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Articlepubs.acs.org/JPCAFragment Molecular Orbital Nonadiabatic Molecular Dynamics forCondensed Phase SystemsBen Nebgen and Oleg V. Prezhdo*Downloaded via UNIV OF SOUTHERN CALIFORNIA on November 7, 2019 at 23:10:13 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.Department of Chemistry, University of Southern California, Los Angeles, California 90037, United StatesABSTRACT: A method for efficiently simulating nonadiabaticmolecular dynamics (NAMD) of nanoscale and condensed phasesystems is developed and tested. The electronic structure,including force and nonadiabatic coupling, are obtained with thefragment molecular orbital (FMO) approximation, which providessignificant computational savings by splitting the system intofragments and computing electronic properties of each fragmentsubject to the external field due to other all other fragments. Theefficiency of the developed technique is demonstrated by studyingthe effect of explicit solvent molecules on excited state relaxation inthe Fe(CO)4 complex. The relaxation in the gas phase occurs on a50 fs time scale, which is in excellent agreement with previouslyrecorded femtosecond pump probe spectroscopy. Adding asolvation shell of ethanol molecules to the simulation results inan increase in the excited state lifetime to 100 fs, in agreement with recent femtosecond X-ray spectroscopy measurements.1. INTRODUCTIONThe surface hopping (SH) formulation of quantum-classicalnonadiabatic (NA) dynamics, as first explored by Tully in1971,1 has become an important tool in the moderncomputational chemistry toolbox. It is seeing increased use indescribing electron motion in systems such as smallmolecules,2 5 quantum dots,6 8 conjugated π systems,9 16bulk-heterojunctions,17,18 and metal complexes.19 Thesesystems exhibit interesting chemical and physical properties,including singlet fission,12,14,20,21 electron transfer,22,23 protontransfer,4,24 and other excited state reactions that will proveuseful in solving the future energy crisis. However, NAmolecular dynamics (NAMD) methods, such as Ehrenfestdynamics25 28 and surface hopping,1,29 can be very computationally demanding, especially with ab initio description ofelectronic structure. Although full ab initio NAMD calculationshave been performed on solution phase systems in the past,30approximations such as frozen density embedding31 provecritical when large systems or systems with significantenvironmental contributions are simulated.2,32 Current solutions to this problem include parametrizing classical orsemiclassical force fields to ab initio calculations,33 35 orperforming QM/MM calculations with the environment beingsimulated classically.36 A more direct solution, developed in thecurrent work, employs the FMO molecular dynamics(FMOMD) method37 41 to simplify the computationalcomplexity of ab initio NAMD. The FMO technique is usedto compute both the MD trajectory and the NA couplingconstants required for NAMD calculations.The FMO methodology was developed in 1999 by Kitauraand co-workers to treat polymers, molecules in solution, andother systems that can be easily divided into fragments.42 Since 2016 American Chemical Societythen, the method has been used to successfully study a varietyof systems, ranging from proteins,43 such as ubiquitin44 andhuman estrogen receptor,45 to condensed phase reactions.39,46Both the time saving nature of fragmentation due to thenonlinear scaling of quantum simulations and the ease ofparallelization47 have put the FMO method in a good positionto handle the quantum chemistry problems of the future. In theFMO methodology, a large system is initially divided intofragments consisting of a small number of heavy atoms. After aHückel guess is made on each fragment, ab initio calculationsare performed on individual fragments in the presence of theelectric field from all other fragments. The process is repeateduntil the electron densities of each fragment are self-consistentwith the densities on other fragments. This results in anefficient way to obtain the gradient for MD. Here, the FMOmethodology is extended to computation of NA couplingneeded for NAMD.To illustrate and test the developed FMO-NAMD approach,we consider excited state dynamics of the Fe(CO)4 complex inthe gas