Non-adiabatic transitions near avoided crossings: theory and numerics

We present a review of rigorous mathematical results about non-adiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.     

A proposal for the theoretical treatment of multi-electronic-state molecular dynamics: Hemiquantal dynamics with the whole dim basis (HWD). A test on the evolution of excited Ar3 cluster ions

A method which couples a model Hamiltonian to hemiquantal dynamics is proposed as a general theoretical treatment of multistate molecular processes. A test application to the Ar₃⁺ system is performed which involves four nuclear degrees of freedom and six quasidiabatic states. The method proves efficient for dealing with non-adiabatic transitions occurring at singularities like conical intersections and avoided crossings between potential surfaces.     

The dissociative chemisorption of methane on Ni(100): reaction path description of mode-selective chemistry

We derive a model for the dissociative chemisorption of methane on a Ni(100) surface, based on the reaction path Hamiltonian, that includes all 15 molecular degrees of freedom within the harmonic approximation. The total wavefunction is expanded in the adiabatic vibrational states of the molecule, and close-coupled equations are derived for wave packets propagating on vibrationally adiabatic potential energy surfaces, with non-adiabatic couplings linking these states to each other. Vibrational excitation of an incident molecule is shown to significantly enhance the reactivity, if the molecule can undergo transitions to states of lower vibrational energy, with the excess energy converted into motion along the reaction path. Sudden models are used to average over surface impact site and lattice vibrations. Computed dissociative sticking probabilities are in good agreement with experiment, with respect to both magnitude and variation with energy. The ν(1) vibration is shown to have the largest efficacy for promoting reaction, due to its strong non-adiabatic coupling to the ground state, and a significant softening of the vibration at the transition state. Most of the reactivity at 475 K is shown to result from thermally assisted over-the-barrier processes, and not tunneling.     

Global potential energy surfaces for the Al+(1S) + H2 system

Global, three-dimensional multireference ab initio potential energy surfaces have been calculated for the AlH2+ system for the two lowest energy singlet states and the lowest energy triplet state. These surfaces were calculated using the multireference configuration interaction level of theory with a large basis set. The accuracy of the surfaces were checked against available experimental data and previous theoretical investigations. The areas of surface crossings between the ground state singlet surface and the lowest energy triplet surface and the first excited singlet surface have been thoroughly investigated in all three dimensions and found to give rise to two regions of surface crossings--an "early" crossing (reduced H2 distance) and a "late" crossing (enlarged H2 distance). It is anticipated that both of these crossings will be important in modeling the dynamics of the system. Each of the global potential energy surfaces were fit by interpolation methodology to obtain analytic representations of the surfaces. A representative classical simulation on the ground state singlet surface was performed and discussed.     

Exciton states of dynamic DNA double helices: alternating dCdG sequences

The present communication deals with the excited states of the alternating DNA oligomer (dCdG)5.(dCdG)5 which correspond to the UV absorption band around 260 nm. Their properties are studied in the frame of the exciton theory, combining molecular dynamics simulations and quantum chemistry data. It is shown that the dipolar coupling undergoes important variations with the site and the helix geometry. In contrast, the energy of the monomer transitions within the double helix is not sensitive to the local environment. It is thus considered to be distributed over Gaussian curves whose maximum and width are derived from the experimental absorption spectra of nucleosides in aqueous solution. The influence of the spectral width on the excited state delocalization and the absorption spectra is much stronger than that of the oligomer plasticity. About half of the excited states are delocalized over at least two bases. Many of them result from the mixing of different monomer states and extend on both strands. The trends found in the simulated spectra, when going from non-interacting monomers to the duplex, are in agreement with experimental observations. Conformational changes enhance the diversity of the states which can be populated upon excitation at a given energy. The states with larger spatial extent are located close to the maximum of the absorption spectrum.     

