arXiv subjects

T. R. S. Prasanna

Publications and source records attributed to T. R. S. Prasanna.

15 recordsLinked to original sources

arXiv2025

Theoretical issues in the accurate computation of the electron-phonon interaction contribution to the total energy

We report the computation of the Standard Hamiltonian of a coupled electron-phonon system by accurately computing the electron-phonon interaction (EPI) contribution to the total energy. This gives the most accurate ab initio total energy till date. However, our results show that the per-atom EPI energy is unit-cell-size dependent due to the partial-Fan-Migdal term that arises from the antisymmetric nature of the crystal wavefunction. Due to this, only energy differences between polytypes, in supercells with identical number of atoms, are meaningful, rather than per-atom total energy. This violates our understanding of Quantum Mechanics applied to periodic solids and raises serious theoretical questions. In his original (1951) paper, Fan suggested, without specifying any reason, that second-order perturbation theory applied to the whole crystal is of questionable validity. Our results support Fan's suggestion for the reason that the partial-FM term makes the per-atom total energy unit-cell-size dependent. This leads to a new fundamental problem in condensed matter physics, viz. second-order perturbation theory is invalid for whole crystals, an entire class. It is essential to resolve this problem, especially because it causes the standard Hamiltonian, the starting point of EPI studies and the most accurate ab initio total energy, to be of questionable validity.

cond-mat.mtrl-sci↗

arXiv2023

Electron-phonon interaction contribution to the total energy of group IV semiconductor polymorphs: evaluation and implications

In density functional theory (DFT) based total energy studies, the van der Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are included to obtain energy differences between polymorphs. We propose and compute a new correction term to the total energy, due to electron-phonon interactions (EPI). We rely on Allen's general formalism, which goes beyond the Quasi-Harmonic Approximation (QHA), to include the free energy contributions due to quasiparticle interactions. We show that, for semiconductors and insulators, the EPI contributions to the free energies of electrons and phonons are the corresponding zero-point energy contributions. Using an approximate version of Allen's formalism in combination with the Allen-Heine theory for EPI corrections, we calculate the zero-point EPI corrections to the total energy for cubic and hexagonal polytypes of Carbon, Silicon and Silicon Carbide. The EPI corrections alter the energy differences between polytypes. In SiC polytypes, the EPI correction term is more sensitive to crystal structure than the vdW and ZPVE terms and is thus essential in determining their energy differences. It clearly establishes that the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our results are consistent with the experimental results of Kleykamp. Our study enables the inclusion of EPI corrections as a separate term in the free energy expression. This opens the way to go beyond the QHA by including the contribution of EPI on all thermodynamic properties.

cond-mat.mtrl-sci↗

arXiv2022

Critical role of electron-phonon interactions in determining the relative stability of Boron Nitride polymorphs

Despite several first principles studies, the relative stability of BN polymorphs remains controversial. The stable polymorph varies between the cubic (c-BN) and hexagonal (h-BN) depending on the van der Waals (vdW) dispersion approximation used. These studies are unable to explain the main experimental results, c-BN is stable, the relative stability order and the large energy difference between h-BN and c-BN (greater than 150 meV/formula unit). In this study, we introduce contributions from electron-phonon interactions (EPI) to the total energy of BN polymorphs. This clearly establishes c-BN is the stable polymorph irrespective of the vdW approximation. Only by including EPI contributions do the ab initio results match, for the first time, the main experimental results mentioned above. The EPI contribution to the total energy is strongly sensitive to chemical bonding (approximately twice in $sp^2$-bonded layered over $sp^3$-bonded polymorphs) and to crystal structure. The crucial role of EPI contributions is seen in $sp^2$-bonded layered BN polymorphs where it is greater than the vdW contribution. Given that h-BN is a prototype layered material, in bulk or 2D form, our results have a broader relevance, that is, including EPI correction, along with vdW approximation, is vital for the study of energetics in layered materials.