phase and in solution. Gas phase photodegradation ofFe(CO)5 to form Fe(CO)4 has been extensively studied overthe last few decades to gain a better understanding ofphotodegradation of metal complexes.48 53 Briefly, Fe(CO)5is excited by a 267 nm photon to the first singlet excited state(S1).50 Then, in less than 100 fs, a CO ligand is eliminated,while the molecule still remains in the excited state.50 Followingthe elimination of a ligand, the complex decays into the muchmore stable S0 state, though this state is still higher than theReceived: June 3, 2016Revised: July 21, 2016Published: August 18, 20167205DOI: 10.1021/acs.jpca.6b05607J. Phys. Chem. A 2016, 120, 7205 7212

ArticleThe Journal of Physical Chemistry Atriplet ground state.50,54 The lifetime of the S1 state isdependent on environmental effects. Recent advances in Xray laser femtosecond spectroscopy54,55 has allowed furthercharacterization of the photodegradation of Fe(CO)5 inethanol. Important differences between the gas phase andsolution phase processes have been observed. In particular, it isobserved that the lifetime of the S1 state of Fe(CO)4 in solutionis increased by a factor of 4 over that of the same molecule inthe gas phase, namely, from 50 to 200 fs. Further, the orderingbetween the decay of the S1 state and the attachment of theethanol molecule to the iron core is unknown.54 The NAMDFMO interface is used to investigate this process.SijIJ ⟨φi I φjJ⟩S̅ ijIJ ⟨φ(t )iI φ(t 1) jJ ⟩IJE E Ẽ IIJΔt φIi ⟩Hereis a single basis function located on monomer I, trepresents the current time step, and (t 1) represents theprevious time step. The derivative overlap matrices as well asthe Fock matrices are essential in computing the nonadiabaticcouplings for the FSSH calculations as discussed below.2.2. Calculation of the Nonadiabatic Couplings. Toperform nonadiabatic coupling calculations on the full system,the dimer Fock and overlap matrices are combined to form anapproximate Fock and overlap matrix for the whole system.Because the overlap matrices will not depend on the order ofterms kept in the FMO calculation, they can be obtainedexactly from the dimer calculation by combining the dimermatrices in block fashion.2. THEORY2.1. Fragment Molecular Orbital Method. In thissection the fragment molecular orbital method will be brieflydiscussed. The underlying principal of FMO is the many-bodyexpansion, which is a prescription for computing properties of alarge system using only calculations performed on smallsubsystems, or fragments. For instance, the energy manybody expansion is56I⟨φ(t )iI φ(t ) jJ ⟩ ⟨φ(t )iI φ(t 1) jJ ⟩S′ijIJ ẼIJK ··· ẼIJKIJE ̃ EIJ EI E JHere, Ẽ IJ is the interaction energy between two monomers andcan be computed by computing the dimer energy andsubtracting the two monomer energies. Similar equationsexist for the three and higher body energy terms. One of themain features of the many-body expansion is that if it is nottruncated it will simplify to the exact energy, thus offering aclear path to improve the quality of calculations. Additionally,this many-body expansion holds for many properties of thesystem, facilitating the calculation of things like the energygradient for molecular dynamics calculations.A brief summary of running an FMO calculation will be givenhere with a more detailed description to be found in the reviewby Fedorov and Kitaura.46 The calculation begins by dividingthe system into fragments to use as pieces of the many-bodyexpansion. Ab-initio calculations are then performed on each ofthese fragments, which generate an initial electron density oneach fragment. With these densities, single electron electrostaticinteractions are added to each monomer Hamiltonian on thebasis of the effects of the other nearby fragments and the abinitio calculation is then repeated on each monomer includingthese effects. These monomer calculations are then repeateduntil the interfragment electrostatic interactions are selfconsistent. After the monomer calculations are completed,higher order cluster calculations are performed. Usually thesehigher order clusters include either just dimer calculations(FMO2) or dimer and trimer calculations (FMO3). This paperremains restricted to FMO2 for computational expediency.To interface the FMO method to FSSH, we will need thefollowing three