arXiv subjects

Rajendra R. Zope

Publications and source records attributed to Rajendra R. Zope.

At least 37 records · Page 2Linked to original sources

arXiv2019

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction

Self-interaction (SI) error, which results when exchange-correlation contributions to the total energy are approximated, limits the reliability of many density functional approximations. The Perdew-Zunger SI correction (PZSIC), when applied in conjunction with the local spin density approximation (LSDA), improves the description of many properties, but overall, this improvement is limited. Here we propose a modification to PZSIC that uses an iso-orbital indicator to identify regions where local SI corrections should be applied. Using this local-scaling SIC (LSIC) approach with LSDA, we analyze predictions for a wide range of properties including, for atoms, total energies, ionization potentials, and electron affinities, and for molecules, atomization energies, dissociation energy curves, reaction energies, and reaction barrier heights. LSIC preserves the results of PZSIC-LSDA for properties where it is successful and provides dramatic improvements for many of the other properties studied. Atomization energies calculated using LSIC are better than those of the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and close to those obtained with the Strongly Constrained and Appropriately Normed (SCAN) meta-GGA. LSIC also restores the uniform gas limit for the exchange energy that is lost in PZSIC-LSDA. Further performance improvements may be obtained by an appropriate combination or modification of the local scaling factor and the particular density functional approximation.

cond-mat.mtrl-sci↗

arXiv2019

Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional

Despite the success of density functional approximations (DFAs) in describing the electronic properties of many-electron systems, the most widely used approximations suffer from self-interaction errors (SIE) that limit their predictive power. Here we describe the effects of removing SIE from the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA) using the Fermi-Lowdin Orbital Self-Interaction Correction (FLOSIC) method. FLOSIC is a size-extensive implementation of the Perdew-Zunger self-interaction correction (PZ-SIC) formalism. We find that FLOSIC-SCAN calculations require careful treatment of numerical details and describe an integration grid that yields reliable accuracy with this approach. We investigate the performance of FLOSIC-SCAN for predicting a wide array of properties and find that it provides better results than FLOSIC-LDA and FLOSIC-PBE in nearly all cases. It also gives better predictions than SCAN for orbital energies and dissociation energies where self-interaction effects are known to be important, but total energies and atomization energies are made worse. For these properties, we also investigate the use of the self-consistent FLOSIC-SCAN density in the SCAN functional and find that this DFA@FLOSIC-DFA approach yields improved results compared to pure, self-consistent SCAN calculations. Thus FLOSIC-SCAN provides improved results over the parent SCAN functional in cases where SIEs are dominant, and even when they are not, if the SCAN@FLOSIC-SCAN method is used.

physics.chem-ph↗

arXiv2019

Stretched or noded orbital densities and self-interaction correction in density functional theory

Semi-local approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.

physics.chem-ph↗

arXiv2013

Substituent-level Tuning of Frontier Orbital Energy Levels in Phthalocyanine/C60 Donor-Acceptor Charge Transfer Pairs

We have calculated several low-lying Charge Transfer (CT) excited-state energies for four non-covalently bound dyads composed of a sulfonated-ZnPc coupled to C60. Our results show that the di- and tri-sulfonated systems yield a CT state as the lowest-energy excited state in the system. In contrast, an energy re-ordering for the tetra-sulfonated ZnPc system leads to local excitations lying lower in energy than the CT state, displaying a possible deactivation pathway obstructing charge separation. Since several different donor-acceptor relative orientations may co-exist at an organic heterojunction, we compare the energetics of a few low-lying CT states for the end-on geometry of a di-sulfonated system to its co-facial orientation counterpart. The calculated CT excitation energies are larger for the end-on orientation in comparison to the co-facial structure by ~1.5 eV, which results principally from a substantial decrease in exciton binding energy in going from the co-facial to the end-on orientation. Furthermore, changes in relative donor-acceptor orientation have a larger impact on the CT energies than changes in donor-acceptor distance. TDDFT calculations on the various sulfonated ZnPc donor molecules show a significant splitting of the Q-band for only one of the four donor systems. Our present calculations, in line with previous experimental studies, show that the systematic variation of chemical functional groups is a promising avenue for the substituent-level tuning of various physical properties of organic semiconductors.

cond-mat.mtrl-sci↗

arXiv2013

The Effect of Structural Conformational Changes on Charge Transfer States in a Light-Harvesting Carotenoid-diaryl-Porphyrin-C60 Molecular Triad

