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Maitra NT. Charge transfer in time-dependent density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:423001. [PMID: 28766507 DOI: 10.1088/1361-648x/aa836e] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
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Khosravi E, Abedi A, Rubio A, Maitra NT. Electronic non-adiabatic dynamics in enhanced ionization of isotopologues of hydrogen molecular ions from the exact factorization perspective. Phys Chem Chem Phys 2017; 19:8269-8281. [DOI: 10.1039/c6cp08539c] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
An exact-factorization perspective of enhanced ionization in isotopologues of H2+ demonstrates the concept of the exact potential driving the electrons in non-adiabatic motion of molecules in strong fields, and sets a new platform for introducing various approximations.
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Luo K, Fuks JI, Maitra NT. Studies of spuriously shifting resonances in time-dependent density functional theory. J Chem Phys 2016; 145:044101. [DOI: 10.1063/1.4955447] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Maitra NT. Perspective: Fundamental aspects of time-dependent density functional theory. J Chem Phys 2016; 144:220901. [DOI: 10.1063/1.4953039] [Citation(s) in RCA: 228] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fuks JI, Nielsen SEB, Ruggenthaler M, Maitra NT. Time-dependent density functional theory beyond Kohn–Sham Slater determinants. Phys Chem Chem Phys 2016; 18:20976-85. [DOI: 10.1039/c6cp00722h] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Different choices of initial Kohn Sham wavefunction shape the time-dependent exchange–correlation potential.
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Khosravi E, Abedi A, Maitra NT. Exact Potential Driving the Electron Dynamics in Enhanced Ionization of H(2)(+). PHYSICAL REVIEW LETTERS 2015; 115:263002. [PMID: 26764989 DOI: 10.1103/physrevlett.115.263002] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2015] [Indexed: 06/05/2023]
Abstract
It was recently shown that the exact factorization of the electron-nuclear wave function allows the construction of a Schrödinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the nuclear degrees of freedom and any external fields. Here we study the exact potential acting on the electron in charge-resonance enhanced ionization in a model one-dimensional H(2)(+) molecule. We show there can be significant differences between the exact potential and that used in the traditional quasistatic analyses, arising from nonadiabatic coupling to the nuclear system, and that these are crucial to include for accurate simulations of time-resolved ionization dynamics and predictions of the ionization yield.
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Agostini F, Abedi A, Suzuki Y, Min SK, Maitra NT, Gross EKU. The exact forces on classical nuclei in non-adiabatic charge transfer. J Chem Phys 2015; 142:084303. [PMID: 25725727 DOI: 10.1063/1.4908133] [Citation(s) in RCA: 60] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
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Fuks JI, Luo K, Sandoval ED, Maitra NT. Time-resolved spectroscopy in time-dependent density functional theory: an exact condition. PHYSICAL REVIEW LETTERS 2015; 114:183002. [PMID: 26000998 PMCID: PMC6135656 DOI: 10.1103/physrevlett.114.183002] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Indexed: 05/17/2023]
Abstract
A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to an exact condition for the exchange-correlation potential of time-dependent density functional theory. The Kohn-Sham potential typically continues to evolve after the field is turned off, which leads to time dependence in the response frequencies of the Kohn-Sham response function. The exchange-correlation kernel must cancel out this time dependence. The condition is typically violated by approximations currently in use, as we demonstrate by several examples, which has severe consequences for their predictions of time-resolved spectroscopy.
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Luo K, Fuks JI, Sandoval ED, Elliott P, Maitra NT. Kinetic and interaction components of the exact time-dependent correlation potential. J Chem Phys 2015; 140:18A515. [PMID: 24832323 DOI: 10.1063/1.4867002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction components and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional two-electron systems. We find that often, but not always, the kinetic contribution is largely responsible for these features that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the interaction component, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. Non-adiabatic features of the kinetic component were also larger than those of the interaction component in cases that we studied when there is negligible step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case.
