A new table‐direct CI (TDCI) scheme based on the table CI method for the direct computation of Hamiltonian matrix elements whose basis functions are linear combinations of spin‐adapted functions ψα is presented, in which the explicit calculation and storage of the Hamiltonian matrix H in the basis {ψα} is avoided. Two algorithms are provided for the matrix element evaluation; (i) within the iterative Davidson diagonalization procedure of H and (ii) within the individualized configuration selection scheme of Buenker and Peyerimhoff, as included in the MRD‐CI program of these authors. The new algorithm is employed to compute the equilibrium structural parameters of the lowest X 2A1 and A 2B2 states of NO2, solving secular equations of dimension 190 000 spin‐adapted functions (384 000 determinants, 32 000 configurations), as well as the Te value for the corresponding transition.

A new table-direct configuration interaction method for the evaluation of Hamiltonian matrix elements in a basis of linear combinations of spin-adapted functions

▪ Abstract In this overview we discuss the vibrational spectrum of phosphaethyne, HCP, in its electronic ground state, as revealed by complementary experimental and theoretical examinations. The main focus is the evolution of specific spectral patterns from the bottom of the potential well up to excitation energies of approximately 25,000 cm−1, where large-amplitude, isomerization-type motion from H–CP to CP–H is prominent. Distinct structural and dynamical changes, caused by an abrupt transformation from essentially HC bonding to mainly PH bonding, set in around 13,000 cm−1. They reflect saddle-node bifurcations in the classical phase space—a phenomenon well known in the nonlinear dynamics literature—and result in characteristic patterns in the spectrum and the quantum-number dependence of the vibrational fine-structure constants. Two polar opposites are employed to elucidate the spectral patterns: the exact solution of the Schrodinger equation, using an accurate potential energy surface and an effective...

HCP CPH ISOMERIZATION: Caught in the Act

Three practical methods for computing sums and densities of states of fully coupled anharmonic vibrations are compared. All three methods are based on the standard perturbation theory expansion for the vibrational energy. The accuracy of the perturbation theory expansion is tested by comparisons with computed eigenvalues and/or experimental vibrational constants taken from the literature for three- and four-atom molecules. For a number of examples, it is shown that the Xij terms in the perturbation theory expansion account for most of the anharmonicity, and the Yijk terms also make a small contribution; contributions from the Zijkl terms are insignificant. For molecules containing up to ∼4 atoms, the sums and densities of states can be computed by using nested DO-loops, but this method becomes impractical for larger species. An efficient Monte Carlo method published previously is both accurate and practical for molecules containing 3−6 atoms but becomes too slow for larger species. The Wang−Landau algorit...

Sums and densities of fully coupled anharmonic vibrational states: a comparison of three practical methods.

We report detailed vibrational, rotational, and electronic (V,R,E) distributions of nascent NO(X 2Π1/2,3/2) deriving from monoenergetic unimolecular reactions of expansion‐cooled NO2. Near UV excitation above dissociation threshold (25 130.6 cm−1) prepares molecular eigenstates which are admixtures of the optically active 1 2B2 state and the ground X 2A1 electronic state. The strong mixings among the vibronic states result in vibrational predissociation from states of predominantly ground state character, and the NO product state distributions (PSDs) are compared with the predictions of several statistical theories. The PSDs are combined with previously measured O(3PJ) distributions and unimolecular reaction rates, thereby providing a complete description of the decomposition of NO2 at these excess energies. All the rotational distributions show prominent fluctuations and structures, but tend on average to follow the statistical distributions predicted by phase space theory (PST). This behavior is observ...

The monoenergetic unimolecular reaction of expansion‐cooled NO2: NO product state distributions at excess energies 0–3000 cm−1

Time resolved, subpicosecond resolution measurements of photoinitiated NO2 unimolecular decomposition rates are reported for expansion cooled and room temperature samples. The molecules are excited by 375–402 nm tunable subpicosecond pulses having bandwidths ≥20 cm−1 to levels which are known to be thorough admixtures of the 2B2 electronically excited state and the 2A1 ground electronic state. Subsequent decomposition is probed by a 226 nm subpicosecond pulse that excites laser‐induced fluorescence (LIF) in the NO product. When increasing the amount of excitation over the dissociation threshold, an uneven, ‘‘step‐like’’ increase of the decomposition rate vs energy is observed for expansion cooled samples. The steps are spaced by ∼100 cm−1 and can be assigned ad hoc to bending at the transition state. Relying on experimental estimates for the near threshold density of states, we point out that simple transition state theory predictions give rates that are consistent with these measured values. The rates ar...

Probing the NO2→NO+O transition state via time resolved unimolecular decomposition

The laser induced dispersed fluorescence spectra (L.I.D.F.S.) of jet cooled NO2 molecules in emission from 11 different vibronic levels located between 22 006 and 23 625 cm−1 was recorded. The corresponding variety of Franck–Condon accesses has allowed the observation of the complete set of the 191 lowest vibrational levels of the X 2A1 ground state, located up to 10 000 cm−1. The vibrational band origins were measured to within typically 0.3 cm−1, assigned (n1, n2, n3), and fitted with a 24 coefficient Dunham expansion giving a typical residual error of 0.5 cm−1. Furthermore, the vibrationless A 2B2 level has probably also been observed at 9737 cm−1. A perturbative model of the X 2A1–A 2B2 vibronic interaction has been used in order to calculate the energy shift of the high vibrational levels (around 10 000 cm−1) of the X 2A1 state.

Laser induced dispersed fluorescence spectra of jet cooled NO2: The complete set of vibrational levels up to 10 000 cm−1 and the onset of the X̃ 2A1–Ã 2B2 vibronic interaction

A. Delon

Papers

Laser induced dispersed fluorescence spectra of jet cooled NO2: The complete set of vibrational levels up to 10 000 cm−1 and the onset of the X̃ 2A1–Ã 2B2 vibronic interaction