We present a detailed study of charge transfer (CT) excited states for a large number of structural conformations in a light-harvesting Carotenoid-diaryl-Porphyrin-C60 (CPC60) molecular triad. The molecular triad undergoes a photoinduced charge transfer process exhibiting a large excited state dipole moment, making it suitable for application to molecular-scale opto-electronic devices. An important consideration is that the conformational flexibility of the CPC 60 triad impacts its dynamics in solvents. Since experimentally measured dipole moments for the triad of ~110 Debye (D) and ~160 Debye strongly indicate a range in conformational variability for the triad in the excited state, studying the effect of conformational changes on the CT excited state energetics furthers the understanding of its charge transfer states. We have calculated the lowest CT excited state energies for a series of 14 triad conformers, where the structural conformations were generated by incrementally scanning a 360 degree torsional (dihedral) twist at the C60-porhyrin linkage and the porphyrin-carotenoid linkage. Additionally, five different CPC60 conformations were studied to determine the effect of pi-conjugation and particle-hole Coulombic attraction on the CT excitation energies. Our calculations show that structural conformational changes in the triad show a variation of ~0.4 eV in CT excited state energies in the gas-phase. The corresponding calculated excited state dipoles show a range of 88 D - 188 D.

cond-mat.mtrl-sci↗

arXiv2013

Electronic structure and charge transfer excited states of a multichromophoric antenna

The electronic structure of a multichromophoric molecular complex containing two of each borondipyrromethane dye, Zn-tetraphenyl-porphyrin, bisphenyl anthracene and a fullerene are studied using density functional theory. The snowflake shaped molecule behaves like an antenna capturing photon at different frequencies and transferring the photon energy to the porphyrin where electron transfer occurs from the porphyrin to the fullerene. Molecular structure of this large complex is first optimized using plane wave projector augmented wave methodology. Subsequent electronic structure calculations are performed using the real space methodology using an all electron pseudopotential basis set containing total of 12478 basis functions. The results show that the HOMO and a state below the HOMO are primarily localized on one of the porphyrins while the LUMO resides mainly on the fullerene component of the complex. The energies of the HOMO and LUMO states in the complex, as adjudged by the ionization potential and the electron affinity values, show significant differences with respect to their values in participating subunits in isolation. We have systematically examined the effect of structural strain and the presence of ligands on the ionization energy and the electron affinity. Finally, we have calculated a few lowest charge transfer energies involving electronic transitions from a the porphyrin component to the fullerene subunit of the complex using the perturbative delta-SCF method. Our predicted value of the lowest charge transfer excited state (1.67 eV) is comparable to the experimental estimate of the charge transfer energy of a similar complex.

cond-mat.mtrl-sci↗

arXiv2010

Equilibrium structure and vibrational spectra of sila-adamantane

The recent synthesis of a four-fold silylated sila-adamantane molecule (C$_{24}$H$_{72}$Si$_{14}$, T$_d$), [J. Fischer, J. Baumgartner, and C. Marschner, {\it Science} {\bf 310,} (2005) 825] is the first attempt of making the silicon analogue of adamantane. It has adamantane-like Si$_{10}$ core, capped by methyl and sily-methyl ligands. We report its electronic structure, vibrational spectrum, and the infra-red and Raman spectra calculated within the density functional formalism using large polarized Gaussian basis sets. The properties of sila-adamantane are compared with exact silicon analogue Si10H16 of adamantane. Results show that replacing hydrogens in Si10H16, by methyl and silymethyl ligands results in expansion of the Si10 core and results in large number of peaks in the Raman spectrum. The Si-C stretch at 664 1/cm and methyl deformations frequencies compare well with recent measurements of vibrational frequencies of methylated silicon surface.

physics.chem-ph↗

arXiv2008

The vibrational stability and electronic structure of B80 fullerene-like cage

We investigate the vibrational stability and the electronic structure of the proposed icosahedral fullerene-like cage structure of B80 [Szwacki, Sadrzadeh, and Yakobson, Phys. Rev. Lett. {\bf 98}, 166804 (2007)] by an all electron density functional theory using polarized Gaussian basis functions containing 41 basis functions per atom. The vibrational analysis of B$_{80}$ indicates that the icosahedral structure is vibrationally unstable with 7 imaginary frequencies. The equilibrium structure has $T_h$ symmetry and a {\em smaller} gap of 0.96 eV between the highest occupied and lowest unoccupied molecular orbital energy levels compared to the icosahedral structure. The static dipole polarizability of B$_{80}$ cage is 149 \AAA and the first ionization energy is 6.4 eV. The B$_{80}$ cage has rather large electron affinity of 3 eV making it useful candidate as electron acceptor if it is synthesized. The infra-red and Raman spectra of the highly symmetric structure are characterized by a few absorption peaks.

cond-mat.mtrl-sci↗

arXiv2008

Static dielectric response of icosahedral fullerenes from C60 to C2160 by an all electron density functional theory

