tunneling pathways of protein electron transfer calculated with a fragment molecular orbital method

Practical ways to calculate the tunneling matrix elements and analyze the tunneling pathways for protein electron-transfer (ET) reactions with a fragment molecular orbital (FMO) method are presented. The straightforward use of minimal basis sets only for the atoms involved in the covalent bond detachment in FMO can properly describe the ETs through the protein main-chains with the cost-effective two-body corrections (FMO2) without losing the quality of double-zeta basis sets. The current FMO codes have been interfaced with density functional theory, polarizable continuum model, and model core potentials, with which the FMO-based protein ET calculations can consider the effects of electron correlation, solvation, and transition-metal redox centers. The reasonable performance of the FMO-based ET calculations is demonstrated for three different sets of protein-ET model molecules: (1) hole transfer between two tryptophans covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, (2) ET between two plastoquinones covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, and (3) hole transfer between ruthenium (Ru) and copper (Cu) complexes covalently bridged by a stretch of a polyglycine linker as a model for Ru-modified derivatives of azurin.

Collective dynamics of Zr-based bulk metallic glasses

The collective dynamics for the longitudinal as well as the transverse modes of the phonon eigenfrequencies are carried out for three Zr-based bulk metallic glasses (BMGs) in the present paper by employing pseudopotential theory. The theoretical phonon models proposed by Hubbard-Beeby (HB), Takeno-Goda (TG) and Bhatia-Singh (BS) are used to generate the phonon dispersion curves (PDC). The elastic and thermodynamic properties have also been investigated for the said BMGs by using the elastic limit of the phonon dispersion curves. The screening impact was also observed by using five different forms of local field functions due to Hartree (H), Taylor (T), Ichimaru and Utsumi (IU), Faridet al. (F) and Sarkaret al. (S) for the aforesaid properties. The derived results are seen to be in qualitative agreement with the available experimental and theoretically calculated data, as they confirm the applicability of Shaw's constant core model potential and self-consistent phonon theory for such studies.

Thermodynamic properties and anomalous behavior of double-Gaussian core model potential fluids.

The structural, thermodynamic, and vapor-liquid equilibria properties of the double-Gaussian core model (DGM) potential are studied via molecular simulation. Results are presented for the pressure (p), potential energy (U), isochoric and isobaric heat capacities (C_{V,p}), isothermal compressibility (β_{T}), isochoric thermal pressure coefficient (γ_{V}), thermal expansion coefficient (α_{p}), speed of sound (ω_{0}), and the Joule-Thomson coefficient (μ_{JT}), which are compared with simulations for the Gaussian core model (GCM) potential. A feature of the simulations is that both the GCM and DGM potentials reproduce many of the anomalous properties of water, such as a maximum density, γ_{V}<0, maximum values for both α_{p} and β_{T}, and minimum values in both C_{p} and ω_{0}. The presence of attractive interaction enhances the anomalies and also yields some additional features such as a more structured vapor phase and Joule-Thomson inversion.

Spin-Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods.

The spin-orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ nd] q ( q = 1-4 and 6-9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin-orbit couplings (SOC) using one-electron Breit-Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations-relativistic elimination of small components (RESC), third-order Douglas-Kroll-Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction-were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ nd]5, the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d] q configuration ( q = 2-4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d] q configuration ( q = 6-8), the energy lowering of all 4F7/2, 5D1, and 5D3 states due to the SOC effects is smaller than those of the other SM states. This difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

Computing UV–vis spectra of 1-bromo-1-propene: a comparison of model core potential and all-electron basis sets

Vacuum ultraviolet (VUV) spectroscopy can be used to identify different isomers in complicated mixtures of many molecules. In this work, calculated VUV spectra are compared with spectra of experimental mixtures to benchmark appropriate computational methods. Because the benchmark molecule, 1-bromo-1-propene, contains a heavy atom, both all-electron and model core potential basis sets were investigated. Time-dependent density functional theory (TD-DFT) can accurately compute electronic excited states at low-energy excitations and was cross-checked at higher energies against results from the symmetry adapted cluster–configuration interaction (SAC–CI) method. TD-DFT was determined to be satisfactory at low energies; however, excitation energies can deviate by 0.5 eV at high energies. TD-DFT with both all-electron and model core potential basis sets produced satisfactory excitation energies for the lower excited states. This method is also satisfactory at predicting spectra produced experimentally, including a mixture of isomers (cis- and trans-1-bromo-1-propene), with the exception of underestimating oscillator strength.