Oxidation and Reduction Pathways in the Knowles Hydroamination via a Photoredox-Catalyzed Radical Reaction**

Systematic reaction path exploration revealed the entire mechanism of Knowles's light-promoted catalytic intramolecular hydroamination. Bond formation/cleavage competes with single electron transfer (SET) between the catalyst and substrate. These processes are described by adiabatic processes through transition states in an electronic state and non-radiative transitions through the seam of crossings (SX) between different electronic states. This study determined the energetically favorable SET path by introducing a practical computational model representing SET as non-adiabatic transitions via SXs between substrate's potential energy surfaces for different charge states adjusted based on the catalyst's redox potential. Calculations showed that the reduction and proton shuttle process proceeded concertedly. Also, the relative importance of SET paths (giving the product and leading back to the reactant) varies depending on the catalyst's redox potential, affecting the yield.     

Nonadiabatic transitions in chemical reactions: A quantum mechanical study

This work presents an exact quantum mechanical treatment of a reactive three-atom collinear model system incorporating nonadiabatic couplings. It was assumed that nonadiabatic transitions are induced by the vibrational motion only. The main findings are: (i) The reaction process can create conditions in which weak nonadiabatic couplings terms ( for which the Massey parameter was round 10) may cause large probabilities (～0.5) for transitions from one electronic surface to the other. In other words, the reaction process is able in certain cases to create a near resonance situation which makes the non-adiabatic transition almost independent of the magnitude of the coupling term. For this to happen the two surfaces need not be proximate, nor need they “almost” cross along a certain line (ii) In cases where the main nonadiabatic transitions take place outside the interaction region one may, at least qualitatively, decouple the reaction process from the nonadiabatic one. Thus, under the conditions specified one may first treat the reactive system on the ground state surface without including the excited interacting surface and then treat the nonadiabatic process independently.     

Inelastic collisions of cold polar molecules in nonparallel electric and magnetic fields

The authors present a detailed study of low-temperature collisions between CaD molecules and He atoms in superimposed electric and magnetic fields with arbitrary orientations. Electric fields do not interact with the electron spin of the molecules directly but modify their rotational structure and, consequently, the spin-rotation interactions. The authors examine molecular Stark and Zeeman energy levels as functions of the angle between the fields and show that rotating fields may induce and shift avoided crossings between the Zeeman levels of the rotationally ground and rotationally excited states of the molecule. The dynamics of molecular collisions are extremely sensitive to external fields near these avoided crossings and it is shown that molecular collisions may be controlled by varying both the strength and the relative orientation of the fields. The effects observed in this study are due to interactions of the isolated molecules with external fields so the conclusions should be relevant for collisions of molecules with other atoms or collisions of molecules with each other. This study demonstrates that electric fields may be used to enhance or suppress spin-rotation interactions in molecules. The spin-rotation interactions induce nonadiabatic couplings between states of different total spins in systems of two open-shell species and it is suggested that electric fields might be used for controlling nonadiabatic spin transitions and spin-forbidden chemical reactions of cold molecules in a magnetic trap.     

Experimental and theoretical studies of the quenching of Li(3p,4p) by N2

Quenching mechanisms of the Li3p and Li4p states in collision with the nitrogen molecule are studied by laser-induced fluorescence spectroscopy and by a quantum chemical calculation. The Li3p state is observed to be efficiently quenched to the Li3s state detected as intense 3s-->2p emission. The Li4p state is efficiently quenched to the Li4s and Li3d states detected as 4s-2p and 3d-2p emissions, respectively. The potential-energy surfaces for the Li(2s-4p)N2 states show a large number of conical intersections and avoided crossings resulting from the couplings between the ionic [Li+(N2)-] and covalent configurations. There are a large number of stable excited states, and we give here the spectroscopic constants for the lowest two stable isomers correlating to Li2p+N2.     

Theoretical study of the photoinduced transfer among the ground state and two metastable states in [Fe(CN)5NO]2-

Ab initio calculations were performed to investigate photoinduced transfers among the ground state (GS) and two metastable states (MS1 and MS2) of [Fe(CN)5NO]2-. We obtained the global potential energy surface of the electronic ground state by a scheme of multireference singly and doubly excited configuration interaction followed by a Davidson-type quadruple correction (MRSDCI+Q). The ground state surface has three local minima corresponding to GS, MS1, and MS2. The character of bond between Fe and the nitrosyl group are discussed. We carried out calculations of the lower five electronic excited states by MRSDCI+Q. The main configurations of these lower five excited states were represented by the dFe-->pi*NO transition accompanied by considerable back-donation. The potential energy surfaces of the six states, including the ground state, were obtained by state averaged complete active space self-consistent field calculations. The surfaces have several conical intersections and avoided crossings in the reaction pathway. The photoinduced transfers among GS, MS1, and MS2 are caused by the nonadiabatic effect near these crossings.     

