Authors:
B. Paulus and K. Rosciszewski
J. Phys.: Condens. Matter 19, 346217 (2007)
For using wavefunction-based correlation methods in solids it is
necessary to have reliable Hartree-Fock results for the infinite system of interest.
Therefore we perform Hartree-Fock calculations for the group Ia alkali-metals
(Li to Cs) and group Ib
noble metals (Cu, Ag and Au). We optimized for the periodic system a basis set of valence-double-zeta quality,
for the lighter atoms an all-electron basis set, for the heavier atoms small-core pseudopotentials
are used to deal with the scalar-relativistic effects.
We determine
the cohesive energy, the lattice constant and
bulk modulus.
We used the counterpoise correction for the free atom to minimize the
basis set superposition error occurring for finite basis sets.
The effects of the counterpoise correction not only for the cohesive energy but
also for the lattice structure and bulk modulus are discussed in detail.
Authors:
B. Paulus
Int. J. of Modern Physics B {\bf 21}, 2204 (2007), (Conference Proceedings)
The method of increments is a wavefunction-based ab initio correlation method for solids, which
explicitly calculates
the many-body wavefunction of the system.
After a Hartree-Fock treatment of the infinite system
the correlation
energy of the solid is expanded
in terms of localised orbitals or of a group of localised orbitals.
The method of increments has been applied to a great variety of materials with a band gap,
but in this paper the extension to metals is described. The application to solid mercury is
presented, where we achieve very good agreement of the calculated ground-state properties
with the experimental data.
Authors:
Y. Wang and B. Paulus
Chem. Phys. Lett. 441, 187 (2007)
Authors:
E. Voloshina and B. Paulus
Phys. Rev. B 75, 245117 (2007)
Authors:
U. Wedig, M. Jansen, B. Paulus, K. Rosciszewski and P. Sony
Phys. Rev. B. 75, 205123 (2007)
The main idea of this paper is to revisted the problem of
the distorted hcp lattices of Zn and Cd in comparison to the
ideal hcp lattice of Mg. We perform different ab-initio methods
to evaluate the cohesive energy, lattice constants and elastic constants.
Within different DFT approaches we achieve very different results,
therefore additional explicit correlated ab-inito approaches are
necessary to illuminate the problem of the origin of the strong
distortion if the hcp lattice of Zn and Cd.
Authors:
E. Voloshina, N. Gaston and B. Paulus
J. Chem. Phys. 126, 134115 (2007)
In order to apply ab-initio wavefunction-based correlation methods to
metals, it is desirable to split the calculation into a mean-field part
and a correlation part. Whereas the mean-field part (here Hartree-Fock)
is performed in the extended periodic system, it is necessary to use for
the correlation part local wave-function based correlation methods in
finite fragments of the solid. For these finite entities it is
necessary to construct an embedding.
We suggest an embedding scheme which has itself no metallic character
but can mimic the metal in the internal region, where the atoms are
correlated.
With this embedding it is also possible to localize the metallic orbitals
in the central part. The long range non-additive contributions of metallicity
and correlation are treated with the method of increments.
In this paper we present different ways to construct such an
embedding and discuss the influence of the embedding on the correlation
energy of the solid.
Authors:
B. Paulus and A. Mitin
Lecture Series on Computer and Computational Science 7B, 935 (2006)
The method of increments, which is a wavefunction-based correlation method
for solids, is extended to metals.
Whereas the Hartree-Fock energy is calculated in the infinite periodic solid,
the correlation energy of the solid is expanded
in terms of localised orbitals or a group of localised orbitals.
For the metals the so-called correlation energy increments are determined
in finite, properly embedded fragments of the metal.
First applications to the ground-state properties of solid mercury yield
very good agreement with experiment
In this paper we present the extension of
the method to solid barium.
Whereas the metallic
character in mercury is due to the hybridisation of the 6s2 electrons with the 6p
orbitals, in barium it is due to the hybridisation with the 5d orbitals.
Due to a proper embedding scheme we can model the electronic structure of bulk barium and
in the case of barium we have to use multi-reference methods for the incremental treatment
of the correlation energy.