Structures and properties of Np(NO3)nq (n=16, q=-2+3) coordination compound

In the process of nuclear waste disposal, the valuable uranium and plutonium are recycled and separated by dissolving the spent fuel in nitric acid. However, transuranic Np greatly influences the process of separation and recovery. Therefore, it is vital to study the structure and properties of nitrate, which is combined with neptunium ions and nitric acid. Furthermore, there are few researches about nitrate formed by tetravalent neptunium ions. So in this article, by using B3LYP hybrid method of density functional theory, the Gaussian 03 program is used to optimize the geometric construction of the coordination compounds Np(NO3)nq (n=1-6, q=-2-+3) formed by the tetravalent neptunium ions (Np4+) and nitrate ion (NO3-). Under the relativistic effective core potential model, the structure parameters and properties are reported. It is found that NO3- coordinates to Np4+ as a bidentate ligand, and the NpN and NpO bonds are the shortest in Np(NO3)22+, while the binding energy of the Np(NO3)4 is the largest. The infrared spectra of Np(NO3)4 are calculated in the gas and liquid phase. Comparing with the available experimental data, the reliability of the calculation results in this work is confirmed.

Fragment molecular orbital (FMO) calculations on DNA by a scaled third-order Møller-Plesset perturbation (MP2.5) scheme

A series of fragment molecular orbital (FMO) calculations on DNA models was performed to assess the reliability of the scaled third-order Møller-Plesset perturbation method (MP2.5) (Pitoňák et al., Chem. Phys. Chem., 10 (2009) 282) for the incorporation of higher-order electron correlation. The Watson-Crick H-bonding (horizontal interaction) and the 1,2-stacking (vertical interaction) of four combinations of two base pairs (AT:AT, AT:TA, AT:GC, and CG:GC) were calculated at the levels of MP2, MP3 (nonscaled), MP2.5, and coupled cluster singles and doubles with perturbative triples (CCSD(T)). The comparison showed sufficient agreement between MP2.5 and the reference CCSD(T), and indicated that MP2.5 is an inexpensive but precise alternative to costly CCSD(T). The influence of basis sets including the model core potential (MCP) was also examined for the two base pairs. The Watson-Crick H-bonding interaction energies were fairly uninfluenced by these methods. In contrast, the values of the stacking interactions among bases quantitatively varied depending on the calculation options. As a cost-effective procedure, the FMO-MP2.5/MCP calculations were applied to a couple of realistic DNA models explicitly solvated by water: a 12-base-pair model and a 10-base-pair model cross-linked with cis-platin (Pt(NH3)2). The H-bonding and stacking interactions in them were discussed from a biochemical viewpoint.

Superconducting State Parameters of BMG Superconductors

We present the theoretical investigations of the superconducting state parameters (SSPs) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ∗, transition temperature TC, isotope effect exponent α and effective interaction strength N0V of some bulk metallic glasses (BMG) superconductors by employing the well-known empty core model potential of Ashcroft for the first time. Five well-known screening functions are used to study the screening influence on the aforesaid properties. Also, the present results confirm the superconducting phase in the BMG superconductors. A strong dependency of the SSPs of the BMG superconductors on the valence Z is found.

Soft repulsive interactions, particle rearrangements and size selection in the self-assembly of nanoparticles at liquid interfaces.

In the adsorption of nanoparticles at liquid interfaces, soft and short ranged repulsive effective interactions between the nanoparticles at the interface may eventually induce crowding, slow dynamics and jamming at high surface coverage. These phenomena can interfere during the adsorption process, significantly slowing down its kinetics. Here, by means of numerical simulations, we find that modifying the effective interactions, which can be achieved for example by grafting differently functionalized polymer shells on the bare nanoparticles, may qualitatively change such interplay. In particular our results suggest that, in the presence of ultrasoft particle interactions such as the ones described by a Gaussian Core Model potential, a small size polydispersity can be sufficient to decouple the adsorption kinetics from the slow dynamics that develops at the interface, due to a qualitative change from an irreversible adsorption controlled by particle rearrangements at the interface to one dominated by size selection mechanisms. These findings may be useful to achieve higher surface coverages and faster adsorption kinetics.

Reliability of Density Functional and Perturbation Theories for Calculating Core-Ionization Spectra of Free Radicals

The C 1s, N 1s, and O 1s ionization energies were calculated for the three stable nitroxide free radicals, viz., tempo and its two analogues, and compared to their most recent high-resolution core photoelectron spectra. We compare the performance of unrestricted and restricted open shell based ΔHF, ΔMP2, and ΔB3LYP methods. A mixed basis set is employed in all cases, which consists of the core-valence correlation-consistent triple-ζ basis set (cc-pCVTZ or cc-pwCVTZ) on the atom whose core-electron binding energy is calculated, model core potentials on the remaining first row atoms, and the cc-pVDZ basis set on the hydrogen atoms. The best overall performance for the three free radicals is offered by the restricted open shell based ΔB3LYP method. Surprisingly, both the restricted open and unrestricted second-order perturbation theories perform relatively poorly and typically do not warrant additional computational effort over the reference ΔHF methods. This is particularly true of the ΔZAPT method, which exhibits a number of grave failures that render it unsuitable for calculating the core-ionization spectra.

