Simulations of the dissociation of small helium clusters with ab initio molecular dynamics in electronically excited states Kristina D. Closser, Oliver Gessner, and Martin Head-Gordon Citation: The Journal of Chemical Physics 140, 134306 (2014); doi: 10.1063/1.4869193 View online: http://dx.doi.org/10.1063/1.4869193 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/13?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Multiple time step integrators in ab initio molecular dynamics J. Chem. Phys. 140, 084116 (2014); 10.1063/1.4866176 Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. II. Photoionization J. Chem. Phys. 135, 154302 (2011); 10.1063/1.3649943 Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. I. Photoabsorption J. Chem. Phys. 135, 154301 (2011); 10.1063/1.3649942 Ground state structures and excited state dynamics of pyrrole-water complexes: Ab initio excited state molecular dynamics simulations J. Chem. Phys. 128, 034304 (2008); 10.1063/1.2822276 Molecular dynamics simulation with an ab initio potential energy function and finite element interpolation: The photoisomerization of cis-stilbene in solution J. Chem. Phys. 108, 8773 (1998); 10.1063/1.475397
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.129.164.186 On: Fri, 19 Dec 2014 16:54:44
THE JOURNAL OF CHEMICAL PHYSICS 140, 134306 (2014)
Simulations of the dissociation of small helium clusters with ab initio molecular dynamics in electronically excited states Kristina D. Closser,1,2 Oliver Gessner,2 and Martin Head-Gordon1,2,a) 1
Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA Ultrafast X-Ray Science Laboratory, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 2
(Received 21 December 2013; accepted 11 March 2014; published online 4 April 2014) The dynamics resulting from electronic excitations of helium clusters were explored using ab initio molecular dynamics. The simulations were performed with configuration interaction singles and adiabatic classical dynamics coupled to a state-following algorithm. 100 different configurations of He7 were excited into the 2s and 2p manifold for a total of 2800 trajectories. While the most common outcome (90%) was complete fragmentation to 6 ground state atoms and 1 excited state atom, 3% of trajectories yielded bound, He∗2 , and 20 eV) for electronic excitations, the non-uniformity of the cluster sizes, and the multitude of simultaneously progressing dynamic channels pose significant challenges.3, 14 Recent work at Lawrence Berkeley National Lab has added greatly to the current understanding of electronically excited states and found, at least for large clusters, that excitations lead to different relaxation channels based on the energy and location of the initial excitation.9–12 However, significant uncertainties remain on the mechanism of the excitation decay, especially at the atomic scale. Theoretical studies of helium clusters have also been rather limited due to the inherent challenges in computing excited states of extended systems with many nearly degenerate states. Large scale semi-empirical models, such as the step potential model with hard sphere scattering,11, 12 and the liquid drop model,3, 15 do not contain any microscopic information and are not capable of capturing atomic level details. Ab initio dynamics of ground-state neutral16, 17 and ionized helium clusters18 have been investigated, but dynamics in the excited states remain elusive. Our earlier work19 on 7- and 25-atom clusters and that of von Haeften and Fink20 on He7 probed a) Electronic mail: [email protected]
0021-9606/2014/140(13)/134306/12/$30.00
the vertically excited states of small helium clusters yielding insight at the atomic level for static states. However, these did not account for any dynamics resulting from the initial excitation. Treating both the nuclei and electrons quantum mechanically rapidly becomes intractable as the system size grows. Thus, most ab initio molecular dynamics (AIMD) calculations rely on mixed quantum-classical methods where the nuclei are propagated classically and the electrons quantum mechanically on a single state of the system. Adiabatic or Born-Oppenheimer AIMD of ground electronic states has an extensive history and can be a useful tool for studying non-stationary systems.21, 22 This method does not require any foreknowledge of the behavior of the system, and the adiabatic approximation is generally valid as long as the Born-Oppenheimer approximation holds. Near conical intersections and avoided crossings, the motion of nuclei and electrons cannot be straightforwardly separated and the adiabatic picture breaks down. Attempts to expand AIMD to excited states and nonadiabatic dynamics have met with varying degrees of success.23–30 The most common methods for contending with interacting potential surfaces, which give rise to non-adiabatic transitions, are variations of Tully’s surface hopping.31–33 Surface hopping algorithms probabilistically allow switching between surfaces and necessarily involve large numbers of trajectories for each initial state. They also lack a fully rigorous derivation, and are especially problematic when multiple nearly degenerate regions exist or when passing through more than one interaction region.34, 35 Alternative methods for computing molecular dynamics involve following the excited state Born-Oppenheimer (adiabatic) surface, transforming to a diabatic representation, and Ehrenfest (mean-field) dynamics.36 All of these also have their weaknesses: purely Born-Oppenheimer dynamics often do not give physically relevant results,37 converting to diabatic representations is not entirely well defined,38, 39 and Eherenfest dynamics are not microscopically reversible.36