quantities computed from the FMO-MD run,namely, the Fock matrix for each fragment and fragment pair(FI and FIJ), the atomic orbital overlap matrix for each fragmentpair (SIJ), and the overlap between atomic orbitals onsubsequent time steps (S̅IJ). The first two of these quantitiesare normally computed during a FMO-MD calculation, whereasthe code to compute the third quantity was added to an inhouse copy of Gamess. The two overlap matrices are used tocompute the derivative overlap matrix (S′IJij ) as follows: S(t )1 S(t )1N S(t ) S(t )N1 S(t )N (4) S′(t )1 S′(t )1N S′(t ) S′(t )N1 S′(t )N (5)In the event of the FMO calculation not performing a dimercalculation between to fragments because it is deemed to be tooinsignificant of a contribution, the overlap matrix between thesetwo monomers is assumed to be zero.To obtain the Fock matrix for the full system, we apply themany-body expansion in much the same way that otherquantities are computed in the FMO method.F FI F ̃IJ F ̃IJK . FIIJ(6)IJK̃IJIwhere F is the Fock matrix for monomer I, F is the two-bodyenergy for dimer IJ, etc. The many-body expansion of the Fockmatrix is truncated at the order of the underlying FMOsimulation, which is 2 in this paper:F FI F ̃IJIIJ(7)where the two-body contribution to the Fock matrix can bewrittenIJF ̃ F IJ F I F J(8)Once the approximate Fock matrix is obtained, it istransformed into an orthonormal basis using the full systemoverlap matrix and diagonalized, in a method analogous to asingle iteration of the Hartree Fock procedure. The transformed Fock matrix will be denoted F̅ to avoid confusion withthe time derivatives:F̅ (S 1/2)T F(S 1/2)(9)Diagonalizaing this matrix results in the transformed orbitalcoefficients C̅ and the orbital energies ε, where7206DOI: 10.1021/acs.jpca.6b05607J. Phys. Chem. A 2016, 120, 7205 7212

ArticleThe Journal of Physical Chemistry AC S 1/2C̅(10)Finally, the full system molecular orbitals can be expressed interms of these obtained coefficients: ψi ⟩ F2 0 0 0 0 0 FN dij ΨidΨjdtψpi ,mmi ,mdψdt pj ,m(15)dψdt pj ,m Cpdij (16)i ,m, kφkk(12)ddt Cpj,m, lφl(17)lApplying the chain rule and recalling that both C and φ aretime-dependent quantities can simplify this expression to onedependent on only the orbital coefficients and previouslycomputed overlap matrices.(C p l(t ) C p l(t 1))Mdij Cpj,mj,mki ,mΔt CpkC pj , m lS′kl (t )l ,kSkl(t )M l ,ki ,m(18)Finally, these nonadiabatic couplings and the orbital energiesobtained from the diagonalization of the approximate Fockmatrix are then fed into the standard surface hopping equations,discussed below.2.3. Overview of Nonadiabatic Molecular Dynamics.NAMD dynamics is a widely used method,8,9,57 63 and fewestswitches SH (FSSH) is the most popular NAMD technique.Introduced by Tully in 1990,1 FSSH minimizes the number ofhops, which is a desirable feature in condensed phasesimulations, and satisfies several important criteria, includingtrajectory branching, internal consistency and detailed balancebetween transitions upward and downward in energy.58 Later,FSSH was advanced to include decoherence effects,64 toaccount for the superexchange mechanism of populationtransfer,63,65 and to resolve the numerical problem withFSSH probabilities in cases of small NA coupling.66 Due tothe short time scales of the excited state decay in the currentsystem, the original FSSH algorithm is employed.The NAMD methodology is rooted in the time-dependentSchrödinger equation:(13)pi,j is a list determining which orbitals are occupied in the i’thstate, and  is the antisymmetric operator. Nonadiabaticcoupling matrix elements are computed between these states inthe same way they are computed for other surface hoppingmethods:dij ψpFrom here the expansion of the full system orbitals into thebasis functions can be applied to compute the value of di,j:̂ Ψ⟩i A ψp ⟩i ,j Because orbitals are orthogonal, di,j will only be nonzero ifthe two states differ by only a single orbital. Define pi,m and pj,mas the indices of the single different orbital for states i and j.This Fock matrix represents uncoupled monomers and, becauseit is block diagonal, will have eigenvectors that are themonomer orbitals assuming the overlaps between basisfunctions on different monomers are small. This simple resulteffectively represents the zeroth-order case in