Direct molecular simulation of the Grüneisen parameter and density scaling exponent in fluid systems

Direct molecular-simulation results of the thermodynamic Grüneisen parameter, γG, and the density scaling exponent, γ, are reported for the Lennard-Jones and the Gaussian core model potential in extended fluid-phase regions, and are compared with results calculated from equations of state. The direct molecular simulation method is based on the calculation of so-called phase-space functions and allows, in principle, the investigation of any thermodynamic property without any restrictive approximation. The Grüneisen parameter and the density scaling exponent are key quantities in the theory of strongly correlating liquids. Therefore, we paid special attention on the relationship between γG and γ for the Lennard-Jones system as a strongly correlating fluid. Because the Grüneisen parameter can be related to experimentally accessible thermodynamic properties, we analysed in detail the decomposition of γG into the thermal expansion coefficient, the isothermal compressibility, the isochoric heat capacity, and the thermal pressure coefficient. Moreover, we show that a predicted effective density scaling exponent of γ≈6 for the Lennard-Jones fluid can be found close to the triple point of the system. The investigation of γG for the Gaussian core model, which is not a strongly correlating fluid, revealed anomalous behaviour at higher densities with negative values of γG.

A Quantum Chemical Study on Hydration of Ra (II): Comparison with the Other Hydrated Divalent Alkaline Earth Metal Ions

The thermodynamic properties and electronic structure of hydrated Ra2+ have been investigated using ab initio quantum chemical calculations that apply the relativistic model core potential method and compared with those of the other hydrated divalent alkaline earth metal ions (Mg2+, Ca2+, Sr2+, and Ba2+). The solvation free energies calculated for [Ra (H2O)n]2+ (n = 1–9) in a continuum dielectric media (semi-continuum model) showed that the hydration number of Ra2+ is in the range of 7–9. Natural population analysis (NPA), natural bond orbital (NBO) analysis and localized molecular orbital energy decomposition analysis (LMO-EDA) showed that the dominant interaction between hydrated Ra2+ ions and solvent water molecules is electrostatic interaction to form coordination bonds which have a strong ionic bond character. On the other hand, not only electrostatic interaction but also covalent interaction accompanying charge-transfer from solvent water molecules to the central ion are important in the interaction between hydrated Mg2+ or Ca2+ (lighter divalent alkaline earth metal ions) and solvent water molecules.

Basis set effects in simple compounds of heavy rare gases

Rare-gas hydrides of the type HRgX (Rg = Xe or Rn and X = F, Cl, Br, or I) have been studied using Møller–Plesset and density functional theory methods. Six model core potentials and their associated basis sets were used, with relativistic effects included implicitly. The effects of polarization, correlating, and diffuse basis functions were investigated. Molecular geometries of the metastable hydrides and transition states along the decomposition pathway were computed together with corresponding energies of formation and decomposition. The results of quantum theory of atoms in molecules analysis further elucidate the interactions between atoms in HRgX species and confirm the results of analyses obtained from the natural bond orbitals approach.

Superconducting State Parameters Of Binary Metallic Glasses

Ashcroft’s empty core (EMC) model potential is used to study the superconducting state parameters (SSPs) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature TC, isotope effect exponent αand effective interaction strength NOV of some binary metallic glasses based on the superconducting (S), conditional superconducting (S’) and non-superconducting (NS) elements of the periodic table. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used for the first time with EMC potential in the present investigation to study the screening influence on the aforesaid properties. The TC obtained from the H-local field correction function are in excellent agreement with available theoretical or experimental data. In the present computation, the use of the pseudo-alloy-atom model (PAA) was proposed and found successful. Present work results are in qualitative agreement with such earlier reported experimental values which confirm the superconducting phase in all metallic glasses. A strong dependency of the SSPs of the metallic glasses on the valence ‘Z’ is identified.

Calculation of Parameter of Ashcroft’s Potential Using Vacancy Formation Energy for some BCC Metals: Li, Na, K, Rb, Cs, Ba

The graphs for variation of vacancy formation energy ( ) with rc of Ashcroft's empty core model potential for different exchange and correlation functions are shown for six bcc metals, viz. Li, Na, K, Rb, Cs and Ba. Fitted value of for Li, Na, K, Rb, Cs and Ba are respectively 1.343, 1.694, 2.205, 2.384, 2.962 and 2.337 atomic unit (AU).