Interfacing the Ab Initio Multiple Spawning Method with Electronic

Article pubs.acs.org/JPCA

Interfacing the Ab Initio Multiple Spawning Method with Electronic Structure Methods in GAMESS: Photodecay of trans-Azomethane Alexander Gaenko,†,‡ Albert DeFusco,§ Sergey A. Varganov,∥ Todd J. Martínez,⊥ and Mark S. Gordon*,†,‡ †

Ames Laboratory, ‡Department of Chemistry, Iowa State University, Ames, Iowa 50010, United States § Center for Simulation and Modeling, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States ∥ Department of Chemistry, University of Nevada, Reno, Reno Nevada 89557-0216, United States ⊥ Department of Chemistry, Stanford University, Stanford, California 94305-5080, United States S Supporting Information *

ABSTRACT: This work presents a nonadiabatic molecular dynamics study of the nonradiative decay of photoexcited trans-azomethane, using the ab initio multiple spawning (AIMS) program that has been interfaced with the General Atomic and Molecular Electronic Structure System (GAMESS) quantum chemistry package for on-the-fly electronic structure evaluation. The interface strategy is discussed, and the capabilities of the combined programs are demonstrated with a nonadiabatic molecular dynamics study of the nonradiative decay of photoexcited trans-azomethane. Energies, gradients, and nonadiabatic coupling matrix elements were obtained with the state-averaged complete active space self-consistent field method, as implemented in GAMESS. The influence of initial vibrational excitation on the outcome of the photoinduced isomerization is explored. Increased vibrational excitation in the CNNC torsional mode shortens the excited state lifetime. Depending on the degree of vibrational excitation, the excited state lifetime varies from ∼60−200 fs. These short lifetimes are in agreement with time-resolved photoionization mass spectroscopy experiments.

1. INTRODUCTION

beyond the Born−Oppenheimer approximation are necessary to follow the evolution of molecules upon photoexcitation. Several trajectory-based nonadiabatic dynamics methods exist that have been found to be extremely useful in understanding excited state phenomena. The Ehrenfest approximation6 introduces a quantum-classical coupling via a mean-field back-reaction force acting on classically moving nuclei.7 The trajectory-based Ab initio Multiconfigurational Ehrenfest (AI-MCE) method, developed by Saita and Shalashilin,8 uses adiabatic electronic states and the nonadiabatic coupling matrix element to form the Ehrenfest force. The surface hopping (SH) method developed by Tully9 models nonadiabatic processes as stochastic hops between adiabatic potential energy surfaces. The SH method has been extensively utilized10 with both on-the-fly ab initio electronic structure evaluation and fitted potentials. A number of methods go beyond the adiabatic (Born−Oppenheimer) approximation by computing electronic and nuclear wave functions. For example, the nuclear-electronic orbital (NEO) method, implemented in GAMESS, represents the mixed electronic-nuclear wave function as a linear combination of Gaussian basis functions;11,12 together with the dynamic reaction path method,13

1,2

Solar energy is inherently intermittent, and an efficient method to store the energy is required for later use; chemical storage is a viable approach for accumulating solar energy at large scales. Hence, understanding and mimicking the naturally occurring solar-to-chemical energy conversion process (photosynthesis) is a key to the development of renewable energy sources.3 For example, the photosynthetic apparatus in plants, algae, and bacteria harvests light through electronic excitation of a multichromophoric antenna array, and then the excitation energy is directed to a reaction center, where it is stored as chemical energy for future use by the organism.4 Computational studies have been extremely valuable in elucidating the relationship between the structure and efficiency of photochemical systems. Ab initio molecular dynamics (AIMD) methods provide the capability to simulate the time-dependent conformational and electronic degrees of freedom of a molecular system. With AIMD methods, the time evolution of a photochemical system can be modeled, while the energies of relevant electronic states are computed “on the fly” using high accuracy ab initio methods.5 As the potential energy surfaces of neighboring electronic states of photochemical systems become more closely spaced, the behavior of the electronic and nuclear degrees of freedom become increasingly nonadiabatic. Hence, nonadiabatic dynamics methods that go © 2014 American Chemical Society

