Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Electronic Structure of the Ground and Low-Lying Electronic States of MoB and MoB(+)

Multiconfigurational second-order perturbation theory (CASSCF//CASPT2) and quadruple-zeta ANO-RCC basis sets were employed to investigate the ground and low-lying electronic states of MoB and MoB(+). Spectroscopic constants, potential energy curves, wavefunctions, Mulliken population analyses, and ionization energies are given. The ground state of MoB is of X(6)Pi symmetry (R(e) = 1.968 angstrom, omega(e) = 664 cm(-1), and mu = 2.7 D), giving rise to a Omega = 7/2 ground state after including spin-orbit coupling. For MoB(+), the ground state is computed to be of X(7)Sigma(+) symmetry (R(e) = 2.224 angstrom, omega(e) = 141 cm(-1), and mu = 1.2 D), with an adiabatic ionization energy of 7.19 eV and a vertical one of 7.53 eV. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3362-3370, 2011

The low-lying electronic states of BeAs: a first principles characterization

The electronic structure and spectroscopic properties of a manifold of states of a new molecular species, BeAs, have been investigated theoretically at the complete active space self-consistent field/multireference single and double excitations configuration interaction (CASSCF/MRSDCI) approach, using the aug-cc-pV5Z-PP basis set for arsenic, which includes a relativistic effective core potential, and the cc-pV5Z set for beryllium. Potential energy curves of five quartet and eight doublet (I > + S) states correlating with the five lowest-lying dissociation limit are constructed. The effect of spin-orbit coupling is also included in the description of the ground state, and of the doublet states correlating with the second dissociation channel. Dipole moment functions and vibrationally averaged dipole moments are also evaluated. The similarities and differences between BeAs, BeP, and BeN are analyzed. Spin-orbit effects are small for the ground state close to the equilibrium distance, but avoided crossings between Omega = 1/2 states, and between Omega = 3/2 states changes significantly the I > + S curves for the lowest-lying doublets.

Predicting and characterizing new molecular species at a high-level theoretical approach: HSeCl, HClSe, and SeCl

New molecular species HSeCl, HClSe, and SeCl were investigated at a high level of theory, CCSD(T), with a series of correlation consistent basis sets with extrapolation to the CBS limit. Account has been taken for valence-only and core-valence correlation effects, and of anharmonic effects on the vibrational frequencies. HSeCl is 43.25 kcal mol (1) more stable than HClSe. A barrier (Delta G(#)) of 47.20 kcal mol (1) separates these species. Internuclear distances are generally overestimated by 0.008 angstrom in the valence-only correlation calculations. Inclusion of anharmonicity leads to much improved vibrational frequencies. For SeCl, we estimate Delta H(f) (0 K) = 23.96 and Delta H(f) (298.15 K) = 24.64 kcal mol (1); for HSeCl, we had 4.20 and 4.97 kcal mol (1), respectively. (C) 2010 Elsevier B.V. All rights reserved.

Excited Electronic States, Transition Probabilities, and Radiative Lifetimes of CAs: A Theoretical Contribution and Challenge to Experimentalists

High-level CASSCF/MRCI calculations with a quintuple-zeta quality basis set are reported by characterizing for the first time a manifold of electronic states of the CAs radical yet to be investigated experimentally. Along with the potential energy curves and the associated spectroscopic constants, the dipole moment functions for selected electronic states as well as the transition dipole moment functions for the most relevant electronic transitions are also presented. Estimates of radiative transition probabilities and lifetimes complement this investigation, which also assesses the effect of spin-orbit interaction on the A (2)Pi state. Whenever pertinent, comparisons of similarities and differences with the isovalent CN and CP radicals are made.

