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In this work, we consider symmetric positive definite pencils depending on two parameters. That is, we are concerned with the generalized eigenvalue problem A (x) − λ B (x) v = 0 , where A and B are symmetric matrix valued functions in ℝ n × n , smoothly depending on parameters x ∈ Ω ⊂ ℝ 2 ; furthermore, B is also positive definite. In general, the eigenvalues of this multiparameter problem will not be smooth, the lack of smoothness resulting from eigenvalues being equal at some parameter values (conical intersections). Our main goal is precisely that of locating parameter values where eigenvalues are equal. We first give general theoretical results for the present generalized eigenvalue problem, and then introduce and implement numerical methods apt at detecting conical intersections. Finally, we perform a numerical study of the statistical properties of coalescing eigenvalues for pencils where A and B are either full or banded, for several bandwidths. [ABSTRACT FROM AUTHOR]

We explore the excited-state intramolecular proton transfer process of quinophthalone theoretically. This molecule possesses three low-lying singlet excited states ( S 1 , S 2 and S 3 ) in a narrow energy gap of less than the N–H stretching frequency. Dynamics simulations show nonadiabatic wavepacket transfer to S 2 and S 3 upon initiating the wavepacket on S 1 . Multiple accessible conical intersections that lie in the Franck–Condon region facilitate the nonadiabatic wavepacket transfer. Nuclear densities associated with the proton transfer promoting vibrations would start accumulating on S 2 and S 3 within a few tens of femtoseconds, validating the involvement of these vibrations in the nonadiabatic events that occur before the proton transfer process. Our findings emphasize the necessity of refined kinetic models for assigning the time constants of ultrafast transient spectroscopy measurements due to the simultaneous evolution of nonadiabatic events and proton transfer kinetics in quinophthalone. [ABSTRACT FROM AUTHOR]

Carbonyl oxides, or Criegee intermediates, play an important role in many physicochemical processes occurring in the Earth's atmosphere. Criegee intermediates are chemically active compounds that easily react with other atmospheric components, promoting the formation of OH and CH3 radicals, toxic compounds of nitrogen, and various acids. Traditionally, the literature considers reactions involving only those carbonyl oxides that are the most stable in the troposphere under the standard atmospheric conditions. In this study, it is shown that in the mesosphere and ionosphere, where the total concentration of molecules is low and the intensity of UV radiation and the number of free electrons are high, reactions involving electronically excited states of the Criegee intermediates CH3CHOO play a significant role. In this case, we should take into account the features of the decomposition of all isomers of the CH3CHOO molecule. [ABSTRACT FROM AUTHOR]

The crystal structure of 5-azacytosine was proposed by the X-ray diffraction pattern of the compound and the performed Rietveld analysis. The crystal structure solutions were achieved with the simulated annealing procedure. The model molecule for the procedure was taken from the BLYP/aug-cc-pVDZ optimization of the N1(H) oxo-amino tautomer of the compound. The refined unit cell parameters are: a = 12.82916 Å, b = 9.47282 Å, c = 3.66363 Å, and space group P212121. The studied excited-state reaction paths of the H-detachment processes of two oxo-amino tautomers show a possibility for mutual phototransformation of the two oxo-amino tautomers: N1(H) and N5(H). The driven states of this photoreaction are the 1nσ* and 1πσ* excited states. [ABSTRACT FROM AUTHOR]

We have carried out a combined theoretical (at the TDDFT BLYP/6-311++G** level of theory) and experimental study of the mechanism of phototautmerization of the N(3)H oxo tautomer of isocytosine dissolved in a water medium. The study reveals that this photoreaction occurs along the 1πσ* excited-state reaction paths of the oxo and hydroxy tautomers of the compound through conical intersections S0/S1. The last strucutres are located at the CASSCF level for both tautomers. [ABSTRACT FROM AUTHOR]