Received: August 14, 2014 Revised: October 18, 2014 Published: October 20, 2014 10902

dx.doi.org/10.1021/jp508242j | J. Phys. Chem. A 2014, 118, 10902−10908

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time-resolved spectroscopy46 and nonadiabatic dynamics simulations54 have shown that the photodecay of transazomethane from the n−π* excited state to the ground state occurs within 500 fs. This paper is organized as follows: In Section 2, the GAMESS-AIMS interface used in this work is briefly discussed. In Section 3, the computational details and the results of the GAMESS-AIMS study of the photodecay of trans-azomethane from the n−π* excited state are presented. Concluding remarks are presented in Section 4.

the NEO method is especially suitable for studying nonadiabatic phenomena involving hydrogen transfer without introducing explicit time-dependence. Wavepacket propagation schemes provide a more complete description of nonadiabatic dynamics than is possible with trajectory-based methods such as Ehrenfest and SH. The multiconfigurational time dependent Hartree method (MCTDH)14,15 has been used successfully for this purpose. Unfortunately, fully flexible wavepacket schemes scale poorly with dimensionality and generally require analytic functional forms for the potential energy surfaces and their couplings. Ab initio multiple spawning (AIMS)16 is an adaptive basis set nuclear wave function method that has been used to simulate excited state population decay through quantum coherence between electronic states17−19 without empirical parameters. AIMS has been employed to discern competing pathways in observable spectra involving more than one electronic state19 and to simulate time-resolved photoelectron spectra (TRPES).20−26 In some cases, the SH and AIMS methods have been shown to provide comparable results for population decay,27 but the AIMS method includes short time coherence effects that cannot be treated in single trajectory methods like SH.16,28 AIMS has been used with a number of different electronic structure packages for on-the-fly ab initio molecular dynamics calculations,18,29,30 including Molpro31 for on-the-fly ab initio calculations.30 Related methods include those based on Gaussian wavepackets such as the coupled coherent states method32 and the frozen Gaussian variant of MCTDH known as vMCG33 and the direct dynamics DD-vMGC variation.34 Recently, the ab initio multiple cloning (AIMC) method35 has been developed in which each trajectory basis function is propagated by the Ehrenfest equations of motion. To understand photochemical processes in complex media, the ability to study photochemical processes in extended molecular systems is essential.36 It has been demonstrated that fragmentation methods, such as the fragment molecular orbital (FMO) and effective fragment potential (EFP) methods, available in the GAMESS (General Atomic and Molecular Electronic structure System) package,37,38 are able to treat extended systems, such as solvated molecules, proteins and polysaccharides.39 The EFP method has been interfaced to ab initio excited state methods to model solvent effects on absorption spectra40 and photochemical processes. Local multireference methods,41 available in the GAMESS package,42 are also able to treat molecular systems in the ground and excited states efficiently. Thus, interfacing the GAMESS package with AIMS facilitates the use of fragmentation methods for AIMD simulations on extended systems. Such applications will be explored in future work. In the present work, the photodecay of trans-azomethane, CH3NNCH3, from the n−π* excited state is used as a benchmark and demonstration of the new AIMS-GAMESS interface. In 1929, Ramsperger studied the photodissociation of azomethane, to produce methyl radicals.43 The experiments performed by Ramsperger could not determine if the methyl radical products were obtained by a concerted or stepwise mechanism. Since then, many more experimental and theoretical studies of the photodissociation of azomethane have been performed.44−49 Gas phase surface hopping simulations have been carried out, using both fitted ab initio potential energy surfaces50−53 and on-the-fly quantum chemical methods.54 While the competition between concerted and stepwise dissociation may not be completely understood, both

