arXiv subjects

Nandini Ananth

Publications and source records attributed to Nandini Ananth.

At least 19 recordsLinked to original sources

arXiv2024

MixPI: Mixed-Time Slicing Path Integral Software for Quantized Molecular Dynamics Simulations

Path Integral Molecular Dynamics (PIMD) is a well established simulation technique to compute exact equilibrium properties for a quantum system using classical trajectories in an extended phase space. Standard PIMD simulations are numerically converged by systematically increasing the number of classical 'beads' or replicas used to represent each particle in the quantum system. Currently available scientific software for PIMD simulations leverage the massively parallel (with respect to number of beads) nature of the classical PIMD Hamiltonian. For particularly high-dimensional systems, contraction schemes designed to reduce the overall number of beads per particle required to achieve numerical convergence are also frequently employed. However, these implementations all rely on using the same number of beads to represent all atoms/particles, and become inefficient in systems with a large number of atoms where only a handful contribute significant quantum effects. Mixed time slicing (mixTS) offers an alternate path to efficient PIMD simulations by providing a framework where numerical convergence can be achieved with different numbers of beads for different types of atoms. Unfortunately, mixTS is not available in existing PIMD software. In this paper, we introduce MixPI for atomistic mixTS-PIMD simulations within the open-source software package CP2K. We demonstrate the use of MixPI in two different benchmark systems: we explore the use of mixTS in computing radial distributions functions for water, and in a more significant demonstration, for a solvated Co2+ ion represented as a classical Co3+ ion in water with an explicit, quantized 1024-bead electron localized on the metal ion.

physics.chem-ph↗

arXiv2024

Hybrid Quantum Algorithm for Simulating Real-Time Thermal Correlation Functions

We present a hybrid Path Integral Monte Carlo (hPIMC) algorithm to calculate real-time quantum thermal correlation functions and demonstrate its application to open quantum systems. The hPIMC algorithm leverages the successes of classical PIMC as a computational tool for high-dimensional system studies by exactly simulating dissipation using the Feynman-Vernon influence functional on a classical computer. We achieve a quantum speed-up over the classical algorithm by computing short-time matrix elements of the quantum propagator on a quantum computer. We show that the component of imaginary-time evolution can be performed accurately using the recently developed Probabilistic Imaginary-Time Evolution (PITE) algorithm, and we introduce a novel low-depth circuit for approximate real-time evolution under the kinetic energy operator using a Discrete Variable Representation (DVR). We test the accuracy of the approximation by computing the position-position thermal correlation function of a proton transfer reaction.

quant-ph↗

arXiv2024

Semiclassical Dynamics in Wigner Phase Space I : Adiabatic Hybrid Wigner Dynamics

The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In paper I, focusing on adiabatic single surface processes, we derive the well-known Double Herman-Kluk (DHK) approximation for real-time correlation functions in Wigner phase space, and connect it to the Linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important `system' degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the `bath') at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators, and the decoherence of vibrational probability density of a model I$_2$ Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign-problem and employs a reduced dimensional prefactor bringing calculations of complex system-bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes.

physics.chem-ph↗

arXiv2024

Semiclassical Dynamics in Wigner Phase Space II : nonadiabatic Hybrid Wigner Dynamics

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important `system' degrees of freedom to be quantized using high-level Double Herman-Kluk SC theory while describing the rest (the `bath') using classical-limit Linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.

physics.chem-ph↗

arXiv2024

Mean-Field Ring Polymer Rates Using a Population Dividing Surface

Mean-field Ring Polymer Molecular Dynamics (MF-RPMD) offers a computationally efficient method for the simulation of reaction rates in multi-level systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, the dividing surface must be chosen to explicitly sample kinked ring polymer configurations where at least one bead is in a different electronic state than the others. Building on this, we introduce a population difference coordinate and a kink-constrained dividing surface, and we test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems as well as spin-boson models. We demonstrate that this new MF-RPMD rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

physics.chem-ph↗

arXiv2023

A Linearized Semiclassical dynamics study of the multi-quantum vibrational relaxation of NO scattering from a Au(111) Surface

The vibrational relaxation of NO molecules scattering from an Au(111) surface has served as the focus of efforts to understand nonadiabatic energy transfer at metal-molecule interfaces. Experimental measurements and previous theoretical efforts suggest that multi-quantal NO vibrational energy relaxation occurs via electron hole pair excitations in the metal. Here, using a Linearized Semiclassical approach, we accurately predict the vibrational relaxation of NO from $\nu_i=3$ state for different incident translational energies. We also accurately capture the central role of transient electron transfer from the metal to the molecule in mediating vibrational relaxation process, but fall short of quantitatively predicting the full extent of multi-quantum relaxation for high incident vibrational excitations ($\nu_i = 16$).

quant-ph↗

arXiv2023

Nonadiabatic simulations of photoisomerization and dissociation in ethylene using ab initio classical trajectories