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Suzuki Y, Abedi A, Maitra NT, Gross EKU. Laser-induced electron localization in H2+: mixed quantum-classical dynamics based on the exact time-dependent potential energy surface. Phys Chem Chem Phys 2015; 17:29271-80. [DOI: 10.1039/c5cp03418c] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
The exact nuclear time-dependent potential energy surface for laser-induced electron localization is studied with a view to developing a mixed quantum-classical dynamics method for strong-field processes.
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Fuks JI, Maitra NT. Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer. Phys Chem Chem Phys 2014; 16:14504-13. [DOI: 10.1039/c4cp00118d] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Adiabatic TDDFT fails for time-resolved charge-transfer in a simple model, even when linear response spectra is accurate.
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Abedi A, Maitra NT, Gross EKU. Response to “Comment on ‘Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction”' [J. Chem. Phys. 139, 087101 (2013)]. J Chem Phys 2013; 139:087102. [DOI: 10.1063/1.4818523] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Fuks JI, Elliott P, Rubio A, Maitra NT. Dynamics of Charge-Transfer Processes with Time-Dependent Density Functional Theory. J Phys Chem Lett 2013; 4:735-739. [PMID: 26281927 DOI: 10.1021/jz302099f] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We show that whenever an electron transfers between closed-shell molecular fragments, the exact correlation potential of time-dependent density functional theory develops a step and peak structure in the bonding region. This structure has a density dependence that is nonlocal both in space and in time that even the exact adiabatic ground-state exchange-correlation functional fails to capture it. For charge-transfer between open-shell fragments, an initial step and peak vanish as the charge-transfer state is reached. The inability of usual approximations to develop these structures leads to inaccurate charge-transfer dynamics. This is illustrated by the complete lack of Rabi oscillations in the dipole moment under conditions of resonant charge transfer for an exactly solvable model system. The results transcend the model and are applicable to more realistic molecular complexes.
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Abedi A, Maitra NT, Gross EKU. Correlated electron-nuclear dynamics: exact factorization of the molecular wavefunction. J Chem Phys 2013; 137:22A530. [PMID: 23249067 DOI: 10.1063/1.4745836] [Citation(s) in RCA: 132] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It was recently shown [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] that the complete wavefunction for a system of electrons and nuclei evolving in a time-dependent external potential can be exactly factorized into an electronic wavefunction and a nuclear wavefunction. The concepts of an exact time-dependent potential energy surface (TDPES) and exact time-dependent vector potential emerge naturally from the formalism. Here, we present a detailed description of the formalism, including a full derivation of the equations that the electronic and nuclear wavefunctions satisfy. We demonstrate the relationship of this exact factorization to the traditional Born-Oppenheimer expansion. A one-dimensional model of the H(2)(+) molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: we show how features of its structure indicate the mechanism of dissociation. We compare the exact TDPES with potential energy surfaces from the time-dependent Hartree-approach, and also compare traditional Ehrenfest dynamics with Ehrenfest dynamics on the exact TDPES.
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Elliott P, Fuks JI, Rubio A, Maitra NT. Universal dynamical steps in the exact time-dependent exchange-correlation potential. PHYSICAL REVIEW LETTERS 2012; 109:266404. [PMID: 23368591 DOI: 10.1103/physrevlett.109.266404] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2012] [Indexed: 06/01/2023]
Abstract
We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially nonlocal and time nonlocal dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of nonequilibrium dynamical situations relevant for modeling of photochemical or physical processes: field-free evolution of a nonstationary state, resonant local excitation, resonant complete charge transfer, and evolution under an arbitrary field. A lack of these steps in the usual approximations yields inaccurate dynamics, for example, predicting faster dynamics and incomplete charge transfer.