140, 134306-1
© 2014 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.129.164.186 On: Fri, 19 Dec 2014 16:54:44
134306-2
Closser, Gessner, and Head-Gordon
Our primary interest here is to determine the fate of helium cluster excitations. Since the excitations are into a dense manifold of states it is impractical to run statistically relevant numbers of trajectories in all possible states. Thus, we have adopted a slightly different approach and use a deterministic algorithm, which is similar to Born-Oppenheimer dynamics much of the time, but preferentially follows the diabatic state when near-degeneracies occur. A single trajectory for each excited state is launched with zero kinetic energy (KE), which implies that all kinetic energy developed during the course of the trajectory is a direct result of the forces exerted by the excited state. After the initial excitation, a recently developed state following algorithm selects the subsequent state based on the character and energy of the previous state.40 The high cost of calculating trajectories “on the fly” dictates the underlying electronic structure method be as efficient as possible. For excited states, time-dependent density functional theory (TDDFT) is often the best option. It is efficient and can give very good results, provided the functional is chosen carefully.25, 26, 30 Wavefunction based methods are also attractive in some cases as they generally have more predictable errors. However, with the notable exceptions of configuration interaction singles (CIS) and time-dependent Hartree-Fock (TDHF), they are computationally more demanding.23, 27, 28 For most systems, CIS and TDHF yield poorer results than TDDFT due to the lack of electron-correlation, but in certain circumstances they may be preferable. One such instance is with Rydberg states that suffer from self-interaction error for standard density functionals.41, 42 Previously, we reported19 theoretical studies on the static excited states of small clusters (Hen , n = 7, 25) for 2s and 2p excited states. It was found that a good description of the excited states could be obtained using comparatively cheap CIS calculations and that the potential well depths, at least for the 2s and 2p states, correlated strongly with the blue shift of the excitation. Here, we investigate the fate of He7 excitations by AIMD coupled with state following, and present the results of atomically resolved dynamics for relaxation of He∗7 clusters excited initially into the n = 2 manifold (
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.129.164.186 On: Fri, 19 Dec 2014 16:54:44
THE JOURNAL OF CHEMICAL PHYSICS 140, 134306 (2014)
Simulations of the dissociation of small helium clusters with ab initio molecular dynamics in electronically excited states Kristina D. Closser,1,2 Oliver Gessner,2 and Martin Head-Gordon1,2,a) 1
Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA Ultrafast X-Ray Science Laboratory, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 2
(Received 21 December 2013; accepted 11 March 2014; published online 4 April 2014) The dynamics resulting from electronic excitations of helium clusters were explored using ab initio molecular dynamics. The simulations were performed with configuration interaction singles and adiabatic classical dynamics coupled to a state-following algorithm. 100 different configurations of He7 were excited into the 2s and 2p manifold for a total of 2800 trajectories. While the most common outcome (90%) was complete fragmentation to 6 ground state atoms and 1 excited state atom, 3% of trajectories yielded bound, He∗2 , and 20 eV) for electronic excitations, the non-uniformity of the cluster sizes, and the multitude of simultaneously progressing dynamic channels pose significant challenges.3, 14 Recent work at Lawrence Berkeley National Lab has added greatly to the current understanding of electronically excited states and found, at least for large clusters, that excitations lead to different relaxation channels based on the energy and location of the initial excitation.9–12 However, significant uncertainties remain on the mechanism of the excitation decay, especially at the atomic scale. Theoretical studies of helium clusters have also been rather limited due to the inherent challenges in computing excited states of extended systems with many nearly degenerate states. Large scale semi-empirical models, such as the step potential model with hard sphere scattering,11, 12 and the liquid drop model,3, 15 do not contain any microscopic information and are not capable of capturing atomic level details. Ab initio dynamics of ground-state neutral16, 17 and ionized helium clusters18 have been investigated, but dynamics in the excited states remain elusive. Our earlier work19 on 7- and 25-atom clusters and that of von Haeften and Fink20 on He7 probed a) Electronic mail: [email protected]