the many-bodyexpansion and will prevent almost all energy and electrontransfer between monomers.The other limit is where the Fock matrix is obtained from anuntruncated many-body expansion, in which case the Fockmatrix is identical to that obtained from a full system ab initiocalculation. Because the overlap matrix, S, is also identical tothat of the full system, the eigenvectors of this matrix are theorbitals obtained from the full system ab initio calculation.When the FSSH method is applied to these orbitals, the resultwill be identical to that obtained using a FSSH calculation onthe whole system without FMO. Thus, this method maintainsthe core principal of FMO that untruncated FMO calculationwill be identical to a full system calculation performed withoutFMO.Once the orbitals ψi⟩ are obtained, they can be used toconstruct Slater determinants for the ground and excited states,where the excited states are expressed as single Slaterdeterminant wave functions with one or more electrons excitedfrom occupied orbitals to unoccupied orbitals.jl i ,li ,l j ,ll mThis method of obtaining the full system orbitals from thefragment and cluster simulations has two important limits. Thefirst is the limit of using only the one-body terms, where theFock matrix becomes block diagonal with the monomer Fockmatrices making up the diagonal blocks:0 ψp δ p ,p(11) F1 0I F I 0i ,kk Cij φi⟩jddt ψpdij i Ψ(r ,R ,t ) H(r ,R ,t ) Ψ(r ,R ,t ) t(19)where Ψ is the nuclear/electronic wave function, H is thesystem Hamiltonian, r represents the electronic coordinantes,and R is the nuclear coordinates. The wave function can beexpressed as a sum over (adiabatic) electronic states multipliedby a weighting function.(14)where {ψj} are the set of all basis functions for the system.Applying these two equations together, we get the followingquantity for the nonadiabatic coupling. It is important to notethat due to the orthogonality of the orbitals, the antisymmetrizing operator has no effect on this derivation and can be ignored.Ψ(r ,R ,t ) χi (t ,R(t )) Φi(r ,R(t ))j7207(20)DOI: 10.1021/acs.jpca.6b05607J. Phys. Chem. A 2016, 120, 7205 7212

ArticleThe Journal of Physical Chemistry AHere, χi(t,R(t)) is a time-dependent coefficient determining thecontribution of a given electronic state to the evolving wavefunction.The Hamiltonian for the system is the sum of nuclear andelectronic kinetic energies, as well as the electronic potentialenergy determined from the interactions between the nucleiand electrons.H Tnucl Tel Veliron carbon bond from 1.71 to 1.81 Å, though the carbonoxygen bond remained the same at 1.17 Å. Because solventsubstrate interactions have been successfully described in thepast with ground state calculations,78,79 the geometric factorswere deemed to be small enough to use the classical pathapproximation to FSSH.67Dynamics were performed on Fe(CO)4 in the gas phase andFe(CO)4 surrounded by up to 12 ethanol molecules todetermine the effect of solvation on the complex NA dynamics.Ten different initial configuration of atoms for Fe(CO)4surrounded with 12 ethanol molecules were generated withthe Packmol program.80 Dynamics were performed usingvelocity Verlet integrator with a Nose/Hoover thermostat setto 300 K. The initial velocities for the atoms were chosenrandomly from a Boltzmann distribution. The solvated clusterswere held together using a harmonic potential with a forceconstant of 0.75 kcal/(mol Å2) that began 6.5 Å from thecenter of the box. Similar procedures for containing a box ofmolecules have been used in other applications.39,81 Recentwork on FMO with periodic boundary conditions may allow amore accurate treatment of the boundary in the future.402.5. Timing. Timings for FMO calculations have been wellreported on in the past.41,47,82 A brief overview of the timingsassociated with the current NAMD calculations is presented inTable 1. Simulations on Fe(CO)4 with 12 ethanol molecules(21)This form for the Hamiltonian can be substituted into thetime-dependent Schrödinger equation, along with the assumedform for each electronic state, to produce a series of differentialequations governing the evolution of the expansion coefficienti χi (t ,R(t )) t (1)(2) ddijij 2 Tnucl Ei(t ,R) 2 χ (t ,R(t ))M2M ij (22)This equation is simplified further by combining the diagonalpart