2. GAMESS-AIMS INTERFACE In the present work, an AIMD simulation is performed within a client-server paradigm, in which the dynamics code AIMS acts as a client, providing a molecular geometry and requesting an evaluation of the electronic properties from the server electronic structure code GAMESS. At each time step of an AIMS simulation, the molecular geometry and guess molecular orbital (MO) vectors are provided to GAMESS. After the electronic structure evaluation using the input geometry and MOs, AIMS expects the following quantities from GAMESS: (i) energy and gradient vector for each electronic state of interest, (ii) converged configuration interaction (CI) vectors, MO vectors, and the overlap matrix between the guess and the final MO vectors, (iii) oscillator strengths and transition dipole moments for each electronic state, and (iv) nonadiabatic coupling matrix elements between the electronic states. GAMESS must preserve the phase of the converged CI and MO vectors so that AIMS can correctly integrate the equations of motion. An interface code that facilitates the exchange of the required quantities between GAMESS and AIMS was implemented in Fortran 90.55 Additional details are provided in the Supporting Information (SI). 3. NONADIABATIC DECAY OF THE n−π* EXCITED STATE OF TRANS-AZOMETHANE 3.1. Computational Details. AIMS-GAMESS simulations of the nonadiabatic decay of the n−π* excited state were carried out using the state averaged (SA)-complete active space self-consistent field (CASSCF) method with an active space of six electrons in four orbitals, denoted CASSCF(6,4), and the 631G(d) basis set. The active space contains the CC π and π* orbitals and the two lone-pair orbitals on the nitrogen atoms. Sellner et al.54 used the SA-CASSCF(6,4)/6-31G(d), where the ground state and the n−π* excited state were given equal weight, and multireference configuration interaction (MRCI) methods to study the photodecay of trans-azomethane from the n−π* excited state with the Tully surface hopping method. They found good agreement between the CASSCF method and high-level MRCI methods for the photodecay from the n−π* excited state. In this work, the ground state structures of the cis and trans isomers have been optimized with the CASSCF(6,4)/6-31G(d) method. The conical intersection geometry has been optimized with SA-CASSCF(6,4)/6-31G(d), where the ground state and the n−π* excited state have been given equal weights. Singlepoint energies for the ground state and for the n−π* excited state were computed with SA-CASSCF(6,4)/6-31G(d) at the ground state optimized geometries of the cis and trans isomers. The energies are reported relative to the trans-azomethane ground state energy. 10903



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3.3. Conical Intersection Topography. The topography of the potential energy surface near the CASSCF optimized conical intersection is shown in Figure 3 along the tuning

3.2. Excitation Energy and Conical Intersection Region. Good agreement is found between the SA-CASSCF n−π* excitation energy, reported in this work to be 3.82 eV, and the experimental value of 3.6 eV.56 The excitation energy is also in agreement with the excitation energies reported by Sellner et al.54 obtained using several high-level methods. Figure 1 shows the ground and excited state energies for

Figure 3. Energies of the ground state and the n−π* excited state near the S0/S1 conical intersection along displacements in the branching plane along the g⃗IJ and h⃗IJ vectors. The energies are shown relative to the total energy of the degenerate ground and excited states at the optimized conical intersection geometry. The gI⃗ J and h⃗IJ vectors were calculated with SA-CASSCF(6,4)/6-31G(d) at the optimized conical intersection geometry and are shown in Figure 4.

vector gI⃗ J and the coupling vector hIJ⃗ .58 The tuning vector is defined in eq 1 to be the nuclear gradient of the difference between the energy of the n−π* excited state I and the energy of the ground state J. The coupling vector, defined in eq 2, is proportional to the nonadiabatic coupling matrix element (NACME) between the ground state and n−π* excited state. Figure 1. Ground (S0, red font) and n−π* (S1 blue) energies of the cis, trans, and S0/S1 conical intersection optimized geometries. All energies are relative to the trans ground state energy. The geometries were optimized with SA-CASSCF(6,4)/6-31G(d).

gIJ⃗ =

∂ (EI − EJ ) ∂R⃗

hIJ⃗ = (EI − EJ ) ψI |

azomethane at the optimized cis, trans, and conical intersection geometries. The conical intersection geometry was optimized at the SA-CASSCF(6,4)/6-31G(d) level, where the ground state and the n−π* excited state were given equal weights, using the NACME gradient projection method.57 The CNNC dihedral angle was found to be 94.2° at the optimized conical intersection geometry shown in Figure 2.

(1)

∂ |ψ ⟩ ∂R⃗ J

(2)

In eqs 1 and 2 EI and EJ are the energies of the ground and excited electronic states, ψI and ψJ are the wavefucntions of the two states, and R denotes the nuclear coordinates. The origin of Figure 3 is the CASSCF optimized conical intersection geometry. The gI⃗ J and hIJ⃗ vectors, which have been calculated with SA-CASSCF(6,4)/6-31G(d) at the optimized conical intersection geometry, are displayed in Figure 4. Using the topographical indicators introduced by Yarkony,59,60 conical intersections can be classified as either peaked or sloped. A peaked intersection allows for very fast population transfer from the excited state to the ground state in a nonadiabatic process. A sloped intersection may exhibit multiple recrossing events near the conical intersection and slow down the photodecay process. The dimensionless quantity |s|59,60 in eqs 3−6 is used to classify a conical intersection as either peaked or sloped and is derived using both the seam coordinate sI⃗ J, defined in eq 3, and the gI⃗ J and hIJ⃗ vectors: sIJ⃗ =

sx =

Figure 2. SA-CASSCF(6,4)/6-31G(d) optimized S0/S1 conical intersection geometry. The CNNC dihedral angle is 94.2°. 10904