We simulate the nonadiabatic dynamics of photo-induced isomerization and dissociation in ethylene using ab initio classical trajectories in an extended phase space of nuclear and electronic variables. This is achieved by employing the Linearized Semiclassical Initial Value Representation (LSC-IVR) method for nonadiabatic dynamics where discrete electronic states are mapped to continuous classical variables using either the Meyer-Miller Stock-Thoss representation or a more recently introduced spin mapping approach. Trajectory initial conditions are sampled by constraining electronic state variables to a single initial excited state, and by drawing nuclear phase space configurations from a Wigner distribution at finite temperature. An ensemble of classical ab initio trajectories are then generated to compute thermal population correlation functions and to analyze the mechanisms of isomerization and dissociation. Our results serve as a demonstration that this parameter-free semiclassical approach is computationally efficient and accurate, identifying mechanistic pathways in agreement with previous theoretical studies, and also uncovering dissociation pathways observed experimentally.

physics.chem-ph↗

arXiv2022

Non-Linear Correlation Functions and Zero-Point Energy Flow in Mixed Quantum-Classical Semiclassical Dynamics

Mixed Quantum Classical (MQC)-IVR is a recently introduced semiclassical framework that allows for selective quantization of the modes of a complex system. In the quantum limit, MQC reproduces the semiclassical Double Herman-Kluk IVR results, accurately capturing nuclear quantum coherences and conserving zero-point energy. However, in the classical limit, while MQC mimics the Husimi-IVR for real-time correlation functions with linear operators, it is significantly less accurate for non-linear correlation functions with errors even at time zero. Here, we identify the origin of this discrepancy in the MQC formulation and propose a modification. We analytically show that the modified MQC approach is exact for all correlation functions at time zero, and in a study of zero-point energy (ZPE) flow, we numerically demonstrate that it correctly obtains the quantum and classical limits as a function of time. Interestingly, while classical-limit MQC simulations show the expected, unphysical ZPE leakage, we find it is possible to predict and even modify the direction of ZPE flow through selective quantization of the system, with the quantum-limit modes accepting energy additions but preserving the minimum quantum mechanically required energy.

physics.chem-ph↗

arXiv2022

A Semiclassical Framework for Mixed Quantum Classical Dynamics

Semiclassical approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature we introduce Modified Filinov filtration as a powerful tool for mixed quantum-classical simulations in a uniform semiclassical framework.

physics.chem-ph↗

arXiv2021

A Skew Dividing Surface for Accurate Nonadiabatic Mean-Field Ring Polymer Rates

Mean-Field Ring Polymer Molecular Dynamics (MF-RPMD) is a powerful, efficient, and accurate method for approximate quantum dynamic simulations of multi-level system dynamics. Initial efforts to compute nonadiabatic reaction rates using MF-RPMD were not successful; recent work showed that this can be remedied by including a simple, if adhoc, correction term that accounts for the formation of `kinked' or mixed electronic state ring polymer configurations. Here, we build on this idea, introducing a electronic state population based reaction coordinate and novel skew dividing surface that constrains nuclear positions to configurations where the reactant and product state potentials are near-degenerate and that samples kinked electronic state configurations. We then demonstrate the numerical accuracy of this method in computing rates for a series of nonadiabatic model systems.

physics.chem-ph↗

arXiv2020

Multistate ring polymer instantons and nonadiabatic reaction rates

We present two multistate ring polymer instanton (RPI) formulations, both obtained from an exact path integral representation of the quantum canonical partition function for multistate systems. The two RPIs differ in their treatment of the electronic degrees of freedom; whereas the Mean-Field (MF)-RPI averages over the electronic state contributions, the Mapping Variable (MV)-RPI employs explicit continuous Cartesian variables to represent the electronic states. We compute both RPIs for a series of model two-state systems coupled to a single nuclear mode with electronic coupling values chosen to describe dynamics in both adiabatic and nonadiabatic regimes. We show that the MF-RPI for symmetric systems are in good agreement with previous literature, and we show that our numerical techniques are robust for systems with non-zero driving force. The nuclear MF-RPI and the nuclear MV-RPI are similar, but the MV-RPI uniquely reports on the changes in the electronic state populations along the instanton path. In both cases, we analytically demonstrate the existence of a zero-mode and we numerically and that these solutions are true instantons with a single unstable mode as expected for a first order saddle point. Finally, we use the MF-RPI to accurately calculate rate constants for adiabatic and nonadiabatic model systems with the coupling strength varying over three orders of magnitude.

physics.chem-ph↗

arXiv2019

Semiclassical dynamics in the mixed quantum-classical limit

The semiclassical Double Herman-Kluk Initial Value Representation is an accurate approach to computing quantum real time correlation functions, but its applications are limited by the need to evaluate an oscillatory integral. In previous work, we have shown that this `sign problem' can be mitigated using the modified Filinov filtration technique to control the extent to which individual modes of the system contribute to the overall phase of the integrand. Here we follow this idea to a logical conclusion: we analytically derive a general expression for the mixed quantum-classical limit of the semiclassical correlation function - AMQC-IVR, where the phase contributions from the `classical' modes of the system are filtered while the `quantum' modes are treated in the full semiclassical limit. We numerically demonstrate the accuracy and efficiency of the AMQC-IVR formulation in calculations of quantum correlation functions and reaction rates using three model systems with varied coupling strengths between the classical and quantum subsystems. We also introduce a separable prefactor approximation that further reduces the computational cost, but is only accurate in the limit of weak coupling between the quantum and classical subsystems.