of the second-order derivative term with electronic energyand ignoring the off-diagonal part.In a fully quantum description of NA dynamics, χi(t,R(t))represents a nuclear wave packet associated with the ithelectronic state. A quantum-classical approximation employs aclassical description of nuclear motion, turning χi(t,R(t)) intoan expansion coefficient, ci(t),Ψ(r ,R ,t ) ci(t ) φi(r ,R(t ))iTable 1. Comparison between the Time (s) Required ToPerform a Single Time Step on the Given System Both Usingthe FMO Method and Running the Whole System in a SingleCalculationa(23)using FMOwithout FMOEquation 4 transforms intoi dci(t ) t12 ethanol molecules (3nodes)64 ethanol molecules (8nodes)809975960aA calculation involving 64 ethanol molecules could not be performedwithout FMO due to memory limitations. (εiδij i dij)cjj(24)were run both with the FMO method and as a large single abinitio calculation. FMO offered a 17% speedup in thecalculation, which is promising as the system is small byFMO standards. As more ethanol molecules are added,calculations run without FMO will quickly become infeasible.Indeed, dynamics were also performed on a system containing asingle Fe(CO)4 and 64 ethanol molecules. Though datasufficient for statistical sampling needed to converge NAMDcalculations were not collected, due to the computationalexpense and success of the smaller simulations, the availableresults do illustrate how FMO can be used to efficientlysimulate larger systems. Even though the larger system contains4.5 times more electrons, it only required 3 times as much CPUtime. Note the difference in the number of nodes used for the12 and 64 ethanol simulations, Table 1. This better than linearscaling is due to the dynamic load balancing implemented inthe FMO method, which works better with many small jobs todistribute between the nodes. A calculation with 64 ethanolmolecules could not be performed as a single piece forcomparison with the FMO calculation due to memoryconstraints.The only pieces of information that must be obtained fromquantum calculations, then, are the state energies, εi, and thenonadiabatic coupling matrix elements, dij, the calculation ofwhich has been discussed above.Once the MD trajectory and the electronic data are gatheredusing GAMESS, 1000 stochastic FSSH calculations areperformed using the PYXAID computational suite ofprograms.67,68 PYXAID was released under the GNU licenseon the basis of the NAMD methodologies developed in thePrezhdo group and applied to a variety of nanoscalesystems.69 712.4. Computational Details. Density functional theory(DFT) and time-dependent DFT (TDDFT) calculations wereperformed in Gamess72 using the PBE073 functional and the 631G basis74,75 for all non-iron atoms. For the iron atom, themodel core potential (MCP) method at the TZP level was usedto reduce the computational complexity by removing coreelectrons.76 Model core potentials are designed to obtain thecorrect correlation and nodal structure of valence orbitals.77These core potentials have previously been interfaced with theFMO method to compute polypeptide fragments in solution.37Fe(CO)4 with no environmental effects was optimized inboth the ground and first excited state to determine the effectof electronic excitation on the geometry of the molecule. Thisrevealed that excitation resulted in a slight elongation in the3. RESULTS3.1. Validation. To validate our underlying DFTcalculations, a simple single-point comparison between DFT7208DOI: 10.1021/acs.jpca.6b05607J. Phys. Chem. A 2016, 120, 7205 7212

ArticleThe Journal of Physical Chemistry Ausing the 6-31G/MCP basis as used in the dynamicssimulations, DFT with a CC-PVTZ83 basis, and EOMCCSD84 using the 6-31G/MCP basis (Table 2). This analysisTable 2. Table of Transition Energy, Dipole Moment, andOrbital Transition for the First Excited State of Fe(CO)4Obtained Using Various Methodsamethodexcitationenergy(eV)ground statetransitiondipolemomentmagnitudeorbital transitionDFT, 6-31G/MCPDFT, CC-PVTZEOM-CCSD, 6-31G/MCP1.5771.5221.6790.260.250.4635, 36 3741 4236 37Figure 2. Isolated Fe(CO)4 with no additional ethanol molecules. Thecomputed lifetime of the S1 state is 50.8 fs, in excellent agreement withthe experimental value of 47 fs.T0 state. This is a good indication that the simulations areworking as