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Roy D, Marianski M, Maitra NT, Dannenberg JJ. Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: dispersion, induction, and basis set superposition error. J Chem Phys 2012; 137:134109. [PMID: 23039587 PMCID: PMC3477180 DOI: 10.1063/1.4755990] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2012] [Accepted: 09/17/2012] [Indexed: 11/14/2022] Open
Abstract
We compare dispersion and induction interactions for noble gas dimers and for Ne, methane, and 2-butyne with HF and LiF using a variety of functionals (including some specifically parameterized to evaluate dispersion interactions) with ab initio methods including CCSD(T) and MP2. We see that inductive interactions tend to enhance dispersion and may be accompanied by charge-transfer. We show that the functionals do not generally follow the expected trends in interaction energies, basis set superposition errors (BSSE), and interaction distances as a function of basis set size. The functionals parameterized to treat dispersion interactions often overestimate these interactions, sometimes by quite a lot, when compared to higher level calculations. Which functionals work best depends upon the examples chosen. The B3LYP and X3LYP functionals, which do not describe pure dispersion interactions, appear to describe dispersion mixed with induction about as accurately as those parametrized to treat dispersion. We observed significant differences in high-level wavefunction calculations in a basis set larger than those used to generate the structures in many of the databases. We discuss the implications for highly parameterized functionals based on these databases, as well as the use of simple potential energy for fitting the parameters rather than experimentally determinable thermodynamic state functions that involve consideration of vibrational states.
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Yang ZH, Maitra NT, Burke K. Effect of cusps in time-dependent quantum mechanics. PHYSICAL REVIEW LETTERS 2012; 108:063003. [PMID: 22401064 DOI: 10.1103/physrevlett.108.063003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2011] [Indexed: 05/31/2023]
Abstract
Within nonrelativistic quantum mechanics, spatial cusps in initial wave functions can lead to nonanalytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time analytic.
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Gross EKU, Maitra NT. Introduction to TDDFT. FUNDAMENTALS OF TIME-DEPENDENT DENSITY FUNCTIONAL THEORY 2012. [DOI: 10.1007/978-3-642-23518-4_4] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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Abstract
We investigate the accuracy and efficiency of the semiclassical frozen Gaussian method in describing electron dynamics in real time. Model systems of two soft-Coulomb-interacting electrons are used to study correlated dynamics under non-perturbative electric fields, as well as the excitation spectrum. The results show that a recently proposed method that combines exact-exchange with semiclassical correlation to propagate the one-body density-matrix holds promise for electron dynamics in many situations that either wavefunction or density-functional methods have difficulty describing. The results also however point out challenges in such a method that need to be addressed before it can become widely applicable.
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Abedi A, Maitra NT, Gross EKU. Exact factorization of the time-dependent electron-nuclear wave function. PHYSICAL REVIEW LETTERS 2010; 105:123002. [PMID: 20867633 DOI: 10.1103/physrevlett.105.123002] [Citation(s) in RCA: 231] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2010] [Indexed: 05/26/2023]
Abstract
We present an exact decomposition of the complete wave function for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wave functions that lead to rigorous definitions of a time-dependent potential energy surface (TDPES) and a time-dependent geometric phase. For the H(2)(+) molecular ion exposed to a laser field, the TDPES proves to be a useful interpretive tool to identify different mechanisms of dissociation.
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Rajam AK, Raczkowska I, Maitra NT. Semiclassical electron correlation in density-matrix time propagation. PHYSICAL REVIEW LETTERS 2010; 105:113002. [PMID: 20867568 DOI: 10.1103/physrevlett.105.113002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2010] [Indexed: 05/29/2023]
Abstract
Lack of memory (locality in time) is a major limitation of almost all present time-dependent density-functional approximations. By using semiclassical dynamics to compute correlation effects in the time propagation of the density matrix, we incorporate memory, including initial-state dependence, as well as changing occupation numbers, and predict more observables in strong-field applications.
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Rajam A, Hessler P, Gaun C, Maitra NT. Phase-space explorations in time-dependent density functional theory. ACTA ACUST UNITED AC 2009. [DOI: 10.1016/j.theochem.2009.04.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Tempel DG, Martínez TJ, Maitra NT. Revisiting Molecular Dissociation in Density Functional Theory: A Simple Model. J Chem Theory Comput 2009; 5:770-80. [DOI: 10.1021/ct800535c] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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49
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Krueger AJ, Maitra NT. Autoionizing resonances in time-dependent density functional theory. Phys Chem Chem Phys 2009; 11:4655-63. [DOI: 10.1039/b902787d] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Maitra NT, Burke K. Comment on “Analysis of Floquet formulation of time-dependent density-functional theory”[Chem. Phys. Lett. 433 (2006) 204]. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.04.091] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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