Time‐dependent molecular fields created by the interaction of an external electromagnetic field with a molecular system

When an external, time‐dependent field interacts with a molecular system various phenomena may take place. However, concentrating on a region close enough to a point of conical intersection, we find that this external field builds up a field similar to an electromagnetic field formed on the one hand by Field‐Dressed nonadiabatic coupling terms which are reminiscent of the Maxwell–Lorentz Vector potentials, and on the other hand via a scalar potential formed by the dipole‐interaction with an external field. In this article, we show that this new field, to be termed Molecular Field, is characterized by several spatial and space‐time Field‐Dressed Curl equations and one, single, space‐time Field‐Dressed Divergence equation. These equations are then shown to yield, just as in the general theory of electromagnetism, the corresponding Field‐Dressed Wave Equations. This achievement could be materialized employing the (1,2) antisymmetric matrix elements of any of the 2×2 dimensional Field‐Dressed nonadiabatic coupling matrices. © 2014 Wiley Periodicals, Inc.     

Derivation of the electronic nonadiabatic coupling field in molecular systems: an algebraic-vectorial approach

In this Communication it is suggested that various elements of the nonadiabatic coupling matrix, tau(jk)(s) are created by the singular nonadiabatic coupling terms of the system. Moreover, given the spatial distribution of these coupling terms in the close vicinity of their singularity points yields, according to this approach, the integrated intensity of the field at every point in the region of interest. To support these statements we consider the conical intersections of the three lower states of the H+H(2) system: From an ab initio treatment we obtain the nonadiabatic coupling terms around each conical intersection separately (at its close vicinity) and having those, create the field at every desired point employing vector-algebra. This approach is also used to calculate the intensity of the Curl of those matrix elements that lack their own sources [tau(13)(s) in the present case]. The final results are compared with relevant ab initio calculations.     

The non-adiabatic nanoreactor: towards the automated discovery of photochemistry

The ab initio nanoreactor has previously been introduced to automate reaction discovery for ground state chemistry. In this work, we present the nonadiabatic nanoreactor, an analogous framework for excited state reaction discovery. We automate the study of nonadiabatic decay mechanisms of molecules by probing the intersection seam between adiabatic electronic states with hyper-real metadynamics, sampling the branching plane for relevant conical intersections, and performing seam-constrained path searches. We illustrate the effectiveness of the nonadiabatic nanoreactor by applying it to benzene, a molecule with rich photochemistry and a wide array of photochemical products. Our study confirms the existence of several types of S₀/S₁ and S₁/S₂ conical intersections which mediate access to a variety of ground state stationary points. We elucidate the connections between conical intersection energy/topography and the resulting photoproduct distribution, which changes smoothly along seam space segments. The exploration is performed with minimal user input, and the protocol requires no previous knowledge of the photochemical behavior of a target molecule. We demonstrate that the nonadiabatic nanoreactor is a valuable tool for the automated exploration of photochemical reactions and their mechanisms.

The nonadiabatic nanoreactor is a tool for automated photochemical reaction discovery that extensively explores intersection seams and links conical intersections to photoproduct distributions.     

Nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization—Microscopic mechanism of superconducting state transition: Model study of MgB2

The theory of the nonadiabatic electron–vibration interactions has been applied to the study of MgB₂ superconducting state transition. It has been shown that at nonadiabatic conditions in which the Born–Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on the nuclear momenta, the fermionic ground‐state energy of the studied system can be stabilized by nonadiabatic electron–phonon interactions at broken translation symmetry. Moreover, the new arising state is geometrically degenerate; i.e., there are an infinite number of different nuclear configurations with the same fermionic ground‐state energy. The model study of MgB₂ yields results that are in a good agreement with the experimental data. For distorted lattice, with 0.016 Å/atom of in‐plane out‐of‐phase B? B atoms displacements out of the equilibrium (E_2g phonon mode) when the nonadiabatic interactions are most effective, it has been calculated that the new arising state is 87 meV/unit cell more stable than the equilibrium–high symmetry clumped nuclear structure at the level of the Born–Oppenheimer approximation. The calculated T_c is 39.5 K. The resulting density of states exhibits two‐peak character, in full agreement with the tunneling spectra. The peaks are at ±4 meV, corresponding to the change of the π band density of states, and at ±7.6 meV, corresponding to the σ band. The superconducting state transition can be characterized as a nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization (NASICKELES). © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Conical intersection of the ground and first excited states of water: energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