Authors:
N. Gaston and B. Paulus
Lecture Series on Computer and Computational Science 7B, 891 (2006)
Mercury condenses at 233K into the rhombohedral structure
with a bond length a=3.005 A and an angle of 70.53 degree.
In contrast, zinc and cadmium adopt the hexagonal close-packed (hcp) structure,
but with an anomolous c/a ratio which is far from ideal hcp.
Density functional methods fail to describe either of these structures accurately.
An application of the method of increments to these metals, including correlation via
coupled cluster calculations on finite fragments of the solid, allows the systematic
inclusion and comparison of the competing effects that leads to the observed structures.
Authors:
N. Gaston, B. Paulus, K. Rosciszewski, P. Schwerdtfeger and H. Stoll
Phys. Rev. B 74, 094102 (2006)
Mercury condenses at 233K into the rhombohedral structure
with an angle of 70.53 degree. Theoretical predictions of this
structure are difficult. While a Hartree-Fock treatment yields
no binding at all, density-functional (DFT) approaches with
gradient-corrected functionals predict a structure with a significantly too large lattice constant and an
orthorhombic angle of about 60 degree, which corresponds to an fcc structure.
Surprisingly, the use of the simple LDA functional yields the correct structure and lattice constants
in very good agreement with experiment; relativistic effects are shown to be essential for reaching this agreement.
In addition to DFT results, we present a wavefunction-based correlation treatment
of mercury and discuss in detail the effects of electron correlation
on the lattice parameters of mercury including
$d$-shell correlation and the influence of three-body terms in the many-body decomposition
of the interatomic correlation energy.
The lattice parameters obtained with this
scheme at the coupled cluster level of theory, CCSD(T), agree within 1.5%
with the experimental values. We further present the bulk modulus calculated
within the wavefunction approach, and compare to LDA and experimental values.
LDA underestimates the bulk modulus severely compared to experiment, which is
contrary to the expected effect of overbinding.
Authors:
C. Buth and B. Paulus
Phys. Rev. B 74, 045122 (2006)
Hydrogen bonding in infinite HF and HCl bent (zig-zag) chains
is studied using the ab initio
coupled-cluster singles and doubles (CCSD) correlation method.
The correlation contribution to the binding energy is
decomposed in terms of non-additive many-body interactions between
the monomers in the chains, the so-called energy increments.
Van der Waals constants for the dispersion interaction
between distant monomers in the infinite chains
are extracted from this decomposition which allows a
partitioning of the correlation contribution to the binding energy
into short-range and long-range terms.
This finding affords to reduce significantly the computational
effort of ab initio calculations for solids as only
the short-range part requires a sophisticated treatment
whereas the long-range part can be summed immediately
to infinite distances.
Authors:
E. Voloshina and B. Paulus
J. Chem. Phys. 124, 234711 (2006)
The ground-state properties of CeO2 were calculated with ab initio quantum-chemical methods. The coupled-cluster
approach is used to correct the Hartree-Fock crystal results for correlations and to systematically improve cohesive energy,
lattice constant and bulk modulus.
Combining the results at the correlated level with corresponding Hartree-Fock data we recover
about 100\,\% of the experimental cohesive energy; lattice constant is accurate to 0.4%; bulk modulus is 8%
higher compared with the experiment. For comparison the results obtained with density functional method are also presented.
Authors:
B. Paulus
Review article, Phys. Rep. 428}, 1 (2006)
An overview of wavefunction-based correlation methods generalized for the application
to solids is presented. These methods explicitely calculate
the many-body wavefunction in contrast to the density-functional theory which relies on the
ground-state density of the system.
This review focusses on the so-called method of increments where the correlation
energy of the solid is expanded
in terms of localized orbitals or of a group of localized orbitals.
The method of increments is applied to a great variety of materials,
from covalent semiconductors to ionic insulators, from large band-gap materials
like diamond to the half-metal $\alpha$-tin, from large molecules like fullerenes
over polymers, graphite to three-dimensional solids. Rare-gas crystals where the
binding is van der Waals like are treated as well as solid mercury, where the
metallic binding is entirely due to correlation. Strongly correlated
systems are examined and the correlation driven metal-insulator transition is described at an
ab-initio level.