physics.chem-ph↗

arXiv2018

Anticipating acene-based chromophore spectra with molecular orbital arguments

Recent synthetic studies on the organic molecules tetracene and pentacene have found certain dimers and oligomers to exhibit an intense absorption in the visible region of the spectrum which is not present in the monomer or many previously-studied dimers. In this article we combine experimental synthesis with electronic structure theory and spectral computation to show that this absorption arises from an otherwise dark charge-transfer excitation 'borrowing intensity' from an intense UV excitation. Further, by characterizing the role of relevant monomer molecular orbitals, we arrive at a design principle that allows us to predict the presence or absence of an additional absorption based on the bonding geometry of the dimer. We find this rule correctly explains the spectra of a wide range of acene derivatives and solves an unexplained structure-spectrum phenomenon first observed seventy years ago. These results pave the way for the design of highly absorbent chromophores with applications ranging from photovoltaics to liquid crystals.

physics.chem-ph↗

arXiv2017

Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation

We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian to treat electronic and nuclear degrees of freedom (dofs) within a consistent dynamic framework. We introduce an efficient symplectic integration scheme, the MInt algorithm, for numerical time-evolution of the nuclear and electronic phase space variables as well as the Monodromy matrix, under the non-separable MMST Hamiltonian. We then calculate the probability of transmission through a curve-crossing in model two-level systems and show that in the quantum limit MQC-IVR is in good agreement with the exact quantum results, whereas in the classical limit the method yields results in keeping with mean-field approaches like the Linearized Semiclassical IVR. Finally, exploiting the ability of MQC-IVR to quantize different dofs to different extents, we present a detailed study of the extents to which quantizing the nuclear and electronic dofs improves numerical convergence properties without significant loss of accuracy.

physics.chem-ph↗

arXiv2017

Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics

The Mixed Quantum-Classical Initial Value Representation (MQC-IVR) is a recently introduced approximate semiclassical (SC) method for the calculation of real-time quantum correlation functions. MQC-IVR employs a modified Filinov filtration (MFF) scheme to control the overall phase of the SC integrand, extending the applicability of SC methods to complex systems while retaining their ability to accurately describe quantum coherence effects. Here, we address questions regarding the effectiveness of the MFF scheme in combination with SC dynamics. Previous work showed that this filtering scheme is of limited utility in the context of semiclassical wavepacket propagation, but we find the MFF is extraordinarily powerful in the context of correlation functions. By examining trajectory phase and amplitude contributions to the real-time SC correlation function in a model system, we clearly demonstrate that the MFF serves to reduce noise by damping amplitude only in regions of highly oscillatory phase leading to a reduction in computational effort while retaining accuracy. Further, we introduce a novel and efficient MQC-IVR formulation that allows for linear scaling in computational cost with the total simulation length, a significant improvement over the more-than quadratic scaling exhibited by the original method.

physics.chem-ph↗

arXiv2017

An Almost Analytical Approach to Simulating 2D Electronic Spectra

We introduce an almost analytical method to simulate 2D electronic spectra as a double Fourier transform of the the non-linear response function (NRF) corresponding to a particular optical pulse sequence. We employ a unitary transformation to represent the total system Hamiltonian in a stationary basis that allows us to separate contributions from decoherence and phonon-mediated population relaxation to the NRF. Previously, one of us demonstrated the use of an analytic, cumulant expansion approach to calculate the decoherence term. Here, we extend this idea to obtain an accurate expression for the population relaxation term, a significant improvement over standard quantum master equation-based approximations. We numerically demonstrate the accuracy of our method by computing the photon echo spectrum of a two-level system coupled to a thermal bath, and we highlight the mechanistic insights obtained from our simulation.

quant-ph↗

arXiv2016

State Space Path Integrals for Electronically Nonadiabatic Reaction Rates

We present a state-space-based path integral method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. We employ an exact path integral in discrete electronic states and continuous Cartesian nuclear variables to obtain a transition state theory (TST) estimate to the rate. A dynamic recrossing correction to the TST rate is then obtained from real-time dynamics simulations using mean field ring polymer molecular dynamics. We employ two different reaction coordinates in our simulations and show that, despite the use of mean field dynamics, the use of an accurate dividing surface to compute TST rates allows us to achieve remarkable agreement with Fermi's golden rule rates for nonadiabatic ET in the normal regime of Marcus theory. Further, we show that using a reaction coordinate based on electronic state populations allows us to capture the turnover in rates for ET in the Marcus inverted regime.

physics.chem-ph↗

arXiv2016

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation

We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting expression is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact propagator lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact propagator, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.

physics.chem-ph↗