arXiv subjects

Ilya G. Ryabinkin

Publications and source records attributed to Ilya G. Ryabinkin.

31 records · Page 2Linked to original sources

arXiv2017

Improved method for generating exchange-correlation potentials from electronic wave functions

Ryabinkin, Kohut, and Staroverov (RKS) [Phys. Rev. Lett. 115, 083001 (2015)] devised an iterative method for reducing many-electron wave functions to Kohn-Sham exchange-correlation potentials, $v_\text{XC}(\mathbf{r})$. For a given type of wave function, the RKS method is exact (Kohn-Sham-compliant) in the basis-set limit; in a finite basis set, it produces an approximation to the corresponding basis-set-limit $v_\text{XC}(\mathbf{r})$. The original RKS procedure works very well for large basis sets but sometimes fails for commonly used (small and medium) sets. We derive a modification of the method's working equation that makes the RKS procedure robust for all Gaussian basis sets and increases the accuracy of the resulting exchange-correlation potentials with respect to the basis-set limit.

physics.chem-ph↗

arXiv2016

Mixed quantum-classical dynamics using collective electronic variables: A better alternative to electronic friction theories

An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely-spaced electronic states. We propose a mixed quantum-classical scheme that addresses this challenge by introducing collective electronic variables. These variables are defined through analytic block-diagonalization applied to the time-dependent Hamiltonian matrix governing the electronic dynamics. We compare our scheme with the Ehrenfest approach and with a full-memory electronic friction model on a one-dimensional "adatom + atomic chain" model. Our simulations demonstrate that collective-mode dynamics with only few (2-3) electronic variables is robust and can describe a variety of situations: from a chemisorbed atom on an insulator to an atom on a metallic surface. Our molecular model also reveals that the friction approach is prone to unpredictable and catastrophic failures.

physics.chem-ph↗

arXiv2016

Topologically correct quantum nonadiabatic formalism for on-the-fly dynamics

On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical intersections introduce non-trivial geometric or Berry phases which require a special treatment for adequate modelling of the nuclear dynamics. We analyze two approaches for nonadiabatic dynamics using the time-dependent variational principle and the adiabatic representation. The first approach employs adiabatic electronic functions with global parametric dependence on the nuclear coordinates. The second approach uses adiabatic electronic functions obtained only at the centres of moving localized nuclear basis functions (e.g. frozen-width Gaussians). Unless a gauge transformation is used to enforce single-valued boundary conditions, the first approach fails to capture the geometric phase. In contrast, the second approach accounts for the geometric phase naturally because of the absence of the global nuclear coordinate dependence in the electronic functions.

physics.chem-ph↗

arXiv2016

On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods

The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabatic dynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabatic dynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: 1) nuclei have kinetic energy lower than DBOC and 2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically.

physics.chem-ph↗

arXiv2015

Fast numerical evaluation of time-derivative nonadiabatic couplings for mixed quantum-classical methods

We have developed a numerical differentiation scheme which eliminates evaluation of overlap determinants in calculating the time-derivative non-adiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater-determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals, and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.

physics.chem-ph↗

arXiv2015

Reduction of Electronic Wavefunctions to Kohn-Sham Effective Potentials

A method for calculating the Kohn--Sham exchange-correlation potential, $v_\text{XC}(\mathbf{r})$, from a given electronic wavefunction is devised and implemented. It requires on input one- and two-electron density matrices and involves construction of the generalized Fock matrix. The method is free from numerical limitations and basis-set artifacts of conventional schemes for constructing $v_\text{XC}(\mathbf{r})$ in which the potential is recovered from a given electron density, and is simpler than various many-body techniques. The chief significance of this development is that it allows one to directly probe the functional derivative of the true exchange-correlation energy functional and to rigorously test and improve various density-functional approximations.

physics.chem-ph↗

arXiv2015

Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects

Adequate simulation of non-adiabatic dynamics through conical intersection requires account for a non-trivial geometric phase (GP) emerging in electronic and nuclear wave-functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave-function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultra-fast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: 1) compensation for repulsive diagonal second order non-adiabatic couplings and 2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.

physics.chem-ph↗

arXiv2014

Non-stochastic matrix Schrödinger equation for open systems

We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This equation describes dynamics of auxiliary wave-functions $\mathbf{m}$, from which the system density matrix can be reconstructed as $\hatρ = \mathbf{m} \mathbf{m}^\dagger$. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy non-conservation in the time-dependent variational principle applied to mixed states of closed systems.

physics.chem-ph↗

arXiv2014

When do we need to account for the geometric phase in excited state dynamics ?

We investigate the role of the geometric phase (GP) in an internal conversion process when the system changes its electronic state by passing through a conical intersection (CI). Local analysis of a two-dimensional linear vibronic coupling (LVC) model Hamiltonian near the CI shows that the role of the GP is twofold. First, it compensates for a repulsion created by the so-called diagonal Born-Oppenheimer correction (DBOC). Second, the GP enhances the non-adiabatic transition probability for a wave-packet part that experiences a central collision with the CI. To assess the significance of both GP contributions we propose two indicators that can be computed from parameters of electronic surfaces and initial conditions. To generalize our analysis to N-dimensional systems we introduce a reduction of a general N-dimensional LVC model to an effective 2D LVC model using a mode transformation that preserves short-time dynamics of the original N-dimensional model. Using examples of the bis(methylene) adamantyl and butatriene cations, and the pyrazine molecule we have demonstrated that their effective 2D models reproduce the short-time dynamics of the corresponding full dimensional models, and the introduced indicators are very reliable in assessing GP effects.

physics.chem-ph↗

arXiv2013

Analysis of geometric phase effects in the quantum-classical Liouville formalism

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in general two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

quant-ph↗

arXiv2013

Geometric phase effects in low-energy dynamics near conical intersections: A study of the multidimensional linear vibronic coupling model

In molecular systems containing conical intersections (CIs), a nontrivial geometric phase (GP) appears in the nuclear and electronic wave-functions in the adiabatic representation. We study GP effects in nuclear dynamics of an N-dimensional linear vibronic coupling (LVC) model. The main impact of GP on low-energy nuclear dynamics is reduction of population transfer between the local minima of the LVC lower energy surface. For the LVC model, we proposed an isometric coordinate transformation that confines non-adiabatic effects within a two-dimensional subsystem interacting with an N-2 dimensional environment. Since environmental modes do not couple electronic states, all GP effects originate from nuclear dynamics within the subsystem. We explored when the GP affects nuclear dynamics of the isolated subsystem, and how the subsystem-environment interaction can interfere with GP effects. Comparing quantum dynamics with and without GP allowed us to devise simple rules to determine significance of the GP for nuclear dynamics in this model.

quant-ph↗

arXiv2013

Geometric phase effects in dynamics near conical intersections: Symmetry breaking and spatial localization

We show that finite systems with conical intersections can exhibit spontaneous symmetry breaking which manifests itself in spatial localization of eigenstates. This localization has a geometric phase origin and is robust against variation of model parameters. The transition between localized and delocalized eigenstate regimes resembles a continuous phase transition. The localization slows down the low-energy quantum nuclear dynamics at zero and low temperatures.

quant-ph↗

arXiv2013

Accurate and efficient approximation to the optimized effective potential for exchange

We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

physics.chem-ph↗