Structural and spectroscopic properties of the diazocarbene radical (CNN) and its ions CNN(+) and CNN(-): a high-level theoretical investigation

The diazocarbene radical, CNN, and the ions CNN(+) and CNN(-) were investigated at a high level of theory. Very accurate structural parameters for the states X(3)Sigma(-) and A(3)Pi of CNN, and X(2)Pi of both CNN(+) and CNN(-) were obtained with the UCCSD(T) method using correlated-consistent basis functions with extrapolations to the complete basis set limit, with valence only and also with all electrons correlated. Harmonic and anharmonic frequencies were obtained for all species and the Renner parameter and average frequencies evaluated for the Pi states. At the UCCSD(T)/CBS(T-5) level of theory, Delta(f)H(0 K) = 138.89 kcal/mol and Delta(f)H(298 K) = 139.65 kcal/mol were obtained for diazocarbene; for the ionization potential and the electron affinity of CNN, 10.969 eV (252.95 kcal/mol), and 1.743 eV (40.19 kcal/mol), respectively, are predicted. Geometry optimization was also carried out with the CASSCF/MRCI/CBS(T-5) approach for the states X(3)Sigma(-) A(3)Pi, and a(1)Delta of CNN, and with the CASSCF/MRSDCI/aug-cc-pVTZ approach for the states b(1)Sigma(+), c(1)Pi, d(1)Sigma(-), and B(3)Sigma(-), and excitation energies (T(e)) evaluated. Vertical energies were calculated for 15 electronic states, thus improving on the accuracy of the five transitions already described, and allowing for a reliable overview of a manifold of other states, which is expected to guide future spectroscopic experiments. This study corroborates the experimental assignment for the vertical transition X (3)Sigma(-) <- E (3)Pi.

Electronic Structure and Chemical Bonding in the Lowest Electronic States of TcN

Multiconfiguration second-order perturbation theory, with the inclusion of relativistic effects and spin-orbit Coupling, was employed to investigate the nature of the ground and low-lying Lambda-S and Omega states of the TcN molecule. Spectroscopic constants, effective bond order, and potential energy curves for 13 low-lying Lambda-S states and 5 Omega states are given, The computed ground state of TcN is of Omega = 3 symmetry (R(e) = 1.605 angstrom and omega(e) = 1085 cm(-1)), originating mainly from the (3)Delta Lambda-S ground state. This result is contrasted with the nature of the ground state for other VIIB transtion-metal mononitrides, including X(3)Sigma(-) symmetry for MnN and Omega = 0(+) symmetry for ReN, derived also from a X(3)Sigma(-) state.

The low-lying electronic states of BeP: a reliable and accurate quantum mechanical prediction

A very high level of theoretical treatment (complete active space self-consistent field CASSCF/MRCI/aug-cc-pV5Z) was used to characterize the spectroscopic properties of a manifold of quartet and doublet states of the species BeP, as yet experimentally unknown. Potential energy curves for 11 electronic states were obtained, as well as the associated vibrational energy levels, and a whole set of spectroscopic constants. Dipole moment functions and vibrationally averaged dipole moments were also evaluated. Similarities and differences between BeN and BeP were analysed along with the isovalent SiB species. The molecule BeP has a X (4)Sigma(-) ground state, with an equilibrium bond distance of 2.073 angstrom, and a harmonic frequency of 516.2 cm(-1); it is followed closely by the states (2)Pi (R(e) = 2.081 angstrom, omega(e) = 639.6 cm(-1)) and (2)Sigma(-) (R(e) = 2.074 angstrom, omega(e) = 536.5 cm(-1)), at 502 and 1976 cm(-1), respectively. The other quartets investigated, A (4)Pi (R(e) = 1.991 angstrom, omega(e) = 555.3 cm(-1)) and B (4)Sigma(-) (R(e) = 2.758 angstrom, omega(e) = 292.2 cm(-1)) lie at 13 291 and 24 394 cm(-1), respectively. The remaining doublets ((2)Delta, (2)Sigma(+)(2) and (2)Pi(3)) all fall below 28 000 cm(-1). Avoided crossings between the (2)Sigma(+) states and between the (2)Pi states add an extra complexity to this manifold of states.

