ALBERT

Notes: Several complementary analyses have been performed in an investigation of the use of reference geometric structures which are not stationary at a given level of theory in the prediction of improved equilibrium anharmonic molecular force fields. Diatomic paradigms for the procedure were established by constructing empirical potential energy functions for the nitrogen and fluorine molecules which not only reproduce the available Rydberg–Klein–Rees data but also provide reliable derivatives through fourth order for ranges of 0.4 A(ring) or greater around the equilibrium bond distance. For comparison, analogous curves were determined at the double-ζ plus polarization (DZP) restricted Hartree–Fock (RHF) level of theory, and the quartic force fields for N2 and F2 were also obtained at the experimental re structures using a (8s5p3d2f1g) basis set and the coupled-cluster singles and doubles method augmented by a perturbative contribution from connected triple excitations [CCSD(T)].The results substantiate the ability of RHF theory to predict correlation-quality, higher-order force constants if an accurate reference geometry from experiment or a higher level of theory is employed. The theoretical foundations of this technique as applied to polyatomic molecular systems have been systematically explored. Mechanisms were analyzed which address the nonzero force dilemma by using various choices of internal coordinates to shift the equilibrium point of theoretical potential energy surfaces. Examples are presented in which the variations in predicted spectroscopic constants arising from different shift coordinate sets are non-negligible. A Cartesian projection scheme for higher-order force fields was developed and implemented to avert internal-coordinate dependences; formulas for higher-order projection matrices and higher-order derivatives of the external variables of a molecular system were concurrently derived. A formalism for the transformation of force fields between internal and Cartesian representations was also constructed which is applicable to arbitrary order. In addition to N2 and F2, case studies were performed on the F2O and N2O molecules, for which electron correlation effects are of unusual importance. Quartic force fields are reported for F2O and N2O at the DZP and TZ(2d1f) CCSD(T) levels of theory, respectively, which provide the best data sets currently available and facilitate the assessment of experimental force constants. The CCSD(T) results are reproduced remarkably well by RHF predictions at the experimental equilibrium structures of these molecules but not at the corresponding RHF optimum geometries. Finally, practical recommendations are made for predictions of higher-order force constants at nonstationary points.

Notes: The [FHCl]− molecular anion has been investigated in detail by means of state-of-the-art ab initio electronic structure methods, including restricted Hartree–Fock (RHF), Møller–Plesset perturbation theory (MP2–MP4), and coupled-cluster and Brueckner methods incorporating various degrees of excitation [CCSD, CCSD(T), BD, BD(T), and BD(TQ)]. The one-particle Gaussian basis sets ranged in quality from F[6s4p2d], Cl[10s7p2d], and H[4s2p] to F[18s13p6d4f], Cl[20s14p7d5f], and H[8s3p2d1f]. The first phase of the investigation focused on the prediction of thermochemical, spectroscopic, and bonding properties of [FHCl]− and the chemical interpretation thereof.The final proposals for the geometric structure and binding energy of the complex are re(H–F)=0.963±0.003 A(ring), Re(H–Cl)=1.925±0.015 A(ring), and D0(HF+Cl−)=21.8±0.4 kcal mol−1. A Morokuma decomposition of the ion-molecule bonding gave the following electrostatic (ES), polarization (PL), exchange repulsion (EX), dispersion (DISP), and charge-transfer plus higher-order mixing (CT+MIX) components of the vibrationless complexation energy: −27.3 (ES), −5.2 (PL), +18.3 (EX), −4.5 (DISP), and −5.0 (CT+MIX) kcal mol−1. The second phase of the work involved the construction of a CCSD global surface from 208 and 228 energy points for linear and bent conformations, respectively, these being fit to rms errors of only 3.9 and 9.3 cm−1, respectively, below 8000 cm−1. The surface was represented by a flexible analytic form which reproduces the quartic force field at equilibrium, exhibits the proper asymptotic properties, and is generally applicable to ion-molecule systems. The final phase of the study entailed the determination of converged J=0 and J=1 variational eigenstates of the [FHCl]− surface to near the HF+Cl− dissociation threshold by employing Jacobi coordinates and vibrational configuration interaction expansions in terms of natural modals.The fundamental vibrational frequencies given by the analysis were ν1=247, ν2=876, and ν3=2884 cm−1. The complete vibrational eigenspectrum was then analyzed in terms of several contemporary dynamical issues, including vibrational adiabaticity, anharmonic resonances, densities of high-lying states, and signatures of quantum ergodicity.

Notes: The full nonrelativistic quantum mechanical vibrational (J=0) kinetic energy operator for sequentially bonded N-atom molecules, expressed in valence stretch, bend, and torsion internal coordinates, is explicitly given. Certain properties of the operator and its possible applications are discussed. © 1995 American Institute of Physics.

Notes: The full quartic force field of the ground electronic state of the silyl anion (SiH3−) has been determined at the CCSD(T)-R12 level employing a [Si/H]=[16s11p6d5f/7s5p4d] basis set. The vibrational energy levels, using the quartic force field as a representation of the potential energy hypersurface around equilibrium, have been determined by vibrational perturbation theory carried out to second, fourth, and sixth order. The undetected vibrational fundamental for the umbrella mode, ν2, is predicted to be 844 cm−1. High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory with basis sets ranging from [Si/H] [5s4p2d/3s2p] to [8s7p6d5f4g3h/7s6p5d4f3g] have been employed to obtain the best possible value for the inversion barrier of the silyl anion. The rarely quantified effects of one- and two-particle relativistic terms, core correlation, and the diagonal Born–Oppenheimer correction (DBOC) have been included in the determination of the barrier for this model system. The final electronic (vibrationless) extrapolated barrier height of this study is 8351±100 cm−1. © 2000 American Institute of Physics.