∂ ⎛ EI + EJ ⎞ ⎟ ⎜ ∂R⃗ ⎝ 2 ⎠

(3)

sIJ⃗ ·gIJ⃗ |gIJ⃗ |2

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computed with the SA-CASSCF(6,4)/6-31G(d) method for either the ground state or the n−π* excited state, starting from the torsionally biased trans-azomethane minimum energy structure, as described in Section 3.4. The AIMS simulations each started with a single trajectory basis function propagated along the n−π* excited state potential energy surface. The nonadiabatic coupling matrix elements (NACME) were computed at every time step during the propagation of the trajectory. More basis functions were spawned onto the ground state potential energy surface in regions of high nonadiabatic coupling. The time-dependent population transfer between the n−π* excited state and the ground state was computed by solving the nuclear Schrödinger equation within the TBF basis set at each time-step. As the primary interest here is in the excited state lifetime, TBFs that are spawned to the ground electronic state are terminated when their population reaches 0.99. The electronic wave function ansatz employed here is insufficiently flexible to describe dissociation on the ground state (a larger active space would be required), as evidenced by discontinuities in the PES when the molecule attempts to extrude a CH3 group. Each simulation was ended when the population of the n−π* excited state decreased to 0.01. The velocity Verlet algorithm with a time step of 0.5 fs was used for the classical propagation of the TBF phase space centers. 3.6. Population Decay of n−π* Excited State of transAzomethane. The photodecay from the n−π* excited state to the ground state as a function of time is plotted for each of the three sets of initial conditions in Figure 5. In each case, the

Figure 4. Branching plane vectors. The tuning vector gI⃗ J is the difference between the energy gradients of the excited state and the ground state at the conical intersection geometry. The tuning vector corresponds roughly to displacement of the CNNC dihedral angle. The h⃗IJ vector is the NACME vector, which is also called the coupling vector. The coupling vector corresponds to displacements of the NN bond and the CNN angle. See eqs 1 and 2 in text for the definitions of the g⃗IJ and h⃗IJ vectors.

sy =

|s| =

sIJ⃗ ·hIJ⃗ |hIJ⃗ |2

s x s x + s ys y

(5) (6)

Conical intersections with values of |s| less than unity can be considered to be peaked. The value of |s| for azomethane calculated with SA-CASSCF(6,4)/6-31G(d) is 0.14; therefore, azomethane is considered to have a peaked conical intersection, leading to the prediction that the photodecay of the n−π* excited state to the ground state should be very fast once a nonadiabatic dynamics simulation approaches the conical intersection geometry. 3.4. Nonadiabatic Dynamics: AIMS Initial Conditions. One-photon excitation to the n−π* state is symmetry forbidden in trans-azomethane. As shown by Szalay et al.,61 the 1Bg n−π* state can borrow intensity from a 1Bu Rydberg state as low as 6.4 eV through the Au CNNC dihedral angle vibrational mode. The intensity borrowing spectrum calculated by Szalay et al. is in accordance with the Herzberg−Teller effect62 since, for the C2h point group, the inner product of the A u and the B g irreducible representations is the B u representation. Following the work of Sellner et al.,54 a torsional bias in the AIMS initial conditions has been introduced in this work to mimic intensity sharing. Three sets of initial conditions for the AIMS simulations were prepared: (i) the Wigner distribution63 in the v = 0 vibrational state, (ii) a quasi-classical distribution64 with 5 quanta of bias in the CNNC torsion angle, and (iii) a quasi-classical distribution with 12 quanta of bias in the CNNC torsion angle. Ten sets of position and momenta were taken from each of the three initial condition ensembles and used as starting points for the AIMS simulations. A total of 30 AIMS simulations were run, each of which spawned an average of 18 trajectories to simulate population transfer from the n−π* excited state to the ground state. 3.5. Ab initio Multiple Spawning Simulation. The AIMS method approximates the nuclear Schrödinger equation by expansion in a basis of frozen Gaussian functions called trajectory basis functions (TBFs).16 In the present work, each TBF was propagated classically along a potential energy surface