Authors:
E. Voloshina and B. Paulus
Theo. Chem. Acc. 114, 259 (2005)
Within the application of the method of local increments to cerium dioxide
high-level quantum chemical calculations, using the coupled-cluster approach
have been performed for (Ce$^{4+}$)$_m$(O$^{2-}$)$_n$ clusters. Two different
embedding approaches were tested. In the first one all
increments were obtained from the Ce$_4$O$_7$-cluster.
In the second approach different clusters were used for evaluating of increments.
Several surrounding have been considered within the second approach.
The advantages and disadvantages of studied embedding schemes are shown.
Authors:
H. Stoll, B. Paulus and P. Fulde
J. Chem. Phys. 123, 144108 (2005)
The incremental scheme for obtaining the energetic properties of
extended systems from wave-function-based ab initio calculations of
small (embedded) building blocks, which has been applied to a variety
of van der Waals-bound, ionic, and covalent solids in the past few years,
is critically reviewed. Its accuracy is assessed by means of model calculations
for finite systems, and the prospects for applying it to delocalized systems are given
Authors:
B. Paulus, K. Rosciszewski, N. Gaston, P. Schwerdtfeger and H. Stoll
Phys. Rev. B 70, 165106 (2004)
A many-body expansion for mercury clusters
does not converge smoothly with increasing cluster size towards the solid state.
Even for smaller cluster sizes (up to n=6), where van
der Waals forces still dominate, one observes bad convergence
behaviour. For solid mercury the convergence of the many-body
expansion can dramatically be improved by an incremental procedure
within an embedded cluster approach. Here one adds the
coupled cluster many-body electron correlation contributions of the
embedded cluster to the bulk HF energy. In this way we obtain
a cohesive energy (not corrected for zero-point vibration) of 0.69 eV
in good agreement with the experimental value of 0.79 eV.
Authors:
B. Paulus
Int. J. Quantum Chem. {\bf 100}, 1026 (2004)
First principle calculations for large extended systems such as the buckminsterfullerene C$_{60}$ are mainly
performed within density-functional theory. They yield reasonable agreement with experiment, but
wavefunction-based correlations methods are desirable
to get an better insight in the correlation properties.
Starting from a Hartree-Fock calculation for the solid, an incremental scheme
relying on localised orbitals is developed for the correlation energy of C$_{60}$.
This many-body expansion converges well with distance of localized bonds involved in
the correlation methods and with order of increments. A detailed knowledge of the influence
of the correlation effects on the binding and the bond alternation is achieved.
Comparison to diamond, graphite and polyacetylene is made.
Authors:
C. Buth and B. Paulus
Chem. Phys. Lett. 398, 44 (2004)
Basis set convergence of the Hartree-Fock and the correlation energy is examined for the
hydrogen bonded infinite bent chains (HF) and (HCl). We employ series of correlation consistent
basis sets up to quintuple-zeta quality together with a coupled cluster method (CCSD) to
describe electron correlation on ab initio level. The Hartree-Fock energy converges rapidly
with increasing basis set quality whereas the correlation energy is found to be slowly
convergent for the same series of basis sets. We study basis set extrapolation for (HF)
and (HCl) and show that it substantially enhances the accuracy of both
the Hartree-Fock and the correlation energy in extended systems.
Authors:
B. Paulus and K. Rosciszewski
Chem. Phys. Lett. 394, 96 (2004)
Solid mercury in the rhombohedral structure is unbound within the self-consistent field (Hartree-Fock)
approximation. The metallic binding is entirely due to electronic correlations.
We determine the
cohesive energy of solid mercury within an ab-initio many-body
expansion for the correlation part.
Electronic correlations in the $5d$ shell contribute about half to the cohesive energy.
Relativistic effects are found to be very important.
Very good agreement with the experimental value is obtained.
Authors:
Walter Alsheimer and Beate Paulus
Eur. Phys. J. B 40, 243 (2004)
At an ab-initio level we study how the Mott metal-insulator transition (MIT)
is affected when the boundary conditions change from periodic to open boundaries.