0021-9606/2014/140(13)/134306/12/$30.00
the vertically excited states of small helium clusters yielding insight at the atomic level for static states. However, these did not account for any dynamics resulting from the initial excitation. Treating both the nuclei and electrons quantum mechanically rapidly becomes intractable as the system size grows. Thus, most ab initio molecular dynamics (AIMD) calculations rely on mixed quantum-classical methods where the nuclei are propagated classically and the electrons quantum mechanically on a single state of the system. Adiabatic or Born-Oppenheimer AIMD of ground electronic states has an extensive history and can be a useful tool for studying non-stationary systems.21, 22 This method does not require any foreknowledge of the behavior of the system, and the adiabatic approximation is generally valid as long as the Born-Oppenheimer approximation holds. Near conical intersections and avoided crossings, the motion of nuclei and electrons cannot be straightforwardly separated and the adiabatic picture breaks down. Attempts to expand AIMD to excited states and nonadiabatic dynamics have met with varying degrees of success.23–30 The most common methods for contending with interacting potential surfaces, which give rise to non-adiabatic transitions, are variations of Tully’s surface hopping.31–33 Surface hopping algorithms probabilistically allow switching between surfaces and necessarily involve large numbers of trajectories for each initial state. They also lack a fully rigorous derivation, and are especially problematic when multiple nearly degenerate regions exist or when passing through more than one interaction region.34, 35 Alternative methods for computing molecular dynamics involve following the excited state Born-Oppenheimer (adiabatic) surface, transforming to a diabatic representation, and Ehrenfest (mean-field) dynamics.36 All of these also have their weaknesses: purely Born-Oppenheimer dynamics often do not give physically relevant results,37 converting to diabatic representations is not entirely well defined,38, 39 and Eherenfest dynamics are not microscopically reversible.36
140, 134306-1
© 2014 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.129.164.186 On: Fri, 19 Dec 2014 16:54:44
134306-2
Closser, Gessner, and Head-Gordon
Our primary interest here is to determine the fate of helium cluster excitations. Since the excitations are into a dense manifold of states it is impractical to run statistically relevant numbers of trajectories in all possible states. Thus, we have adopted a slightly different approach and use a deterministic algorithm, which is similar to Born-Oppenheimer dynamics much of the time, but preferentially follows the diabatic state when near-degeneracies occur. A single trajectory for each excited state is launched with zero kinetic energy (KE), which implies that all kinetic energy developed during the course of the trajectory is a direct result of the forces exerted by the excited state. After the initial excitation, a recently developed state following algorithm selects the subsequent state based on the character and energy of the previous state.40 The high cost of calculating trajectories “on the fly” dictates the underlying electronic structure method be as efficient as possible. For excited states, time-dependent density functional theory (TDDFT) is often the best option. It is efficient and can give very good results, provided the functional is chosen carefully.25, 26, 30 Wavefunction based methods are also attractive in some cases as they generally have more predictable errors. However, with the notable exceptions of configuration interaction singles (CIS) and time-dependent Hartree-Fock (TDHF), they are computationally more demanding.23, 27, 28 For most systems, CIS and TDHF yield poorer results than TDDFT due to the lack of electron-correlation, but in certain circumstances they may be preferable. One such instance is with Rydberg states that suffer from self-interaction error for standard density functionals.41, 42 Previously, we reported19 theoretical studies on the static excited states of small clusters (Hen , n = 7, 25) for 2s and 2p excited states. It was found that a good description of the excited states could be obtained using comparatively cheap CIS calculations and that the potential well depths, at least for the 2s and 2p states, correlated strongly with the blue shift of the excitation. Here, we investigate the fate of He7 excitations by AIMD coupled with state following, and present the results of atomically resolved dynamics for relaxation of He∗7 clusters excited initially into the n = 2 manifold (