A conical intersection between the ground and first-excited states of water is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schr?dinger equation (ACSE). This study is an extension of a previous study in which the ACSE was used to compute the energies around a conical intersection in the triplet excited states of methylene [Snyder, J. W., Jr.; Rothman, A. E.; Foley, J. J.; Mazziotti, D. A. J. Chem. Phys. 2010, 132, 154109]. We compute absolute energies of the 1(1)A' and 2(1)A' states of water (H(2)O) and the location of the conical intersection. The ACSE energies are compared to those from ab initio wave function methods. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. Unlike the situation for methylene, the two states in the vicinity of the conical intersection of water both have the same spatial symmetry. Hence, the study demonstrates the ability of the ACSE to resolve states of the same spatial symmetry that are nearly degenerate in energy. The 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from double-ζ and augmented double-ζ basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.     

Theory of excitation energy transfer regarded as nonadiabatic transition 2: Calculational evidence of nonadiabatic interaction causing intermolecular excitation energy transfer

To clarify whether the excitation energy transfer from a donor molecule or aggregate to a remote acceptor molecule or aggregate can be caused by nonadiabatic interaction as expected in our previous studies 4 ; 5 , we carried out ab initio calculations for three donor–acceptor systems. Even when the acceptor is separated from the donor by 15 Å, it was found that nonadiabatic coupling elements have moderately large values in the nuclear configuration region where the potential energy surfaces at two excited states for the donor–acceptor system are close to each other; otherwise, the conical intersection between the two excited‐state potential energy surfaces appears. In addition, it was found that the adiabatic approximation for the donor–acceptor system holds in the nuclear configuration region in which the initial and final wave packets in the process of the excitation energy transfer lie. These findings lead to the conclusion that the excitation energy transfer between two remote molecules or aggregates can be caused by the nonadiabatic interaction. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 36–43, 2003     

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.     

Quenching of tryptophan (1)(pi,pi*) fluorescence induced by intramolecular hydrogen abstraction via an aborted decarboxylation mechanism

CASSCF computations show that the hydrogen-transfer-induced fluorescence quenching of the (1)(pi,pi*) excited state of zwitterionic tryptophan occurs in three steps: (1) formation of an intramolecular excited-state complex, (2) hydrogen transfer from the amino acid side chain to the indole chromophore, and (3) radiationless decay through a conical intersection, where the reaction path bifurcates to a photodecarboxylation and a phototautomerization route. We present a general model for fluorescence quenching by hydrogen donors, where the radiationless decay occurs at a conical intersection (real state crossing). At the intersection, the reaction responsible for the quenching is aborted, because the reaction path bifurcates and can proceed forward to the products or backward to the reactants. The position of the intersection along the quenching coordinate depends on the nature of the states and, in turn, affects the formation of photoproducts during the quenching. For a (1)(n,pi*) model system reported earlier (Sinicropi, A.; Pogni, R.; Basosi, R.; Robb, M. A.; Gramlich, G.; Nau, W. M.; Olivucci, M. Angew. Chem., Int. Ed. 2001, 40, 4185-4189), the ground and the excited state of the chromophore are hydrogen acceptors, and the excited-state hydrogen transfer is nonadiabatic and leads directly to the intersection point. There, the hydrogen transfer is aborted, and the reaction can return to the reactant pair or proceed further to the hydrogen-transfer products. In the tryptophan case, the ground state is not a hydrogen acceptor, and the excited-state hydrogen transfer is an adiabatic, sequential proton and electron transfer. The decay to the ground state occurs along a second reaction coordinate associated with decarboxylation of the amino acid side chain and the corresponding aborted conical intersection. The results show that, for (1)(pi,pi*) states, the hydrogen transfer alone is not sufficient to induce the quenching, and explain why fluorescence quenching induced by hydrogen donors is less general for (1)(pi,pi*) than for (1)(n,pi*) states.     

