Ground-state Total Energy Research Articles

Relativistic effects for the reaction Sg + 6 CO → Sg(CO)6: Prediction of the mean bond energy, atomization energy, and existence of the first organometallic transactinide superheavy hexacarbonyl Sg(CO)6.

Our ab initio all-electron fully relativistic Dirac-Fock (DF) and nonrelativistic (NR) Hartree-Fock calculations predict the DF relativistic and NR energies for the reaction: Sg + 6 CO → Sg(CO)6 as -7.39 and -6.96 eV, respectively, i.e., our calculated ground state total DF relativistic and NR energies for the reaction product Sg(CO)6 are lower by 7.39 and 6.96 eV than the total DF and NR ground state energies of the reactants, viz., one Sg atom plus six CO molecules, respectively. Our calculated DF relativistic and NR atomization energies (Ae) are 65.23 and 64.82 eV, respectively, and so the contribution of relativistic effects to the Ae of ∼0.40 eV is marginal. The Sg-C and C-O optimized bond distances for the octahedral geometry as calculated in our DF (NR) calculations are 2.151 (2.318 Å) and 1.119 (1.114 Å), respectively. The BSSE correction calculated using the DIRAC code ∼14 kcal/mol. The relativistic DF and NR mean energies predicted by us are 118.8 and 111.9 kJ/mol, respectively, and the contribution of ∼7 kJ/mol due to relativistic effects to the mean energy of Sg(CO)6 is negligible. Ours are the first calculations of the relativistic effects for the atomization energy, mean bond energy, and energy of the reaction for possible formation of Sg(CO)6, and both our relativistic DF and the NR treatments clearly predict for the first time the existence of hexacarbonyl of the transactinide superheavy element seaborgium Sg. In conclusion, relativistic effects are not significant for Sg(CO)6.

Deviations from piecewise linearity in the solid-state limit with approximate density functionals.

In exact density functional theory, the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity." Deviation from this condition is indicative of poor predictive capabilities for electronic structure, in particular of ionization energies, fundamental gaps, and charge transfer. In this article, we take a new look at the deviation from linearity (i.e., curvature) in the solid-state limit by considering two different ways of approaching it: a large finite system of increasing size and a crystal represented by an increasingly large reference cell with periodic boundary conditions. We show that the curvature approaches vanishing values in both limits, even for functionals which yield poor predictions of electronic structure, and therefore cannot be used as a diagnostic or constructive tool in solids. We find that the approach towards zero curvature is different in each of the two limits, owing to the presence of a compensating background charge in the periodic case. Based on these findings, we present a new criterion for functional construction and evaluation, derived from the size-dependence of the curvature, along with a practical method for evaluating this criterion. For large finite systems, we further show that the curvature is dominated by the self-interaction of the highest occupied eigenstate. These findings are illustrated by computational studies of various solids, semiconductor nanocrystals, and long alkane chains.

Structural and elastic properties of ZrN and HfN: ab initio study

The present paper discusses the density functional theory based stability analysis of zirconium nitride and hafnium nitride in its rocksalt (B1), CsCl (B2), and zinc blende (B3) type phases. The ground state total energy calculation approach of the system has been used through the generalized gradient approximation parameterized with revised Perdew–Burke–Ernzerhof as exchange correlation functional. The present theoretical analysis confirms the stability trend of phases from most stable to less stable as B1 → B2 → B3. The study also reports the analysis of elastic properties of these nitrides in its most stable B1-type phase.

Validity of virial theorem in all-electron mixed basis density functional, Hartree-Fock, and GW calculations.

In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.

Highly correlated configuration interaction calculations on water with large orbital bases

A priori selected configuration interaction (SCI) with truncation energy error [C. F. Bunge, J. Chem. Phys. 125, 014107 (2006)] and CI by parts [C. F. Bunge and R. Carbó-Dorca, J. Chem. Phys. 125, 014108 (2006)] are used to approximate the total nonrelativistic electronic ground state energy of water at fixed experimental geometry with CI up to sextuple excitations. Correlation-consistent polarized core-valence basis sets (cc-pCVnZ) up to sextuple zeta and augmented correlation-consistent polarized core-valence basis sets (aug-cc-pCVnZ) up to quintuple zeta quality are employed. Truncation energy errors range between less than 1 μhartree, and 100 μhartree for the largest orbital set. Coupled cluster CCSD and CCSD(T) calculations are also obtained for comparison. Our best upper bound, -76.4343 hartree, obtained by SCI with up to sextuple excitations with a cc-pCV6Z basis recovers more than 98.8% of the correlation energy of the system, and it is only about 3 kcal/mol above the "experimental" value. Despite that the present energy upper bounds are far below all previous ones, comparatively large dispersion errors in the determination of the extrapolated energies to the complete basis set do not allow to determine a reliable estimation of the full CI energy with an accuracy better than 0.6 mhartree (0.4 kcal/mol).

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions.