Ultrafast Exciton Self-Trapping and Delocalization in Cycloparaphenylenes: The Role of Excited-State Symmetry in Electron-Vibrational Coupling

Upon photon absorption, π-conjugated organics are apt to undergo ultrafast structural reorganization via electron-vibrational coupling during non-adiabatic transitions. Ultrafast nuclear motions modulate local planarity and quinoid/benzenoid characters within conjugated backbones, which control primary events in the excited states, such as localization, energy transfer, and so on. Femtosecond broadband fluorescence upconversion measurements were conducted to investigate exciton self-trapping and delocalization in cycloparaphenylenes as ultrafast structural reorganizations are achieved via excited-state symmetry-dependent electron-vibrational coupling. By accessing two high-lying excited states, one-photon and two-photon allowed states, a clear discrepancy in the initial time-resolved fluorescence spectra and the temporal dynamics/spectral evolution of fluorescence spectra were monitored. Combined with quantum chemical calculations, a novel insight into the effect of the excited-state symmetry on ultrafast structural reorganization and exciton self-trapping in the emerging class of π-conjugated materials is provided.     

Slice imaging and wave packet study of the photodissociation of CH3I in the blue edge of the A-band: evidence of reverse 3Q0 ← 1Q1 non-adiabatic dynamics

The photodissociation of CH(3)I in the blue edge (217-230 nm) of the A-band has been studied using a combination of slice imaging and resonance enhanced multiphoton ionization (REMPI) detection of the CH(3) fragment in the vibrational ground state (ν = 0). The profiles of the CH(3) (ν = 0) kinetic energy distributions and the photofragment anisotropies are interpreted in terms of the contribution of the excited surfaces involved in the photodissociation process, as well as the probability of non-adiabatic curve crossing between the (3)Q(0) and (1)Q(1) states. In the studied region, unlike in the central part of the A-band where absorption to the (3)Q(0) state dominates, the I((2)P(J)), with J = 1/2, 3/2, in correlation with CH(3) (ν = 0) kinetic energy distributions show clearly two contributions of different anisotropy, signature of the competing adiabatic and non-adiabatic dynamics, whose ratio strongly depends on the photolysis wavelength. The experimental results are compared with multisurface wave packet calculations carried out using the available ab initio potential energy surfaces, transition moments, and non-adiabatic couplings, employing a reduced dimensionality model. A good qualitative agreement is found between experiment and theory and both show evidence of reverse (3)Q(0)←(1)Q(1) non-adiabatic dynamics at the bluest excitation wavelengths both in the fragment kinetic energy and angular distributions.     

Nonadiabatic effects on peptide vibrational dynamics induced by conformational changes

Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH(3)-CO-NH-CH(2)-CO-NH-CH(3)). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (DFT) [B3LYP/6-31+G(d)] level. The ordering of the energetically most stable isomers (C(7) and C(5)) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C(7) and C(5) minimum energy structures occur on a sub-picosecond time scale (700...800 fs). Vibrationally nonadiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly nonadiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a time scale of 200...500 fs with population transfer of more than 50% between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy.     

Rovibrational spectroscopy and intramolecular dynamics of 1,2-trans-d(2)-ethene in the first C-H stretch overtone region

The first overtone region of the C-H stretching vibration of 1,2-trans-d(2)-ethene (HDC=CDH) was monitored via jet-cooled action spectroscopy and room temperature photoacoustic spectroscopy. The spectra include a strong band, which we assigned as the nu(1)+nu(9) C-H stretch vibration, and five additional bands related to transitions to coupled states. The spectral features were modeled in terms of a six-state deperturbation analysis, revealing the energies of the zero-order states and the relatively strong couplings between the initially excited nu(1)+nu(9) state and the doorway states. Considering these energies and the fundamental frequencies of 1,2-trans-d(2)-ethene and presuming that only low-order resonances are involved in the couplings enabled the assignment of the states. The analysis also allowed obtaining insight on energy flow and to find out that the energy oscillations between the C-H stretch state and the doorway states occur on a subpicosecond time scale.     