The static dielectric response of C60, C180, C240, C540, C720, C960, C1500, and C2160 fullerenes is characterized by an all-electron density-functional method. First, the screened polarizabilities of C60, C180, C240, and C540, are determined by the finite-field method using Gaussian basis set containing 35 basis functions per atom. In the second set of calculations, the unscreened polarizabilities are calculated for fullerenes C60 through C2160 from the self-consistent Kohn-Sham orbitals and eigen-values using the sum-over-states method. The approximate screened polarizabilities, obtained by applying a correction determined within linear response theory show excellent agreement with the finite-field polarizabilities. The static dipole polarizability per atom in C2160 is (4 Angstrom^3) three times larger than that in C60 (1.344 Angstrom^3). Our results reduce the uncertainty in various theoretical models used previously to describe the dielectric response of fullerenes and show that quantum size effects in polarizability are significantly smaller than previously thought.

cond-mat.mtrl-sci↗

arXiv2007

Polarizabilities of Intermediate Sized Lithium Clusters From Density-Functional Theory

We present a detailed investigation of static dipole polarizability of lithium clusters containing up to 22 atoms. We first build a database of lithium clusters by optimizing several candidate structures for the ground state geometry for each size. The full polarizability tensor is determined for about 5-6 isomers of each cluster size using the finite-field method. All calculations are performed using large Gaussian basis sets, and within the generalized gradient approximation to the density functional theory, as implemented in the NRLMOL suite of codes. The average polarizability per atom varies from 11 to 9 Angstrom^3, within the 8-22 size range and show smoother decrease with increase in cluster size than the experimental values. While the average polarizability exhibits a relatively weak dependence on cluster conformation, significant changes in the degree of anisotropy of the polarizability tensor are observed. Interestingly, in addition to the expected even odd (0 and 1 $μ_B$) magnetic states, our results show several cases where clusters with an odd number of Li atoms exhibit elevated spin states (e.g. 3 $μ_B$).

cond-mat.mtrl-sci↗

arXiv2007

Static dipole polarizability of C70 fullerene

The electronic and vibrational contributions to the static dipole polarizability of C70 fullerene are determined using the finite-field method within the density functional formalism. Large polarized Gaussian basis sets augmented with diffuse functions are used and the exchange-correlation effects are described within the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA). The calculated polarizability of C70 is 103 Angstrom^3, in excellent agreement with the experimental value of 102 Angstrom^3, and is completely determined by the electronic part, vibrational contribution being negligible. The ratio of polarizabilities of C70 and C60 is 1.26. The comparison of polarizability calculated with only local terms (LDA) in the PBE functional to that obtained with PBE-GGA shows that LDA is sufficient to determine the static dipole polarizability of C70.

cond-mat.mtrl-sci↗

arXiv2007

Comparative study of unscreened and screened molecular static linear polarizability in the Hartree-Fock, hybrid-density functional, and density functional models

The sum-over-states (SOS) polarizabilities are calculated within the approximate independent electron theories such as the Hartree-Fock approximation and density functional models using the eigenvalues and orbitals obtained from the self-consistent solution of single-particle equations. The SOS polarizabilities are then compared with those calculated using the finite-field method within three widely used single particle models: (1) the Hartree-Fock (HF) method, (2) the three parameter hybrid generalized gradient approximation (B3LYP), and (3) the parameter free generalized gradient approximation due to Perdew-Burke-Ernzerhof (PBE). The comparison is carried out for polarizabilities of 142 molecules calculated using the 6-311++G(d,p) orbital basis at the geometries optimized at the B3LYP/6-311G** level. The results show that the SOS method almost always overestimate the FF polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF method however exception to the trend do exist. The mean absolute errors (MAE) in the screened (FF) and unscreened (SOS) polarizability are 0.78 Å$^3$ for the HF method, 1.87 Å$^3$ for the B3LYP, and 3.44 Å$^3$ for the PBE-GGA. The Hartree-Fock approximation predicts finite-field polarizabilities that are smaller than those predicted by the PBE and B3LYP models. Finally, a simple scheme is devised to obtain FF quality estimate of polarizability from those obtained using the SOS method by exploiting the observed trends.

cond-mat.other↗

arXiv2006

Dipole moments from atomic-number-dependent potentials in analytic density-functional theory

Molecular dipole moments of analytic density-functional theory are investigated. The effect of element-dependent exchange potentials on these moments are examined by comparison with conventional quantum-chemical methods and experiment for the subset of the extended G2 set of molecules that have nonzero dipole moment. Fitting the Kohn-Sham [Phys. Rev. 140, A1133 (1965)] potential itself makes a mean absolute error of less than 0.1 Debye. Variation of alpha (Slater's [Phys. Rev. 81, 385 (1951)] exchange parameter) values has far less effect on dipole moments than on energies. It is argued that in variable alpha methods one should choose the smaller of the two rather than the geometric mean of the two alpha values for the heteroatomic part of the linear-combination-atomic-orbital density. Calculations on the dipole moment of NH2(CH)24NO2 are consistent with earlier calculations and show that varying the differences between alpha values for atoms with different atomic numbers has only short-ranged electrostatic effects.