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground (4)S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

Doping Induced Structural Stability and Electronic Properties of GaN Nanotubes

The present paper discusses the effect of manganese doping on the structural stability and electronic band gap of chiral (2, 1), armchair (3, 3), and zigzag ((6, 0) and (10, 0)) single walled GaN nanotube by using density functional theory based Atomistix Toolkit (ATK) Virtual NanoLab (VNL). The structural stability has been analyzed in terms of minimum ground state total energy, binding, and formation energy. As an effect of Mn doping (1–4 atoms), all the GaN nanotubes taken into consideration show semiconducting to metallic transition first and after certain level of Mn doping changes its trend.

On the Validity of Janak’s Theorem and Ground State Energies of Ensembles of Interacting Quantum <i>N</i>-Particle Systems

It is established that for finite number of electrons, N ∞, and in the limit T = 0, the line of reasoning leading to the proof of Janak’s theorem is flawed, based on the incorrect treatment of a mixed state as a pure state. The derivative discontinuity at integral values of N of the total ground state energy, Ev[N], of an interacting N-particle system under an external single-particle potential, v(r), is shown to follow from general quantum principles governing the behavior of ensembles of systems with varying particle number, and its presence is shown to be independent of the particular approximation used in determining the total ground-state energy of an ensemble.

Reply to “Comment on ‘Nonadiabatic couplings from the Kohn-Sham derivative matrix: Formulation by time-dependent density-functional theory and evaluation in the pseudopotential framework’”

We reply to the Comment by Proetto on our paper [Phys. Rev. A 82, 062508 (2010)] describing correction and extension of our formula. We appreciate the author for correcting a typing mistake in the derivation of our formula, but we also point out that the use of fractional occupation, while being a natural extension for getting the ground-state total energies or excitation energies, is not so straightforward for getting nonadiabatic couplings.

Scaling in the correlation energies of two-dimensional artificial atoms

We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree–Fock, variational quantum Monte Carlo, density functional, and full configuration interaction calculations. We show that the correlation energy, i.e., the true ground-state total energy minus the Hartree–Fock total energy, follows a simple function of the Coulomb energy, confinement strength and number of electrons. We find an analytic expression for this function, as well as for the correlation energy per particle and for the ratio between the correlation and total energies. Our tests for independent diffusion Monte Carlo and coupled-cluster results for quantum dots—including open-shell data—confirm the generality of the scaling obtained. As the scaling also applies well to ≳100 electrons, our results give interesting prospects for the development of correlation functionals within density functional theory.

Stability and semiclassics in self-generated fields

We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B . The total energy includes the field energy \beta \int B^2 and we minimize over all particle states and magnetic fields. In the case of spin- 1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter \beta tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, h\to0 , of the total ground state energy E(\beta, h, V) . The relevant parameter measuring the field strength in the semiclassical limit is \kappa=\beta h . We are not able to give the exact leading order semiclassical asymptotics uniformly in \kappa or even for fixed \kappa . We do however give upper and lower bounds on E with almost matching dependence on \kappa . In the simultaneous limit h\to0 and \kappa\to\infty we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrödinger operator.

Assessment of density functional theory for iron(II) molecules across the spin-crossover transition

Octahedral Fe(2+) molecules are particularly interesting as they often exhibit a spin-crossover transition. In spite of the many efforts aimed at assessing the performances of density functional theory for such systems, an exchange-correlation functional able to account accurately for the energetic of the various possible spin-states has not been identified yet. Here, we critically discuss the issues related to the theoretical description of this class of molecules from first principles. In particular, we present a comparison between different density functionals for four ions, namely, [Fe(H(2)O)(6)](2+), [Fe(NH(3))(6)](2+), [Fe(NCH)(6)](2+), and [Fe(CO)(6)](2+). These are characterized by different ligand-field splittings and ground state spin multiplicities. Since no experimental data are available for the gas phase, the density functional theory results are benchmarked against those obtained with diffusion Monte Carlo, one of the most accurate methods available to compute ground state total energies of quantum systems. On the one hand, we show that most of the functionals considered provide a good description of the geometry and of the shape of the potential energy surfaces. On the other hand, the same functionals fail badly in predicting the energy differences between the various spin states. In the case of [Fe(H(2)O)(6)](2+), [Fe(NH(3))(6)](2+), [Fe(NCH)(6)](2+), this failure is related to the drastic underestimation of the exchange energy. Therefore, quite accurate results can be achieved with hybrid functionals including about 50% of Hartree-Fock exchange. In contrast, in the case of [Fe(CO)(6)](2+), the failure is likely to be caused by the multiconfigurational character of the ground state wave-function and no suitable exchange and correlation functional has been identified.