Techniques developed for investigating nonadiabatic processes in molecular systems are adapted to study the structure and properties of holomorphic and meromorphic functions of a complex variable, $$f(z)=\mathfrak {R}(f)+i\,\mathfrak {I}(f)$$ . The connection is that $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ are correlated two-dimensional scalar functions, interrelated by the Cauchy-Riemann equations. Exploiting this fact, it is demonstrated that $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ of f can be envisaged in Euclidean $${\mathbb {R}}^{3}$$ space as a two-state set of constrained, intersecting two-dimensional potential energy surfaces ( PESs), called the graph of f. Importantly, the analytic and algebraic properties of f dictate the geometric structure evinced in the graph of f. This parallels multi-state sets of higher-dimensional, constrained, intersecting PESs linked with correlated electronic eigenstates of the parameterized molecular Hamiltonian operator. In view of this association, the language and mathematical infrastructure devised by chemists for discussing and analyzing intersections in higher-dimensional PESs are suitably modified for f. Notably, an algorithm capable of optimizing roots and poles of f through analysis of the real, two-dimensional $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ functions is derived, which is based on intersection-adapted coordinate and constrained Lagrangian methodologies. As constrained, intersecting PESs are indispensible for conceptualizing and characterizing the physics governing nonadiabatic phenomena, f represents a foundational bridge to these more abstract constructions. [ABSTRACT FROM AUTHOR]

The mechanisms for the photochemical isomerization reactions are investigated theoretically using a model system of (+)-2-carene-4α-methanol (2-carene) 1, using the CASSCF (eight-electron/six-orbital active space) and MP2-CAS methods and the 6-311( d) and 6-311++G(3 df, 3 pd) basis sets, respectively. The structures of the intersystem crossings, which play a crucial role in these photo-isomerization reactions, are identified. The intermediates and transition structures of the ground state are also calculated to provide a qualitative explanation of the reaction pathways. The model investigations suggest that the preferred reaction route for 1 is as follows: singlet reactant → Franck-Condon region → triplet reactant → triplet transition state → intersystem crossing → intermediate → singlet transition state → photoproduct. In particular, the intersystem-crossing mechanism in this work gives a better explanation and supports the available experimental observations. Two types of reaction pathways that lead to final photoproducts are identified: (path I) ring expansion to form a cycloheptene ring and (path II) ring closure to form a methylcyclohexene structure. Both exhibit a biradical character. These theoretical results agree well with the available experimental observations. [ABSTRACT FROM AUTHOR]

We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value $$n \in \mathbb {Z}$$ of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function $$w$$ satisfies $$|w(x)| \le {\mathrm {const}} \cdot |x|^{-2}$$ as $$|x| \rightarrow \infty $$ , both in monolayer and bilayer graphene. [ABSTRACT FROM AUTHOR]

The Jahn-Teller effect in excited states of nitrosyl complexes was analyzed in terms of the density functional theory at the B3LYP level. This effect was shown to play a role in transitions between metastable isomers and their photoactivated relaxation to the ground state. In the compounds under study, the Jahn-Teller effect can be interpreted as the Renner-Teller effect. The characteristics of the Jahn-Teller potential energy surfaces were determined. [ABSTRACT FROM AUTHOR]

The nucleobases cytosine, uracil, and thymine and their H-bonded complexes with one molecule of water were studied at the CC2/aug-cc-pVDZ level of theory. The excited-state deactivation mechanisms through the conical intersections S/S were investigated. It was found that the ππ excited states of cytosine, the hydroxy tautomer of uracil, and the hydroxy tautomer of thymine relax non-radiatively to the ground state S. However, only monohydrated and anhydrous thymine do not have energy barriers of the ππ excited-state reaction paths. The photophysical reaction of monohydrated thymine could proceed in two directions on the S surface. Graphical abstract: [Figure not available: see fulltext.]. [ABSTRACT FROM AUTHOR]