cond-mat.mtrl-sci↗

arXiv2018

Finite temperature electronic structure of Diamond and Silicon

The electron-phonon interaction contribution to the electronic energies is included in density functional total energy calculations with ab initio pseudopotentials via the Allen formalism [Phys. Rev. B 18, 5217 (1978)] to obtain temperature dependent electronic structure of diamond and silicon. This method allows us to obtain the thermally-averaged ab initio electronic structure in a straightforward and computationally inexpensive way. Our investigations on the finite temperature electronic structure of diamond and silicon lead to a new criterion, temperature transferability, which is required in the ab initio pseudopotentials for temperature dependent studies. The temperature transferability of the Troullier-Martins pseudopotentials used in this work is strongly dependent on the cut-off radius and the inclusion of the unbound 3d$^0$ state. The finite temperature indirect band gaps are highly sensitive to the choice of cut-off radius used in the pseudopotentials. The finite temperature band structures and density of states show that thermal vibrations affect the electron energies throughout the valence and conduction band. We compare our results on the band gap shifts with that due to the Debye-Waller term in the Allen-Heine theory and discuss the observed differences in the zero point and high temperature band gap shifts. Although, the electron energy shifts in the highest occupied valence band and lowest unoccupied conduction band enable to obtain the changes in the indirect and direct band gaps at finite temperatures, the shifts in other electronic levels with temperature enable investigations into the finite temperature valence charge distribution in the bonding region. Thus, we demonstrate that the Allen theory provides a simple and theoretically justified formalism to obtain finite temperature valence electron charge densities that go beyond the rigid pseudo-atom approximation.

cond-mat.mtrl-sci↗

arXiv2017

Angular factor corrections in thin film x-ray diffraction

The current practice of angular (Lorentz, Polarization and absorption (LPA)) corrections in bulk materials for higher angle broad peaks, due to the Kα doublet, are based on the results of Pike (Acta Cryst., 12 (1959) 87-92) and Ladell (Acta Cryst. 14 (1961) 47-53). These results are extended to thin film x-ray diffraction. The current practice in thin film studies of using the absorption factors for monochromatic radiation in LPA corrections is incorrect in both symmetric and grazing incidence x-ray diffraction. The correct expressions for absorption corrections are developed. In addition, a new length scale, the linear regime, is shown to exist for very thin films where the absorption factor and the integrated intensity are independent of the absorption coefficient. For very thin films, it is practically advantageous to use the expressions for the linear regime over those for the thin film regime. The procedures to obtain both the main results are of general validity and can be extended to several thin film diffraction techniques.

cond-mat.mtrl-sci↗

arXiv2015

Finite temperature external potential in crystalline solids

Thermal vibrations alter the external potential. Allen (Phys. Rev. B 18 (1978) 5217) proved that at finite temperatures the pseudopotential form factors are corrected by a Debye-Waller Factor (DWF). We generalize this result to the crystal potential. (The generalization to the all-electron case of the nuclear potential fails due to the breakdown of the rigid-atom approximation.) This finite temperature formalism only gives thermal-averaged properties and no dynamical information can be obtained. Hence, it is labeled the Quasi Ab Initio formalism. Analogous to the use of experimental lattice parameters in ab initio studies, experimental DWF can also be used. The justification is identical; the experimental parameters can be validated by separate ab initio studies. Our work transforms, forty years later, Kasowski's empirical study (Phys. Rev. B. 8 (1973) 1378) into the first ab initio finite temperature band structure calculation. This formalism opens the way to obtain ab initio finite temperature thermal-averaged properties from a single calculation.

cond-mat.mtrl-sci↗

arXiv2011

Role of thermal vibrations in magnetic phase transitions

We address and resolve the fundamental contradiction that has existed from the earliest studies on magnetic phase transitions between theoretical models that ignore the role of thermal vibrations and represent the exchange interaction as a constant, Jij(0), and analysis of neutron diffraction data that always incorporates thermal vibrations even though it is also possible to analyze the same data by ignoring them. Of the two possibilities, ignoring thermal vibrations in both theoretical models and analysis of diffraction data leads to the latter giving different magnetic order parameters for different reciprocal lattice lines. This appears to be the first report of a unique consequence, viz. the assumption to neglect a physical phenomenon turns a single-valued experimental observable into a multiple-valued one where all values are equally valid. This assumption is clearly unacceptable and must be rejected. The second possibility of incorporating thermal vibrations in both leads to single-valued theoretical and experimental order parameters. Thus, analysis of neutron diffraction data constrain the exchange interaction in all theoretical models to be temperature dependent and represented as Jij(T). Additional experimental and theoretical evidences in support of this conclusion are presented.