Figure 5. Time evolution of the population of the n−π* excited state for the three initial conditions. Red: The Wigner distribution in the v = 0 vibrational state. Green: The quasi-classical distribution in the v = 0 vibrational state with an extra 5 quanta in the CNNC torsion mode. Blue: The quasi-classical distribution in the v = 0 vibrational state with an extra 12 quanta in the CNNC torsion mode.

plotted population corresponds to an average over 10 distinct initial conditions. Figure 5 shows that vibrational excitation of the mode corresponding to the CNNC torsion decreases the lifetime of the n−π* excited state by more than 100 fs. The decrease in the lifetime of the n−π* excited state is attributed to increased energy localized in the mode leading from the Franck−Condon structure to the conical intersection geometry shown in Figure 2. With 12 quanta of energy in the CNNC torsion angle, the population of the ground state reaches 90% within 150 fs, which is in agreement with previous surfacehopping simulations.54 At each spawning event, four quantities were recorded: (i) The CNNC dihedral angle, (ii) the energy gap between the 10905



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Figure 6. Histograms of the spawning quantities from all 30 simulations. In each pane, the heights of the histograms have been weighted by the amount of population transfer. The upper pane plots the binned value of the CNNC dihedral angle in green. The CNNC dihedral angle at the optimized conical intersection geometry is shown in red. The middle pane plots the binned energy gap between the ground state and the n−π* excited state. The lower pane is the binned quantity |s| defined in eqs 3−6. The value of |s| at the optimized conical intersection geometry is shown in red.

excited state and the ground state, (iii) the value of |s| and (iv) the amount of population that was transferred from the excited state to the ground state. In Figure 6 quantities (i)−(iii) collected from all 30 AIMS simulations have been binned into a histogram weighted by the amount of population that was transferred from the excited state to the ground state. It is found that the population transfer is most efficient for CNNC dihedral angles near the optimized value of 94.2° and for energy gaps less than 0.002 eV. The values of |s| with large population transfers are also found to be very near the optimized conical intersection value of 0.14. These three quantities confirm the prediction presented in section 3.3 that very fast photodecay of azomethane occurs once the simulation approaches the conical intersection region.

when 12 quanta of energy are added to the CNNC dihedral angle, which is in agreement with previous experimental and theoretical results. No evidence was found for dissociation of CH3 on the excited state surface; only on the ground state surface was significant elongation of the corresponding CN bond observed. It can therefore be concluded that CH3 dissociation occurs on the ground electronic state. In order to establish whether the loss of both CH3 groups occurs in a concerted or stepwise fashion, a more flexible electronic wave function ansatz that can describe simultaneous dissociation of the CH3 groups is needed.

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4. CONCLUSIONS To enable the study of nonadiabatic dynamics of large photosystems (such as solar light harvesting systems), an interface between the GAMESS quantum chemistry software package and the AIMS nonadiabatic dynamics program has been developed. The photoinduced dynamics of the n−π* excited state of trans-azomethane has been studied with the new AIMS-GAMESS interface. Three sets of initial conditions for position and momentum were employed with increasing excitation of the CNNC torsional mode. The simulated lifetime of the n−π* excited state starting from the vibrational ground state was found to be ∼200 fs. As the CNNC torsional mode is more vibrationally excited, the lifetime of the n−π* excited state decreases. The fastest decay time was found to be 150 fs

ASSOCIATED CONTENT

S Supporting Information *

GAMESS-FMS implementation details; (Table S1) list of generalized data exchange API functions with brief descriptions; and (Figure S1) schematic of the client and server interaction via the GDE interface. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 10906



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ACKNOWLEDGMENTS This work was supported by a SciDAC-E grant to MSG from the US Department of Energy, Office of Advanced Scientific Computing Research through the Ames Laboratory and by an NSF grant (OCI-1047577) to TJM. The Ames Laboratory is operated for the US Department of Energy by Iowa State University under contract No. DE-AC02-07CH11358.

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Interfacing the Ab Initio Multiple Spawning Method with Electronic

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