Ultrafast Nonadiabatic Photoisomerization Dynamics Mechanism for the UV Photoprotection of Stilbenoids in Grape Skin

Natural UV photoprotection plays a vital role in physiological protection. It has been reported that UVC radiation can make resveratrol (RSV) and piceatannol (PIC) accumulate in grape skin. In this work, we demonstrated that RSV and PIC could significantly absorb UVA and UVB, and confirmed their satisfactory photostability. Furthermore, we clarified the UV photoprotection mechanism of typical stilbenoids of RSV and PIC for the first time by using combined femtosecond transient absorption (FTA) spectroscopy and time‐dependent density functional theory (TD‐DFT) calculations. RSV and PIC can be photoexcited to the excited state after UVA and UVB absorption. Subsequently, the photoisomerized RSV and PIC quickly relax to the ground state via nonadiabatic transition from the S₁ state at a conical intersection (CI) position between potential energy surfaces (PESs) of S₁ and S₀ states. This ultrafast trans‐cis photoisomerization will take place within a few tens of picoseconds. As a result, the UV energy absorbed by RSV and PIC could be dissipated by an ultrafast nonadiabatic photoisomerization process.     

Existence of strictly diabatic basis sets for the two‐state problem

Some new properties of the nonadiabatic coupling elements are derived, in particular the orthogonality and gauge invariance of their longitudinal and transverse components. A method for constructing a strictly diabatic basis set that makes both the transverse and longitudinal components of the nonadiabatic coupling elements of the two‐state problem vanish identically and is based on introducing overlap between the electronic states in the vicinity of the crossing seam is proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

Ab initio study on the photochemical behavior of styrene

Ab initio complete active space self‐consistent field (CASSCF) and the second order multireference Møller‐Plesset calculations have been performed to examine the photochemical behavior of styrene upon the strong S₀‐S₂ electronic excitation in the low‐lying excited states. The optimized structure at the S₂/S₁ conical intersection (CIX) is characterized by a quinoid structure. The transition state (TS) in S₁ is in the vicinity of the S₂/S₁‐CIX. At the S₁‐TS, two reaction paths branch. One is the relaxation into the stable structure in S₁ and then emission into S₀. The other is the radiationless decay through the S₁/S₀‐CIX. © 2002 Wiley Periodicals, Inc. J Comput Chem 10: 950–956, 2002     

A rigorous approach to the formulation of extended Born‐Oppenheimer equation for a three‐state system

If a coupled three‐state electronic manifold forms a sub‐Hilbert space, it is possible to express the non‐adiabatic coupling (NAC) elements in terms of adiabatic–diabatic transformation (ADT) angles. Consequently, we demonstrate: (a) Those explicit forms of the NAC terms satisfy the Curl conditions with non‐zero Divergences; (b) The formulation of extended Born‐Oppenheimer (EBO) equation for any three‐state BO system is possible only when there exists coordinate independent ratio of the gradients for each pair of ADT angles leading to zero Curls at and around the conical intersection(s). With these analytic advancements, we formulate a rigorous EBO equation and explore its validity as well as necessity with respect to the approximate one (Sarkar and Adhikari, J Chem Phys 2006, 124, 074101) by performing numerical calculations on two different models constructed with different chosen forms of the NAC elements. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

CASSCF study into the mechanism for predissociation of the allyl radical

A theoretical study has been carried out on the allyl radical in its ground and first excited electronic states. Complete active space self‐consistent field (CASSCF) calculations show the presence of a conical intersection between the ground and first excited electronic states (～400 cm^?1 above the adiabatic excited state energy), reached by decreasing the C? C? C angle and twisting the C? C bonds. The presence of this conical intersection provides a likely explanation for the very rapid predissociation in the excited electronic state. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Nonradiative Excited-State Decay via Conical Intersection in Graphene Nanostructures