For that purpose
we apply quantum-chemical methods to sodium rings and chains in order
to investigate the analogue of a MIT. By changing the interatomic distance
we analyse the character of the many-body wavefunction, the charge gap and the static electric dipole polarisability.
To mimic a behaviour found in the ionic Hubbard model,
where a transition from a band to a Mott insulator occurs, we perform
calculations for mixed sodium-lithium rings.
In addition, we ask the question of bond alternation for the pure sodium system and the mixed sodium-lithium
system in order to answer
under which conditions a Peierls distortion occurs.
Authors:
Beate Paulus, Krzysztof Rosciszewski, Herrmann Stoll, Uwe Birkenheuer
submitted to :Phys. Chem. Chem. Phys. (2003)
The local incremental expansion of the correlation energy of extended systems
is applied to non-orthogonal localized orbitals and
compared to the standard approach, which uses orthogonal
Foster-Boys orbitals. Several methods of how to
generate suitable non-orthogonal orbitals for the investigated
covalent systems, bulk silicon and beryllium rings, are discussed.
For the non-orthogonal orbitals the correlation energy contributions from
increments involving more than one correlated orbital decay faster
with the distance between these orbitals than for standard
Foster-Boys orbitals. Also,
the transferability of the individual energy increments from one cluster
to another cluster is better in case of the non-orthogonal orbitals.
Yet, the convergence of the incremental series with the order of the
increments, i.e.\ the number of correlated bonds involved, is somewhat
slower compared to the orthogonal Foster-Boys orbitals.
Authors:
Beate Paulus, Krzysztof Rosciszewski, Peter Fulde, Herrmann Stoll
submitted to :Phys. Rev. B (2003)
We study how the Mott metal-insulator transition (MIT) is affected when we have to deal with electrons with different angular momentum quantum numbers. For that purpose we apply ab-initio quantum-chemical methods to lithium rings in order to investigate the analogue of a MIT. By changing the interatomic distance we analyse the character of the many-body wavefunction and discuss the importance of the $s-p$ orbital quasi-degeneracy within the metallic regime. The charge gap (ionization potential minus electron affinity) shows a minimum and the static electric dipole polarizability has a pronounced maximum at a lattice constant where the character of the wavefunction changes from significant $p$ to essentially $s$-type. In addition, we examine rings with bond alternation in order to answer the question under which conditions a Peierls distortion occurs.
Author:
Beate Paulus
accepted :Phys. Chem. Chem. Phys. 2003, 5, 3364 - 3367
Results of ab-initio calculations at different degrees of accuracy, including coupled-cluster results, are presented for the ground-state structure and the ground-state energy of 16 fullerenes from C$_{20}$ to C$_{36}$. We consider a possible energy gain due to the Jahn-Teller effect and determine the structure for the corresponding symmetries. The binding energies and the relative stabilities of the molecules are calculated in the Hartree-Fock, density functional, second-order perturbation theory and coupled-cluster approaches. We investigate the stability of the fullerenes both as the number of carbon atom is increased and as different isomers with the same number of carbon atoms are considered.
Author:
Beate Paulus
published in: Chem. Phys. Lett. 371, 7 (2003)
Ab-initio electron correlation calculations based on quantum chemical methods are successfully applied to a metallic system. As a test system we select one-dimensional Li$_n$ rings up to $n$=62. The correlation energy is determined within an incremental scheme, where the individual energy increments are calculated with local orbitals. The local orbitals are generated by projecting the atomic $2s$ orbitals onto the occupied Hartree-Fock space. Multi-reference methods are applied to deal with the low-lying excitations in a metal.
Author:K. Rosciszewski and
Beate Paulus
published in: Phys. Rev. B 66, 092102 (2002)
The stabilization of the fcc structure of the heavier rare-gas crystals is mainly due to the zero-point energy (ZPE) calculated at the harmonic level with 2-body contributions only. We evaluate the influence of the anharmonic contributions on the ZPE within the Einstein approximation. For the influence of the 3-body contributions we develop an analytic 3-body potential fitted to coupled-cluster ab initio data. Both, the anharmonic and 3-body contributions change the absolute value of the ZPE, but have no influence on the fcc-hcp energy difference.