SOME DEFORMATION PROPERTIES OF THE EVEN–EVEN YTTERBIUM, HAFNIUM AND TUNGSTEN NUCLEI

The deformation structure of the even–even ytterbium, hafnium and tungsten nuclei is investigated in framework of the collective model, the single-particle Schrödinger fluid model and the cranked Nilsson model. Accordingly, we have calculated the rotational and vibrational energies, the nuclear moments of inertia, the total ground-state energy, the quadrupole moment, the liquid drop (LD) energy, the Strutinsky inertia, the LD inertia, the volume conservation factor [Formula: see text], the smoothed energy, the Bardeen, Cooper and Schrieffer (BCS) energy and the G-value of the ytterbium: 170 Yb , 172 Yb and 174 Yb , hafnium: 176 Hf , 178 Hf and 180 Hf and tungsten: 182 W , 184 W and 186 W nuclei as functions of the deformation parameters β, γ, which are assumed to vary in the ranges (-0.50 ≤ β ≤ 0.50) and (0° ≤ γ ≤ 60°). Also, two polynomials in β are obtained to produce results in good agreement with the corresponding results for the total ground-state energy and the quadrupole moment of the mentioned nine nuclei.

A Kohn–Sham equation solver based on hexahedral finite elements

We design a Kohn–Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C60, C120, and C275H172. It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.

Dephasing in an atom

When an atom in vacuum is near the surface of a dielectric the energy of a fluctuating electromagnetic field depends on a distance between them resulting, as known, in a force called van der Waals. Besides this fluctuation phenomenon there is one associated with formation of a mean electric field, which is equivalent to an order parameter. In this case atomic electrons are localized within atomic distances close to the atom and the total ground state energy is larger, compared to the bare atom, due to the polarization of the dielectric and the creation of a mean electric field locally distributed in the dielectric. The phenomenon differs from the usual ferroelectricity and has a pure quantum origin. This results in (i) an unusual atom–dielectric force different from the van der Waals one and (ii) an anomalous Lamb shift in the atom.

Antisymmetric wave functions for mixed fermion states and energy convexity

We show how ensembles or mixed states can be described in terms of pure states that for Fermions lead to wave functions that are antisymmetric with respect to interchange of particle coordinates (and spin). The pure states are constructed in an augmented Hilbert space spanned by products of ensemble states projected onto mutually nonoverlapping coordinates that prevents the appearance of interference terms under antisymmetrization. As a demonstration of this new formalism, and under the assumptions of a positive interparticle interaction and a corresponding energy that is extensive in the number of particle pairs (pair extensive), we prove the convexity relation, ${E}_{v}[N\ensuremath{-}1]+{E}_{v}[N+1]\ensuremath{\geqslant}2{E}_{v}[N]$, where ${E}_{v}[N]$ denotes the total ground-state energy of $N$ Fermions (electrons) under an external potential $v(\mathbf{r})$.

Accurate explicitly correlated wave functions for two electrons in a square

An explicitly correlated linear-r(12) variational method is developed for a system of two electrons confined to a two-dimensional square well with infinite walls. The wave function is written as an expansion in products of non-negative integer powers of the relative and center-of-mass electronic coordinates and powers of r(12) restricted to 0 and 1. This form indirectly includes higher powers of the interelectronic distance and exhibits a much faster convergence than a similar expansion without r(12)-dependent terms. The method is implemented using high-precision floating-point arithmetic. Ground-state total energies are reported with at least 12 accurate significant figures for squares with sides from 1 to 50 bohrs. The method can be used "as is" for excited states and for two-dimensional rectangular wells. We also show that wave functions for two electrons in a square and in a rectangle have a higher symmetry than can be accounted for by the point group of the system.

Second-Order Møller–Plesset Calculations of Total Ground-State Energies of Tetrahedral and Octahedral Molecules at Equilibrium, Confronted with Some Model-Dependent Scaling Properties

Using second-order Møller-Plesset (MP2) optimized geometries, calculations of total energies of some 20 tetrahedral and octahedral molecules have been carried out. We have then confronted these first-principles results, which of course include a fraction of the electronic correlation energy, with some model-dependent scaling properties. In particular, one scaling relation emerging from the semiclassical Thomas-Fermi electron density method relates the known nuclear-nuclear potential energy, V(nn), at equilibrium to the electron-nuclear term, V(en), and the total kinetic energy.

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

AbstractThe efficiency of noninteger n‐generalized exponential type orbitals (NGETO) rn*−1 e with hyperbolic cosine (HC) cosh (βrμ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Pressure induced phase transitions in transition metal nitrides: Ab initio study

AbstractWe have analyzed the stability of transition metal nitrides (TMNs) XN (X = Ti, Zr, Hf, V, Nb, Ta) in their original rocksalt (B1) and hypothetical CsCl (B2) type phases under high compression. The ground state total energy calculation approach of the system has been used through the generalized gradient approximation (GGA) with the Perdew‐Burke‐Ernzerhof (PBE) type parameterization as exchange correlation functional. In the whole series of nitrides taken into consideration, tantalum nitride is found to be the most stable. We have observed that under compression the original B1‐type phase of these nitrides transforms to a B2‐type phase. We have also discussed the computation of ground state properties, like the lattice constant (a), bulk modulus (B0) and first order pressure derivative of the bulk modulus (B'0) of the TMNs and their host elements.