Chemical groups are known to tune the luminescent efficiencies of graphene-related nanomaterials, but some species, including the epoxide group (−COC−), are suspected to act as emission-quenching sites. Herein, by performing nonadiabatic excited-state dynamics simulations, we reveal a fast (within 300 fs) nonradiative excited-state decay of a graphene epoxide nanostructure from the lowest excited singlet (S₁) state to the ground (S₀) state via a conical intersection (CI), at which the energy difference between the S₁ and S₀ states is approximately zero. This CI is induced after breaking one C−O bond at the −COC− moiety during excited-state structural relaxation. This study ascertains the role of epoxide groups in inducing the nonradiative recombination of the excited electron-hole, providing important insights into the CI-promoted nonradiative de-excitations and the luminescence tuning of relevant materials. In addition, it shows the feasibility of utilizing nonadiabatic excited-state dynamics simulations to investigate the photophysical processes of the excited states of graphene nanomaterials.     

Photochemical reactivity of 2-vinylbiphenyl and 2-vinyl-1,3-terphenyl: the balance between nonadiabatic and adiabatic photocyclization

A mechanism for the photochemical conversion of 2-vinyl-1,3-terphenyl to 8,9a-dihydrophenanthrene (Lewis, F. D.; Zuo, X.; Gevorgyan, V.; Rubin, M. J. Am. Chem. Soc. 2002, 124, 13664-13665) is presented in this study, based on ab initio restricted active space self-consistent field calculations and a molecular mechanics-valence bond dynamics simulation of a model system: the syn isomer of 2-vinylbiphenyl. An extended crossing seam between the ground and first excited electronic states was found to be largely responsible for the efficient photocyclization of the photochemically active syn isomer. This mechanism is nonadiabatic in nature, with an excited-state reaction pathway approaching the crossing region during the initial stage of cyclization. Dynamics simulation shows that this seam is easily accessible by vibrational motion in the branching space, once a small barrier is passed on the S1 excited-state potential energy surface. Ultrafast radiationless decay to the ground state then follows, and the cyclization is completed on this surface. A second possible mechanism was identified, which involves complete adiabatic cyclization on the S1 surface, with decay to the ground state (at a different conical intersection) only taking place once the product is formed. Thus, there is a competition between these two mechanisms-nonadiabatic and adiabatic-governed by the dynamics of the system. A large quantum yield is predicted for the photocyclization of the syn isomer of 2-vinylbiphenyl and 2-vinyl-1,3-terphenyl, in agreement with experimental observations.     

Photostability versus photodegradation in the excited-state intramolecular proton transfer of nitro enamines: competing reaction paths and conical intersections

The phototautomerization mechanism of a model nitro enamine (NEA) chromophore (incorporated in the structure of a highly photolabile pesticide, tetrahydro-2-(nitromethylene)-2H-1,3-thiazine) has been studied using complete active space self-consistent field reaction path computations. The optically accessible 1pipi* excited state of NEA involves separation of charge and correlates diabatically with the ground state of the tautomerized acinitro imine (ANI) form. For optimum photostabilization, the 1pipi* state of NEA should be S1: in this case, the tautomer would be efficiently formed via a diabatic intramolecular proton-transfer pathway passing through an S1/S0 conical intersection, followed by a facile thermal back proton-transfer reaction. However, in NEA itself the lowest excited states correspond to nitro group 1npi* states, and there are additional surface crossings that provide a mechanism for populating the 1npi* manifold. The above results indicate that the high photolability observed for the pesticide [Kleier, D.; Holden, I.; Casida, J. E.; Ruzo, L. O. J. Agric. Food Chem. 1985, 33, 998-1000] has to be ascribed to photochemistry originating on the 1npi* manifold of states, populated indirectly from the 1pipi* state.