cond-mat.mtrl-sci↗

arXiv2011

Physical meaning of the Ewald sum method

The electrostatic potential and energy of point charges in a real crystal, in the presence of thermal vibrations, is obtained as a special case of the Fourier method. Incorporating the role of thermal vibrations in electrostatic energy calculations leads to the physical meaning of the Ewald sum method. The Ewald summation method determines the electrostatic potential and energy of point charges in a crystal at a temperature that is obtained from the width of the Gaussian and not at 0 K. For values of the width of the Gaussian commonly recommended for computational convenience temperatures exceed 10000 K.

cond-mat.mtrl-sci↗

arXiv2009

Role of thermal vibrations in phase transitions

All theoretical models (Heisenberg, Ising etc.) assume a negligible role for thermal vibrations in alloy and magnetic phase transitions. Analysis of diffraction data conclusively proves that this assumption is incorrect. A simple criterion emerges that theoretical models can ignore the role of thermal vibrations only if the Debye-Waller Factor is ignored in the analysis of diffraction data. Diffraction data constrain all theoretical models to incorporate the role of thermal vibrations. This conclusion is also supported by other experimental results, the effect of thermal vibrations on ordering energy that is of the same order of magnitude as ordering energy and an isotope effect on magnetic phase transitions. An electron-phonon interaction (EPI) formalism that incorporates the Debye-Waller Factor in electronic structure calculations already exists and must be adopted for a correct understanding of phase transitions as it can account for all the different experimental results mentioned above. The discrepancy between experimental and theoretical ordering energy in Ni3V is direct evidence for the role of thermal vibrations in altering ordering energy. The inter-nuclear potential energy term converges if zero point vibrations are incorporated and this method can replace the Ewald sum method. The three dimensional Ising model cannot represent order-disorder transition in beta brass, CuZn. An isotope effect is predicted for magnetic phase transitions if the transition temperature is below Debye temperature. The long range order parameter obtained from diffraction data can only be compared with predictions of models that incorporate the role of thermal vibrations and not otherwise.

physics.gen-ph↗

arXiv2009

Relation between ab initio molecular dynamics and electron-phonon interaction formalisms

The relation between ab initio molecular dynamics formalism and the electron-phonon interaction formalism [P.B. Allen and V. Heine, J. Phys. C 9, 2305 (1976)] is explored. The fundamental quantity obtained in the AIMD formalism - total energy for any configuration - is also obtained from the formalism (ES-DWF) that incorporates the role of Debye-Waller Factor in electronic structure calculations. The two formalisms are exactly equivalent and represent the direct and perturbation theory approaches to determine total energy. This equivalence allows either formalism to be used depending on the requirement - ES-DWF for a priori theoretical analysis and AIMD for ab initio modeling of the effect of thermal vibrations. Combining the two formalisms makes the ES-DWF formalism into an ab initio method and increases the range of problems that can be modeled ab initio. It is also theoretically possible to obtain self-consistent band structures from AIMD calculations. This study clarifies the incorrect assumptions regarding the two formalisms that exist in published literature. By combining the two formalisms and including self-energy effects, more accurate results can be obtained, ab initio, within the adiabatic approximation, than by using AIMD alone.