Quantum state-resolved collision relaxation of highly vibrationally excited SO2

Collision depopulation cross sections of 13 single, highly vibrationally excited levels with 45,000 cm(-1) energy in the electronic ground state of SO(2) in collision with CO in a supersonic jet have been measured. The measurements for these single highly excited quantum states are conducted through pressure dependence of the decay of the fluorescence quantum beat resulted from their coupling with the rovibronic levels in the optically allowed transitions to the (140), (210), and (132) C(1)B(2) levels. The relaxation cross sections of these highly excited states, each with well-defined energy and symmetry, range from 27 to 187 A(2) with an average of 71 A(2). This average cross section is much larger than the hard sphere cross section of 48 A(2). The relaxation cross section is also found to be larger for the quantum states with a larger matrix element in coupling with the "bright" electronically excited level. Both observations suggest a substantial contribution from long range interactions in collision relaxation of highly excited molecules.     

Study of ab initio molecular data for inelastic and reactive collisions involving the H3+ quasimolecule

The lowest two ab initio potential energy surfaces (PES), and the corresponding nonadiabatic couplings between them, have been obtained for the H3+ system; the molecular data are compared to those calculated with the diatomic in molecules (DIM) method. The form of the couplings is discussed in terms of the topology of the molecular structure of the triatomic. The method of Baer is employed to generate "diabatic" states and the residual nonadiabatic couplings are calculated. The ab initio results for these are markedly different from the corresponding DIM data, and show the need to consider the third PES.     

Theory of ultrafast nonresonant multiphoton transitions in polyatomic molecules: basics and application to optimal control theory

A systematic approach is presented to describe nonresonant multiphoton transitions, i.e., transitions between two electronic states without the presence of additional intermediate states resonant with the single-photon energy. The method is well suited to describe femtosecond spectroscopic experiments and, in particular, attempts to achieve laser pulse control of molecular dynamics. The obtained effective time-dependent Schrodinger equation includes effective couplings to the radiation field which combine powers of the field strength and effective transition dipole operators between the initial and final states. To arrive at time-local equations our derivation combines the well-known rotating wave approximation with the approximation of slowly varying amplitudes. Under these terms, the optimal control formalism can be readily extended to also account for nonresonant multiphoton events. Exemplary, nonresonant two- and three-photon processes, similar to those occurring in the recent femtosecond pulse-shaping experiments on CpMn(CO)(3), are treated using related ab initio potential energy surfaces.     

改进的半经典动力学模拟二苯乙烯光致顺反异构化反应

发展了一种改进的半经典动力学模拟方法, 并将其程序化用于气相二苯乙烯光致顺反异构化反应的机理研究.新的方法不仅采用e 指数模型改进了原有Zhu-Nakamura 理论中计算电子非绝热跃迁几率的计算方法, 而且将约束哈密顿方法用于限制性分子动力学模拟过程中. 计算结果表明, 采用此方法得到的统计平均的量子产率及反应机理与以前的实验与理论结果吻合较好, 从而可以应用于全量子动力学方法无法进行的大分子体系的动力学研究.     

Role of the F spin-orbit excited state in the F+HD reaction: contributions to the dynamical resonance

We report quantum mechanical calculations of excitation functions (relative reaction cross sections) for the F+HD reaction. We include three potential energy surfaces and an accurate treatment of all couplings (non-adiabatic, spin-orbit, and Coriolis). Comparison with experimental results [Dong, Lee, and Liu, J. Chem. Phys., 113, 3633 (2000)] show excellent agreement for the DF product channel and an improved but not perfect agreement for the HF product channel. In the former case, when weighted by the (16%) fractional population of the spin-orbit excited state (F(*)) in the beam, the overall reactivity of the F(*) is small (approximately 5%). For the HF product channel and with the same (16%) fractional weight, F(*) reactivity makes a contribution of approximately 12% in the high-energy tail of the resonance peak. As a result, averaging over the population of F spin-orbit states in the beam changes the shape of the resonance. The greater the fraction of F(*) in the beam, the less pronounced will be the resonance modulation of the reaction excitation function.