Author:S. Kalovda,B. Paulus, M. Dolg, H. Stoll and H.J. Werner
published in: Phys. Chem. Chem. Phys. 3, 514, (2001)
Results of ab initio and density functional calculations for the geometries and cohesive energies of the closo-hydroborate dianion series B$_n$H$_n^{2-}$\ (n=5-12) and the hypothetical borane B$_4$H$_4$ are presented. The purpose of this contribution is three-fold: first we provide an in-depth comparison of the performance of a whole range of different quantum chemical standard methods ranging from Hartree-Fock over density functional theory and second-order many-body perturbation theory to the coupled-cluster method for the geometries. Second, we give quantitative insight into the relative stabilities of the various cluster compounds. Finally, we investigate approximations in {\it ab initio} calculations making use of the locality of electron correlation in the occupied and virtual orbital spaces.
Author:K. Rosciszewski,
Beate Paulus, P. Fulde and H. Stoll
published in: Phys. Rev. B 62, 5482 (2000)
In order to gain more insight into factors governing the relative stability of the fcc and hcp structures of the rare-gas solids Ne through Xe, we performed {\em ab-initio} coupled-cluster calculations for the most important three- and four-body terms in the many-body expansion of the cohesive energy. These terms are combined with empirical two-body potentials derived from dimer data and with a multipole expansion for the long-range three-body terms. In addition, we calculated phonon spectra, in harmonic approximation, for the two structures. Including zero-point energies, our results agree very well with experimental data for the fcc structure. The hypothetical hcp structure, which is lower in energy with two-body potentials, is destabilized by short-range three-body terms and, even more important, by the contribution of zero-point vibration.
Author:K. Rosciszewski,
Beate Paulus, P. Fulde and H. Stoll
published in: Phys. Rev. B 60, 7905 (1999)
Cohesive energies, lattice constants and bulk moduli have been calculated for the rare-gas crystals Ne through Xe. The results are based on a many-body expansion of the interaction energy, with two- and three-atom contributions evaluated in valence-only coupled-cluster (CCSD(T)) calculations using relativistic pseudopotentials. Although the two-body contributions dominate the cohesive energy in all cases, the influence of three-body contributions is non-negligible and reaches nearly 7\% of the cohesive energy for Xe.
Author:K. Rosciszewski, K. Doll,
B.Paulus, P. Fulde and H. Stoll
published in: Phys. Rev. B 57, 14667 (1998)
Electron-correlation effects on cohesive energy, lattice constant and bulk compressibility of rutile are calculated using an ab-initio scheme. A competition between the two groups of partially covalent Ti-O bonds is the reason that the correlation energy does not change linearly with deviations from the equilibrium geometry, but is dominated by quadratic terms instead. As a consequence, the Hartree-Fock lattice constants are close to the experimental ones, while the compressibility is strongly renormalized by electronic correlations.
Author:
Beate Paulus
published in: Surf. Sci.
408, 195 (1998)
Ab initio multi-reference configuration interaction calculations are performed for the Si(100) surface using a cluster approach. The convergence with respect to the cluster size is checked and the final results are taken from a Si_32 H_28 cluster which models two dimers and six bulk layers. We find for the ideal as well as for the p(1 x 2) reconstruction a singlet ground state consisting of several configurations. The energy gain due to forming the symmetric dimer in the p(1 x 2) structure is 1.75 eV, the bond length of the dimer is 2.35 Angstrom which is very close to the bulk value. In contradiction to the LDA results and in agreement with previous correlation calculations we do not find an asymmetric p( 1 x 2) structure.
Authors:
Beate Paulus,
Martin Albrecht,
published in: Phys. Rev. B, 56, 7339, (1997)
Correlated ab-initio ground-state calculations, using relativistic energy-consistent pseudopotentials, are performed for six II-VI semiconductors. Valence (ns,np) correlations are evaluated using the coupled cluster approach with single and double excitations. An incremental scheme is applied based on correlation contributions of localized bond orbitals and of pairs and triples of such bonds. In view of the high polarity of the bonds in II-VI compounds, we examine both, ionic and covalent embedding schemes for the calculation of individual bond increments. Also, a partitioning of the correlation energy according to local ionic increments is tested. Core-valence (nsp,(n-1)d) correlation effects are taken into account via a core-polarization potential. Combining the results at the correlated level with corresponding Hartree-Fock data we recover about 94% of the experimental cohesive energies; lattice constants are accurate to 1%; bulk moduli are on average 10% too large compared with experiment.