cond-mat.mtrl-sci↗

arXiv2008

Analysis of long range order

A first principles analysis of order-disorder transition in alloys shows that ordering energy is a function of temperature due to thermal vibrations. The inter-nuclear potential energy term converges if zero point vibrations are incorporated and this method can replace the Ewald sum method. Core energy contributions to the ordering energy are stored exclusively in superlattice lines. The effect of electron-phonon interactions on ordering energy is of the same order of magnitude as ordering energy near transition temperatures and cannot be ignored. Ising model and variants are incorrect in explaining alloy phase transitions as they ignore the role of electron-phonon interactions without justification. A theoretical formalism that incorporates the Debye-Waller Factor component of electron-phonon interactions in electronic structure calculations already exists and must be adopted when modeling temperature dependent phenomena. It is suggested that DWF correction will account substantially for the discrepancy between experimental and theoretical ordering energy in Ni3V. Thermal vibrations alter magnetic ordering energy at finite temperatures. The role of electron-phonon interactions in alloy and magnetic phase transitions cannot be ignored and must be incorporated in all models. This will also ensure consistency with x-ray and electron diffraction (alloy transitions) and neutron diffraction (magnetic transitions) results. An isotope effect is predicted for (magnetic) phase transitions if the transition temperature is below Debye temperature. Recent observations of an isotope effect in magnetic phase transitions confirm our above conclusions and imply that the role of electron-phonon interactions must be incorporated in all theories and models of magnetism to avoid contradictions.

cond-mat.mtrl-sci↗

arXiv2008

Correct form of the electron wavefunction in periodic solids

The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the assumption underlying the Born-von Karman periodic boundary condition. The source of the difficulty is the incorrect dependence of the Bloch wavefunction on the wavenumber index k. The mathematically impossible consequences can be overcome if the periodic part of the electron wavefunction is represented as un(r), which is dependent only on the band index, n, and is independent of the wavenumber index k. This correct form of the wavefunction is consistent with the Bloch theorem and with all other properties of Bloch wavefunctions. The correct form is also consistent with the Born-von Karman periodic boundary condition. The correct form of the electronic wavefunction in a periodic solid has profound consequences. It simplifies the calculation of electronic structure as only one wavefunction per band, un(r), needs to be evaluated. It brings about a conceptual unification between the band picture favored by physicists and the bond picture favored by chemists. The correct form of the electron wavefunction will simplify the understanding of many phenomena involving valence electrons.

cond-mat.mtrl-sci↗

arXiv2006

Probabilistic method to determine electron correlation energy

A new method to determine electron correlation energy is described. This method is based on a better representation of the potential due to interacting electrons that is obtained by specifying both the average and standard deviation. The standard deviation is determined from a probabilistic interpretation of the Coulomb interaction between electrons. This leads to a better representation of orbital energies as Ei (plus-minus) delta(Ei), where Ei is the Hartree-Fock orbital energy and delta(Ei), the spread, is an indicator of the magnitude of correlation energy. This new representation of the potential when combined with an empirical constant leads naturally to a new method to determine electron correlation energy. Correlation energy is determined within the independent electron approximation without any contribution from higher energy unoccupied states. A consistent physical interpretation that an electron occupies a given position when other electrons are farther than on average can be made. It is a general technique that can be used to determine correlation energy in any system of particles with inter-particle interaction V(r1, r2) and can be considered to be universal first step beyond mean-field theory.

cond-mat.mtrl-sci↗

arXiv2005

Non-exponential time-correlation function for random physical processes

The exponential correlation function is theoretically incorrect in the entire frequency range of interest for processes described in terms of linear response theory. The Lorentzian lineshape results from an inconsistent assumption of exponential correlation at timescales smaller than the relaxation time. A new correlation function is proposed that avoids the deficiencies of the exponential function. Comparison on dielectric relaxation in gases shows that the new correlation function can be used to fit data satisfactorily instead of the exponential function. The new correlation function is theoretically consistent for all processes described in terms of linear response theory. Its additional mathematical superiority implies that it can be used instead of the exponential function for all such processes.

cond-mat.stat-mech↗

arXiv2004

Form of the exact partition function for the generalized Ising Model

The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is obtained for the probability of occurrence of any configuration. A closed form expression is obtained for the partition function per spin in terms of the energy levels of this cluster with the degeneracies being a function of temperature. On physical grounds it is suggested to be the form of the exact partition function per spin. The partition functions of Ising-like systems all have a common form. For the 3D Ising model seven functions need to be determined to describe the partition function completely. The key to understanding second order phase transitions and critical phenomena lies in the temperature dependence of various degeneracies. It is necessary to develop new techniques to determine the partition function that account for this temperature dependence, as it would represent the underlying physics correctly.

cond-mat.stat-mech↗