Molecular anharmonicity: A computer-aided treatment

We present a new software package for the theoretical treatment of anharmonic vibrational spectra of nonlinear polyatomic molecules. The package, called “B&D,” computes vibrational energies starting from sets of force constants defined as potential energy derivatives. The method employed allows us to combine experimental rotation-vibration data with any information made available from ab initio calculations. The package follows the natural procedure in which a molecular problem is solved, both in the symbolic construction of Hamiltonian operator and basis functions and in the numerical computation of the Hamiltonian matrix elements. The novelty consists in making the entire procedure fully automatic, so that the occurrence of errors is greatly reduced and the laborious process involved in deriving and implementing the Hamiltonian is dramatically simplified. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1716–1730, 1999     

Thermal effects in singly resonant continuous-wave optical parametric oscillators

Stability and tuning characteristics of continuous-wave optical parametric oscillators (CW OPOs) are affected by various thermal effects arising from optical absorption in nonlinear crystals. In this paper, we present an experimental study of such effects in a singly resonant CW OPO. The OPO operates in the 3-μm mid-infrared region and it is based on a MgO-doped periodically poled lithium niobate crystal. We focus our study on two thermally induced phenomena that have been recently reported to exist in singly resonant CW OPOs: optical bi-stability and thermal self-locking. Thermal self-locking effect, which is known to alter the stability and tuning properties of doubly and triply resonant CW OPOs, is shown to be also of importance in singly resonant OPOs. We report the stability and tuning characteristics of a thermally loaded OPO and discuss a simple temperature-tuning method that can be used to scan the OPO idler frequency continuously over several THz.     

Abnormal inversion splitting in NH2D: rotational analysis of the nu5 bending vibrational band system

A high-resolution Fourier transform infrared spectrum of the nu(5) bending vibrational band system region of the partially deuterated ammonia molecule NH(2)D has been measured and rotationally analyzed. The spectrum consists of strong a-type transitions between the states of same vibrational symmetry and weaker c-type transitions between the states of different vibrational symmetry. The Hamiltonian model used includes interaction terms between the rotational states of both upper and lower inversion doublets. The vibrational term values for the symmetric and the antisymmetric component of the upper-inversion doublet are 1,605.637 965(620) cm(-1) and 1,590.993 82(100) cm(-1), respectively, where the numbers in parentheses are one-standard deviations in the least significant digit. These figures are close to the corresponding values 1,605.62 cm(-1) and 1,590.72 cm(-1) obtained recently from results based on high-level ab initio calculations. The order of the vibrational term values is abnormal in the ammonia family, as typically the symmetric state is lower in wavenumber than the antisymmetric one.     

A nine-dimensional calculation of the vibrational OH stretching and HOH bending spectrum of the water trimer

We have studied the vibrational high-frequency spectrum of the water trimer computationally. We expand an earlier study [J. Chem. Phys. A 2009, 113, 9124-9132] where we approximated the water trimer as three individually vibrating water monomer units. Some intramolecular potential energy coupling terms are now included in the previous model. The six OH bond lengths and the three HOH bending angles are used as the internal coordinates. The kinetic energy operator is a sum of the kinetic energy operators of the monomer units. We use the coupled cluster method with single, double, and perturbative triple excitations method [CCSD(T)] with augmented correlation consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set to calculate the potential energy surface (PES). The counterpoise correction is included in the one-dimensional part of the PES. We calculate the vibrational energy eigenvalues using the variational method. The corresponding eigenfunctions are used to obtain the absorption intensities.     