Theoretical Characterization of Hydrogen Polyoxides: HOOH, HOOOH, HOOOOH, and HOOO

We have investigated the polyoxides HOOH, HOOOH, HOOOOH, and HOOO employing the CCSD(T) methodology, and the correlation consistent basis sets. For all molecules, we have computed fundamental vibrational frequencies, structural parameters, rotational constants, and rotation-vibration corrections. For HOOOH, we have obtained a good agreement between our results and microwave and infrared spectra measurements, although for the symmetric OO stretch some important differences were found. Heats of formation were computed using atomization energies, and our recommendation is as follows: Delta H degrees(f,298)(HOOOH) = -21.50 kcal/mol and Delta H degrees(f,298)(HOOOOH) = -10.61 kcal/mol. In the case of HOOO, to estimate the heat of formation, we have constructed three isodesmic reactions to cancel high order correlation effects. The results obtained confirmed that the latter effects are very important for HOOO. The new Delta H degrees(f,298)(HOOO) obtained is 5.5 kcal/mol. We have also calculated the zero-point energies of DO and DOOO to correct the experimental lower limit determined for the Delta H degrees(f,298)(HOOO). The Delta(Delta ZPE) decreases the binding energy of HOOO by 0.56 kcal/mol. Employing the latter value, the new experimental lower limit for Delta H degrees(f,298)(HOOO) is 3.07 kcal/mol, just 2.4 kcal/mol lower than our determination. We expect that the fundamental vibrational frequencies and rotational constants determined for HOOOOH and DOOOOD contribute to its identification in the gas phase. The vibrational spectrum of HOOOOH shows some overlapping with that of HOOOH thus indicating that one may encounter some difficulties in its characterization. We discuss the consequences of the thermochemical properties determined in this work, and suggest that the amount of HOOO present in the atmosphere is smaller than that proposed recently in this journal (J. Phys. Chem A 2007, 111, 4727).

Electronic structure and spectra of a new molecular species: SI. A theoretical contribution

A high level theoretical approach is used to characterize for the first time a manifold of doublet and quartet A + S and Omega states correlating with the first two dissociation channels of an as yet experimentally unknown molecular species, SI, sulfur monoidide. A set of spectroscopic constants is determined, including vibrationally averaged spin-orbit coupling constants, vibrationally averaged dipole moments, and dissociation energies. The transition dipole moment function for the spin-forbidden transition a (4)Sigma -X (2)Pi, and the associated radiative lifetimes were also evaluated. Two possibilities to detect transitions experimentally and to derive spectroscopic constants are suggested. (C) 2011 Elsevier B. V. All rights reserved.

Spin contamination in XOO radicals X = F, Cl, Br, HO: How is the investigation of the HOOO radical affected

We have analysed the effect of spin contamination in the wavefunction of HOOO. At least, two solutions can be found for the HF wavefunction. One, lower in energy, presents a high spin contamination and gives qualitatively incorrect structural parameters. On the other hand, the less contaminated HF reference gives structural parameters that are in better agreement with experiment, and positive spin densities on all atoms. Some of the problems described during previous investigations of HOOO can now be traced to problems in the HF reference. For the first time we report a CCSD(T) estimation of the structure of HOOO cis employing a HF reference with small spin contamination. (C) 2008 Elsevier B.V. All rights reserved.

2-Aminopurine non-radiative decay and emission in aqueous solution: A theoretical study

The minimum energy path along the lowest-lying pi pi* excited state of 2-aminopurine was calculated to elucidate the mechanisms of radiationless decay and emission in water. The sequential Monte Carlo quantum mechanics approach with a multiconfigurational and perturbative description of the wave function was employed to compute the minimum, transition state, and conical intersection. It was found that the barrier in the potential energy surface to access the conical intersection funnel increases in aqueous environment, making the system prone to enlarge the emission yield. These results rationalize the observed enhancement of emission in 2-aminopurine upon increasing of the solvent polarity. (c) 2008 Elsevier B.V. All rights reserved.

Excited states of the CaAl molecule: An MRCI study

Accurate potential energy curves, dissociation energies and spectroscopic constants for several low-lying doublet and quartet electronic states of CaAl were investigated using the CASSCF/MRCI methodology, and the cc-pVQZ basis set. Our results represent an improvement over a previous theoretical description, and also characterizes new higher excited states not previously investigated, thus confirming the assignment of four excited states investigated experimentally. With the theoretical transition moment functions, transition probabilities and radiative lifetimes were estimated via Einstein spontaneous emission coefficients. (c) 2008 Elsevier B. V. All rights reserved.