expected.Following the isolated gas phase simulations, Fe(CO)4bound to a single ethanol molecule was investigated. Thenonradiative decay dynamics obtained from these simulationsare reported in Figure 3. The lifetime of the first excited state inaThese data are provided to verify the accuracy of DFT used with theMCP basis set as applied throughout the remainder of the paper.indicated that the orbital ordering as well as transition strengthand excitation energy were agreed upon by all methods. Thesecalculations were again performed in GAMESS. The oscillatorstrength is provided merely as a confirmation that the methodsare returning the same states. It is not important that theground to first excited state transition is dark because the stateis being populated by a transition from the Fe(CO)5 excitedstate.3.2. Gas Phase Dynamics. Initially, an isolated Fe(CO)4was simulated in the gas phase so that the de-excitation ratecould be compared to experiment and the solution phasesimulations. Figure 1 shows the key orbitals of Fe(CO)4 asFigure 3. Fe(CO)4 bound to a single ethanol molecule. The computedlifetime of the S1 state is 65.5 fs, which is longer than the gas phaseresult, Figure 2.the presence of a single ethanol molecule grows to 65.5 fs from50.8 fs in the gas phase. The increase in the lifetime is a positivereflection of what happens in solution, where experimentallythe lifetime is increased to 200 fs, though the full effect of thecondensed phase environment is not seen yet.3.3. Condensed Phase Dynamics. To model theFe(CO)4 complex in solution, dynamics were carried out onFe(CO)4 in a box of 12 ethanol molecules. Twelve ethanolmolecules were used to simulate the first layer of solvation,while also keeping the simulation relatively affordable.Condensed phase dynamics involves binding of a solventmolecule to the complex. Representative MD frames showingthe system before and after the binding event are shown inFigure 4. The initial conditions of the system were such that theethanol molecule was not bound to the iron center at the outsetof the calculation but became bound at some subsequent time,usually around 400 600 fs after the start of the simulation.This allowed us to compute the nonradiative decay rate of thefirst excited state both before binding and after binding.The 200 fs for each run before the binding event wasaveraged together to produce Figure 5. The data indicate that,prior to ethanol binding to the iron atom, the lifetime of theexcited state is near 100 fs. Although this is not in perfectagreement with the experimental results54 obtained withfemtosecond X-ray spectroscopy and indicating a 200 fslifetime in solution, it does demonstrate a significant increasein lifetime from the 50 fs in the gas phase calculations. Thetrend demonstrated with Figures 2 4 leads us to expect thatadding more solvent molecules will increase the simulated time-Figure 1. Highest four occupied and lowest four unoccupied gas phaseorbitals of Fe(CO)4. The orbitals were computed using DFT and thecombined 6-31G/MCP basis.computed by DFT. The first excited state of the complex wasassumed to be a simple HOMO to LUMO transition, whichagrees well with previous characterization by Wernet et al. thatthe S1 state is π σ* transition.54The results of the NAMD simulations on the gas phasecomplex are reported in Figure 2. A decay rate of 50.8 fs for theS1 S0 transitions was obtained, showing excellent agreementwith the gas phase experimental value of 47 fs obtained bySchmid and co-workers through femtosecond pump probespectroscopy.50 Although the S0 state is not the ground state ofFeCO4, the decay to the lowest singlet state is the primarydecay channel of the S1 state due to spin change to the ground7209DOI: 10.1021/acs.jpca.6b05607J. Phys. Chem. A 2016, 120, 7205 7212