Authors:
Beate Paulus, Fa-Jian Shi,
Hermann Stoll (Institut fuer Theoretische Chemie,
Universitaet Stuttgart, D-70550 Stuttgart, Germany)
published in: J. Phys. Condens. Matter 9, 2745, (1997)
Ground state properties of SiC, AlN, GaN and InN in the zinc-blende and wurtzite structures are determined using an ab initio scheme. For the self-consistent field part of the calculations, the Hartree-Fock program Crystal has been used. Correlation contributions are evaluated using the coupled-cluster approach with single and double excitations. This is done by means of increments derived for localized bond orbitals and for pairs and triples of such bonds. A comparison between the ground state energies of the zinc-blende and wurtzite structure is made: At the Hartree-Fock level, it turns out that for SiC the zinc-blende structure is more stable although the very small energy difference to the wurtzite structure is an indication of the experimentally observed polytypism. For the III-V nitrides the wurtzite structure is found to be significantly more stable than the zinc-blende structure. Electron correlations do not change the Hartree-Fock ground state structures, but energy differences are enlarged by up to 40%. While the Hartree-Fock lattice parameters agree well with experiment, the Hartree-Fock cohesive energies reach only 45% to 70% of the experimental values. Including electron correlations we recover for all compounds about 92% of the experimental cohesive energies.
Authors:
Simon Kalvoda, Beate Paulus, Peter Fulde,
Hermann Stoll (Institut fuer Theoretische Chemie,
Universitaet Stuttgart, D-70550 Stuttgart, Germany)
published in: Phys. Rev B 55, 4027 (1997)
Lattice constants and bulk moduli of eleven cubic III-V semiconductors are calculated using an ab initio scheme. Correlation contributions of the valence electrons, in particular, are determined using increments for localized bonds and for pairs and triples of such bonds; individual increments, in turn, are evaluated using the coupled cluster approach with single and double excitations. Core-valence correlation is taken into account by means of a core polarization potential. Combining the results at the correlated level with corresponding Hartree-Fock data, we obtain lattice constants which agree with experiment within an average error of -0.2%; bulk moduli are accurate to +4%. We discuss in detail the influence of the various correlation contributions on lattice constants and bulk moduli.
Authors:
Beate Paulus, Peter Fulde,
Hermann Stoll (Institut fuer Theoretische Chemie,
Universitaet Stuttgart, D-70550 Stuttgart, Germany)
published in: Phys. Rev. B 54, 2556 (1996)
Cohesive energies for twelve cubic III-V semiconductors with zincblende structure have been determined using an ab-initio scheme. Correlation contributions, in particular, have been evaluated using the coupled-cluster approach with single and double excitations (CCSD). This was done by means of increments obtained for localized bond orbitals and for pairs and triples of such bonds. Combining these results with corresponding Hartree-Fock data, we recover about 92 % of the experimental cohesive energies.
Authors:
Beate Paulus, Peter Fulde,
Hermann Stoll (Institut fuer Theoretische Chemie,
Universitaet Stuttgart, D-70550 Stuttgart, Germany)
published in: Phys. Rev. B 51, 10572 (1995)
Valence energies for crystalline C, Si, Ge, and Sn with diamond structure have been determined using an ab-initio approach based on information from cluster calculations. Correlation contributions, in particular, have been evaluated in the coupled electron pair approximation (CEPA), by means of increments obtained for localized bond orbitals and for pairs and triples of such bonds. Combining these results with corresponding Hartree-Fock (HF) data, we recover about 95 % of the experimental cohesive energies. Lattice constants are overestimated at the HF level by about 1.5 %; correlation effects reduce these deviations to values which are within the error bounds of this method. A similar behavior is found for the bulk modulus: the HF values which are significantly too high are reduced by correlation effects to 97% of the experimental values.