cond-mat.other↗

arXiv2006

Fully analytic implementation of density functional theory for efficient calculations on large molecules

Fullerene like cages and naonotubes of carbon and other inorganic materials are currently under intense study due to their possible technological applications. First principle simulations of these materials are computationally challenging due to large number of atoms. We have recently developed a fast, variational and fully analytic density functional theory (ADFT) based model that allows study of systems larger than those that can be studied using existing density functional models. Using polarized Gaussian basis sets (6-311G**) and ADFT, we optimize geometries of large fullerenes, fullerene-like cages and nanotubes of carbon, boron nitride, and aluminum nitride containing more than two thousand atoms. The calculation of C2160 using nearly 39000 orbital basis functions is the largest calculation on any isolated molecule reported to-date at this level of theory, and it includes full geometry optimization. The electronic structure related properties of the inorganic cages and other carbon fulerenes have been studied.

cond-mat.mtrl-sci↗

arXiv2005

Slater's exchange paramters for analytic and variational xalpha calculations

We treat the local exchange parameter, alpha, of the Slater's Xalpha method as a fitting parameter and determine its value by constraining some physical quantity obtained from the self-consistent solution of the Xalpha method to be equal to its "exact" value. Thus, the alpha values that reproduce the exact atomic energies are obtained for four different combinations of basis sets. A similar set of alpha values that is independent of basis set is obtained from numerical calculation. The alpha values are obtained for the atoms H through Cl. The performance of the analytic Slater-Roothaan (SR) method, that permits calculations to be performed accurate to machine precision, is examined using these set of alpha values for atomization energies of molecules belonging to the G2 set. The calculations indicate that the average absolute and mean errors are larger than those obtained using the Hartree-Fock alpha values in the SR method, but smaller than those for the standard Hartree-Fock theory or Kohn-Sham local density approximation. Alternative set of alpha values is determined by matching the highest occupied eigenvalue of the SR method to negative of the first ionization potential. Finally, the alpha values for the diatomic molecules of these atoms that yield the "exact" atomization energy are obtained. We find that the alpha values for the diatomic molecules show much larger deviation than what is observed for the atomic alpha values. The results obtained are useful in the development of the analytic Slater-Roothaan Xalpha method for molecular calculations.

cond-mat.other↗

arXiv2005

The limitations of Slater's element-dependent exchange functional from analytic density functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density and the one body effective potential of density functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method,where variationality then refers to the error in each two electron integral and not to the total energy. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in the Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in the system. Of several ways of choosing the scaling factors (Slater's exchange parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and the exact atomic, alpha_EA, values. The performance of this simple analytic model with both sets for atomization energies of G2 set of 148 molecules is better than the local density approximation or the HF theory, although the errors in atomization energy are larger than the target chemical accuracy. To improve peformance for atomization energies, the SR method is reparametrized to give atomization energies of 148 molecules to be comparbale to those obtained by one of the most widely used generalized gradient approximations. The mean absolute error in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 Angstrom. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.

cond-mat.other↗

arXiv2005

Electronic structure of fullerene-like cages and finite nanotubes of aluminum nitride

We report density functional study of alternate fullerene-like cage structures and finite closed capped single-wall nanotubes of aluminum nitride. The cages and nanotubes studied are modeled as Al24N24, Al28N28, Al32N32, Al36N36, Al48N48, and Al96N96. The structure optimization and calculation of the electronic structure, vertical ionization potential, and the electron affinity are performed at the all electron level by the analytic Slater-Roothaan method, using polarized Gaussian basis set of double zeta quality. All structures are energetically stable with binding energy of about 10-11 eV per AlN pair. For the larger Al96N96, the fullerene like cage is energetically less favorable than the two-shell cluster that has Al24N24 as an inner shell. The vertical ionization potential and the electronic affinity are in the range 6.7-6.9 eV and 1.5-2.0 eV, respectively. The binding energy show systematic increase with increase in the length of (4,4) nanotube. The energy band gap, determined using the "Delta SCF" method show that these structures are characterized by a fairly large band gap about 4-5 eV, which is however smaller than the gap for the corresponding boron nitride structures.

cond-mat.mtrl-sci↗

arXiv2005

Accurate molecular energies by extrapolation of atomic energies using an analytic quantum mechanical model

Using a new analytic quantum mechanical method based on Slater's Xalpha method, we show that a fairly accurate estimate of the total energy of a molecule can be obtained from the exact energies of its constituent atoms. The mean absolute error in the total energies thus determined for the G2 set of 56 molecules is about 16 kcal/mol, comparable to or better than some popular pure and hybrid density functional models.

cond-mat.mtrl-sci↗