ArticleThe Journal of Physical Chemistry AFigure 6. Fe(CO)4 surrounded by ethanol molecules after one bindsto the iron atom. The computed lifetime of the S1 state is 11.4 fs. Thisindicates that once an ethanol molecule binds to the iron center, thedecay of the excited state will happen soon after.4. CONCLUSIONSHere, the interface between an interface between the FMOmethod in GAMESS and the PYXAID program for computingNAMD dynamics in condensed phase and nanoscale systemshas been detailed. The efficient treatment of many-bodyinteraction with the FMO approximation provides greatcomputational savings in systems that can be easily separatedinto weakly interacting fragments. The computational cost ofthe additional calculations needed for the interface wasdetermined to be negligible, because the NA coupling is aone-electron operator that is straightforward to calculate.The nonradiative decay processes in the Fe(CO)4 complex inthe gas phase and in an ethanol solution is used as a test of theFMO-NAMD method. The calculations have shown excellentagreement with the time-resolved optical and X-ray spectroscopies. The decay rates obtained using our FMO-NAMDmethod give us insight into the order of CO dissociation andethanol binding. Because the lifetime of the excited state is soshort once the ethanol molecule binds to the iron center insolution, we can say with confidence that the CO dissociationfrom excited Fe(CO)5 and ethanol attachment is not aconcerted process. Our calculations suggest that a CO liganddissociates from Fe(CO)5 and forms Fe(CO)4 in the excitedstate. This species then exists in solution for around 100 200 fsbefore rebinding to an ethanol molecule. What still remainsunclear is whether binding of the ethanol causes the relaxationof the S1 state, or whether the relaxation happens before aninteraction with the ethanol molecule. Both mechanisms areconsistent with the current simulation, and more thoroughinvestigation is required.The advantage of the developed method resides in both areduction in computational complexity and the ability to modelinteractions between localized excitations. Future developmentsof the FMO-NAMD approach will include modeling of energytransfer between fragments using data obtained from the dimercalculations performed by the FMO method, the inclusion ofspin orbit coupling values from monomer excited statecalculations to compute intersystem crossing rates, andimplementation and testing of more advanced NAMDtechniques, beyond the most popular FSSH approach.Figure 4. Frames of Fe(CO)4 in a box of ethanol molecules. (A) is aframe pulled before the binding event occurs, and (B) is after thebinding event.Figure 5. Fe(CO)4 surrounded by ethanol molecules before anybinding to the iron center. The computed lifetime of the S1 state is 100fs, representing a significant increase from the gas phase value, which isconsistent with experimental data.scale further, bringing the NAMD results in close agreementwith experiment.After the binding event, the lifetime of the excited statereduces to 11.4 fs, as seen in Figure 6. This is very telling andgives hints as to whether the CO detachment and ethanolattachment are concerted or sequential. The order ofmagnitude acceleration of the nonradiative relaxation dynamicsindicates that the binding of the ethanol group puts a hardupper limit on the lifetime of the excited state. AUTHOR INFORMATIONNotesThe authors declare no competing financial interest.ACKNOWLEDGMENTSThis work was supported as part of the ComputationalMaterials Sciences Program funded by the U.S. Department7210DOI: 10.1021/acs.jpca.6b05607J. Phys. Chem. A 2016, 120, 7205 7212

ArticleThe Journal of Physical Chemistry A(35) Kazaryan, A.; Lan, Z.; Schäfer, L. V.; Thiel, W.; Filatov, M. J.Chem. Theory Comput. 2011, 7, 2189.(36) Mendieta-Moreno, J. I.; Walker, R. C.; Lewis, J. P.; GómezPuertas, P.; Mendieta, J.; Ortega, J. J. Chem. Theory Comput. 2014, 10,2185.(37) Nagata, T.; Fedorov, D. G.; Kitaura, K. Theor. Chem. Acc. 2012,131, 1136.(38) Nakata, H.; Schmidt, M. W.; Fedorov, D. G.; Kitaura, K.;Nakamura, S.; Gordon, M. S. J. Phys. Chem. A 2014, 118, 9762.(39) Komeiji, Y.; Ishikawa, T.; Mochizuki, Y.; Yamataka, H.; Nakano,T. J. Comput. Chem. 2009, 30, 40.(40) Fujita, T.; Nakano, T.; Tanaka, S. Chem. Phys. Lett. 2011, 506,112.(41) Nagata, T.; Brorsen, K.; Fedorov, D. G.; Kitaura, K.; Gordon, M.S. J. Chem. Phys. 2011, 134, 124115.(42) Kitau

semiclassical force fields to ab initio calculations,33 35 or performing QM/MM calculations with the environment being simulated classically.36 A more direct solution, developed in the current work, employs the FMO molecular dynamics (FMOMD) method37 41 to simplify the computational complexity of ab initio NAMD. The FMO technique is used

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