The aim of this text is to present a surface hopping approximation for molecular quantum dynamics obeying a Schrödinger equation with crossing eigenvalue surfaces. After motivating Schrödinger equations with matrix valued potentials, we describe the single switch algorithm and present some numerical results. Then we discuss the algorithm's mathematical justification and describe extensions to more general situations, where three eigenvalue surfaces intersect or the eigenvalues are of multiplicity two. We emphasize the generality of this surface hopping approximation for non-adiabatic transitions. [ABSTRACT FROM AUTHOR]

The first three photoelectron bands of 2-phenylethyl- N, N-dimethylamine (PENNA) are investigated theoretically, paying particular attention to the vibrational structure and to possible nonadiabatic coupling effects. A substantial vibronic interaction is established between the first and second excited cationic states (corresponding to the second and third photoelectron bands). Their coupling to the cationic ground state is found to be rather weak. This is tentatively attributed to the well-known fact that the latter carries a hole at the amine site, while the former two have the electron removed from benzene-type orbitals. The interaction between the two excited cationic states is characterized by a 'hidden' or local symmetry at the phenyl moiety. Preliminary dynamic calculations with two interacting electronic states and four vibrational modes are reported. The computed spectra are compared to experimental results of Weinkauf et al. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

Three conical intersections of monohydrated cytosine, uracil, and thymine were found between the S and S states. The pyrimidine bases in these conical intersections have unusual shape with rather distorted aromatic rings caused by the strong interactions between the pyrimidines and the water molecule. The conical intersections of uracil and thymine monohydrates have structures with considerable out-of-plane deviation of one of the carbonyl groups. The conical intersection of cytosine monohydrate showed a ring cleavage of the N-C bond, while the NH group is almost perpendicular to the aromatic ring. The three conical intersections show a tendency to form Dewar forms. Thus, in the theoretical study we included the possible Dewar forms of the monohydrated pyrimidine bases closely related to the structures of the conical intersections. Graphical abstract: [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The ground and electronically excited singlet states of tetrahydrocannabinol have been studied theoretically using density functional and time-dependent density functional methods. The vertical excitation energies, the equilibrium geometries as well as the adiabatic excitation energies have been determined. Opening of the six-membered ring between the oxygen and carbon atoms has been considered as photochemical reaction path. This mechanism leads to a typical excited-state intramolecular hydrogen-transfer process and produces low-lying S0– S1 intersection (possible conical intersection, CI) which provides a channel for effective radiationless deactivation of the electronically excited state. [ABSTRACT FROM AUTHOR]

The effect of coriolis coupling on the dynamics of H + H2 reaction is examined by calculating the initial state-selected and energy resolved reaction probabilities on the coupled manifold of its degenerate 2p (E') ground electronic state. H3 in this state is prone to the Jahn-Teller (JT) instability and consequently the degeneracy is split upon distortion from its D3h equilibrium geometry. The orbital degeneracy is, however, restored along the D3h symmetry configuration and it results into conical intersections of the two JT split component states. The energetically lower adiabatic component of latter is repulsive, and mainly ('rather solely') drive the H + H2 reaction dynamics. On the otherhand, the upper adiabatic component is of bound type and can only impart non-adiabaticity on the dynamics of lower state. Comparison calculations are therefore also carried out on the uncoupled lower adiabatic sheet to assess the nonadiabatic effect. Exact quantum scattering calculations are performed by a chebyshev polynomial propagator and employing the double many body expansion potential energy surface of the electronic ground state of H3. Reaction probabilities are reported up to a total energy of ∼ 3·0 eV, slightly above the energetic minimum of the seam of conical intersections at ∼ 2·74 eV. Reaction probabilities are calculated up to the total angular momentum, J = 20 and for each value of J, the projection quantum number K is varied from 0 to min (J, Kmax), with Kmax = 4. Probability results are compared and discussed with those obtained without the coriolis coupling. [ABSTRACT FROM AUTHOR]