Ab initio structural and vibrational investigation of sulfuric acid monohydrate

We employ ab initio methods to find stable geometries and to calculate potential energy surfaces and vibrational wavenumbers for sulfuric acid monohydrate. Geometry optimizations are carried out with the explicitly correlated coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)-F12a) with a valence double-ζ basis set (VDZ-F12). Four different stable geometries are found, and the two lowest are within 0.41 kJ mol(-1) (or 34 cm(-1)) of each other. Vibrational harmonic wavenumbers are calculated at both the density-fitted local spin component scaled second-order M?ller-Plesset perturbation theory (DF-SCS-LMP2) with the aug-cc-pV(T+d)Z basis set and the CCSD-F12/VDZ-F12 level. Water O-H stretching vibrations and two highly anharmonic large-amplitude motions connecting the three lowest potential energy minima are considered by limiting the dimensionality of the corresponding potential energy surfaces to small two- or three-dimensional subspaces that contain only strongly coupled vibrational degrees of freedom. In these anharmonic domains, the vibrational problem is solved variationally using potential energy surfaces calculated at the CCSD(T)-F12a/VDZ-F12 level.     

Kinetics of the reactions of chlorinated methyl radicals (CH2Cl, CHCl2, and CCl3) with NO2 in the temperature range 220-360 K

The kinetics of the reactions of chlorinated methyl radicals (CH2Cl, CHCl2, and CCl3) with NO2 have been studied in direct measurements at temperatures between 220 and 360 K using a tubular flow reactor coupled to a photoionization mass spectrometer. The radicals have been homogeneously generated at 193 or 248 nm by pulsed laser photolysis of appropriate precursors. Decays of radical concentrations have been monitored in time-resolved measurements to obtain the reaction rate coefficients under pseudo-first-order conditions with the amount of NO2 being in large excess over radical concentrations. The bimolecular rate coefficients of all three reactions are independent of the bath gas (He or N2) and pressure within the experimental range (1-6 Torr) and are found to depend on temperature as follows: k(CH2Cl + NO2) = (2.16 +/- 0.08) x 10(-11) (T/300 K)(-1.12+/-0.24) cm3 molecule(-1) s(-1) (220-363 K), k(CHCl2 + NO2) = (8.90 +/- 0.16) x 10(-12) (T/300 K)(-1.48+/-0.13) cm3 molecule(-1) s(-1) (220-363 K), and k(CCl3 + NO2) = (3.35 +/- 0.10) x 10(-12) (T/300 K)(-2.2+/-0.4) cm3 molecule(-1) s(-1) (298-363 K), with the uncertainties given as one-standard deviations. Estimated overall uncertainties in the measured bimolecular reaction rate coefficients are about +/-25%. In the reactions CH2Cl + NO2, CHCl2 + NO2, and CCl3 + NO2, the products observed are formaldehyde, CHClO, and phosgene (CCl2O), respectively. In addition, a weak signal for the HCl formation has been detected for the CHCl2 + NO2 reaction.     

Sets of convergence and stability regions

This paper continues the authors' study of the convergence of dynamic iteration methods for large systems of linear initial value problems. We ask for convergence on [0, ) and show how the convergence can be reduced to a graphical test relating the splitting of the matrix to the stability properties of the discretization method.     

Quasinilpotency of the operators in picard-lindelöf iteration

The superlinear convergence of Picard-Lindelöf iteration on finite time intervals is studied by considering the resolvent operator as an operator-valued entire function. The main conclusions of this paper are related to the following fact: the convergence properties of the iteration when applied to a large and sparse system are largely determined by the graph properties of the decomposition and are partly insensitive in terms of the values of the elements of the matrices.     

On the numerical integration of nonlinear initial value problems by linear multistep methods

We study the numerical solution of the nonlinear initial value problem $$\left\{ {\begin{array}{*{20}c} {{{du(t)} \mathord{\left/ {\vphantom {{du(t)} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} + Au(t) = f(t),t > 0} \\ {u(0) = c,} \\ \end{array} } \right.$$ whereA is a nonlinear operator in a real Hilbert space. The problem is discretized using linear multistep methods, and we assume that their stability regions have nonempty interiors. We give sharp bounds for the global error by relating the stability region of the method to the monotonicity properties ofA. In particular we study the case whereAu is the gradient of a convex functional φ(u).