The potential energy surfaces and non-adiabatic dynamics of the C5H6NH protonated Schiff base (PSB3) have been investigated using the OM2 semiempirical Hamiltonian with GUGA configuration interaction. Three approaches to selecting the GUGA-CI active space are evaluated using closed-shell and open-shell molecular orbitals. Energy minima and minimum energy crossing points (MECPs) have been compared with ab initio CASSCF and CASPT2 results. Only the open-shell calculations give a qualitatively correct MECP. Minimum energy path (MEP) calculations demonstrate that a minimal active space gives a barrierless path from the planar S1 minimum to the ground state, whereas larger active spaces result in a small barrier to torsional motion. Surface hopping dynamics calculations indicate that this barrier induces bi-exponential dynamics. The comparable CASSCF S1 energy surface is barrierless, but the CASPT2 surface features an energy plateau, which may also lead to more complex dynamics. [ABSTRACT FROM AUTHOR]

The potential surfaces of the ground and lowest excited states of the [RuCl5NO]2− complex ion were studied by density functional theory. The conical intersections between the potential surfaces of the ground and lowest excited states were found and characterized. The possible routes from the conical intersection points to the ground state and metastable bond isomers were traced. A preliminary scheme, describing photoisomerizations in the complex, was suggested. [ABSTRACT FROM AUTHOR]

We present a comparison of three previously published algorithms for optimising the minimum energy crossing point between two Born–Oppenheimer electronic states. The algorithms are implemented in a development version of the MNDO electronic structure package for use with semiempirical configuration interaction methods. The penalty function method requires only the energies and gradients of the states involved, whereas the gradient projection and Lagrange–Newton methods also require the calculation of non-adiabatic coupling terms. The performance of the algorithms is measured against a set of well-known small molecule conical intersections. The Lagrange–Newton method is found to be the most efficient, with the projected gradient method also competitive. The penalty function method can only be recommended for situations where non-adiabatic coupling terms cannot be calculated. [ABSTRACT FROM AUTHOR]

Reaction dynamics of prototypical, D + H2 and Cl (²P) + H2, chemical reactions occurring through the conical intersections of the respective coupled multi-sheeted potential energy surfaces is examined here. In addition to the electronic coupling, nonadiabatic effects due to relativistic spin-orbit coupling are also considered for the latter reaction. A time-dependent wave packet propagation approach is undertaken and the quantum dynamical observables viz., energy resolved reaction probabilities, integral reaction cross-sections and thermal rate constants are reported. [ABSTRACT FROM AUTHOR]

CASPT2//CASSCF/6-31G* computations are used on the singlet S 1 and S 2 states to map the photoisomerization process of the 11-cis retinal protonated Schiff base in vacuo and to characterize its optical properties. It is shown that the spectroscopic observations recorded in Rhodopsin are reproduced quite well, calling for a substantially neutral effect of the protein. Furthermore, a rationale is proposed for the unreactive population recently observed in Rhodopsin, which is here addressed to the accessible S 2 state, behaving as a trap. The experimental transient absorption and (absorption-wavelength dependent) emission are discussed and interpreted under the light of this novel model. Finally, a planarization of the β-ionone ring is observed on S 1, which may cause a steric lever effect into the protein pocket, thus assisting photoisomerization catalysis. The reported results constitute a solid reference for further studies aimed to rationalize the effect of the environment on the photochemical reactivity of retinal chromophores. [ABSTRACT FROM AUTHOR]

We explore the application of the electron position spread tensor, i.e., a quantitative measure of the electron delocalization and mobility, to the conical intersection regions of three relevant compounds showing either photoisomerization or chemiluminescence properties. The electronic structure of the involved states has been solved using the complete active space self-consistent field method, and the position spread tensor has been computed at the same level of theory. In particular, we show that the total position spread tensor is degenerate between the ground and the excited states, because of the inversion of the electronic nature of the states happening at the crossing areas. We also show that the ground-state position spread tensor shows a discontinuity that may be used to locate conical intersections without the need to explicitly compute the excited-state wavefunction. Furthermore, we also report that the spin partition position spread tensor shows a peculiar behavior presenting values close to zero in two of its principal components. We associate those small values to the degeneracy-lifting coordinates and hence to the conical intersection branching space. [ABSTRACT FROM AUTHOR]