Richard B. Remington

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Linear polyatomic molecules

The inclusion of the anharmonicity of molecular vibrations is an important aspect of the goal of making highly accurate theoreticalpredictions of the spectroscopic properties of molecules. Recently developed analytic third derivative methods for selfconsistent-field(SCF) wavefunctions have made it possible to determine the complete cubic and quartic force fields of polyatomic molecules, thus allowing the treatment of anharmonic effects. Here we continue our systematic evaluation of the performance of such theoretical methods by studying several linear molecules which are well characterized experimentally, viz., HCN, DCN, CO2, N2O, OCS, C2H2, and C2D2. A number of anharmonic molecular properties have been determined, including vibration-rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, rotational constants which include zero-point vibrational corrections, and vibrational and rotational l-type doubling constants. These anharmonic molecular constants are not as well converged with respect to basis set enlargement as those which were previously determined for asymmetric top molecules, apparently because all the molecules considered here contain multiple bonds. However, the reported anharmonic constants at the SCF level of theory are still in reasonably good agreement with the corresponding experimental constants. Significant improvements in accuracy are achieved by incorporating electron correlation at the configuration interaction singles and doubles (CISD) level of theory. Standard spectroscopic perturbationtheory methods are used in this study, which are directly and immediately applicable to larger molecular systems than those studied here.

THE PROTONATED WATER DIMER : EXTENSIVE THEORETICAL STUDIES OF H5O+2

Ab initio quantum mechanical methods have been applied to the H5O+2 system, for which experiments are beginning to appear. These methods include basis sets up to triple‐ζ plus double polarization plus f functions (TZ2Pf ) and levels of correlation up to coupled cluster including single, double, and perturbatively treated connected triple excitations [CCSD(T)]. The potential energy hypersurface is very flat and is sensitive to the level of theory. At the highest level of theory the global minimum is the structure with C2 symmetry, but the transition state with Cs symmetry is only 0.4 kcal/mol higher in energy. Some low energy excursions into C1 symmetry are carefully examined. The theoretical dissociation energy for the H3O+–H2O system is predicted to be 33.4 kcal/mol, and is in good agreement with experimental measurements. The harmonic vibrational frequencies and their infrared intensities at several levels of theory are also reported, and compared to the recent spectroscopic observations in Lee’s labora...

The lithium superoxide radical: symmetry breaking phenomena and potential energy surfaces

Abstract The two lowest electronic states of the lithium superoxide radical, LiO2, have been investigated using ab initio theoretical techniques, including RHF SCF, CISD, Davidson-corrected CISD [CISD + (Q)], UHF SCF, UMP2, UMP3, UMP4(SDTQ), spin-projected UHF and UMP, valence and extravalence CASSCF (CASSCF-v and CASSCF-π), and CISD based on CASSCF natural orbitals (CISD-π). Four basis sets ranging in quality from Li (9s4p/5s2p), O (9s5pld/5s3pld) to Li (10s5pld/6s4pld), O(11s7p2dlf/6s5p2dlf) were employed, these being designated TZP, QZ2P, QZ2P+R, and QZ2P+R+f. The investigation encompassed dissociation energies, relative energies of various conformations, geometrical structures, vibrational frequencies, infrared and Raman intensities, dipole moments, cubic force fields, vibration-rotation interaction constants, and symmetry breaking phenomena. The onset of spatial symmetry breaking in the electronic orbitals of the TZP RHF reference wavefunction for X 2A2 LiO2 leads to an irremovable singularity in the quadratic force constant for antisymmetric LiO stretching at the isosceles-triangle (C2v) geometry d(OO) = 1.3266 A and r(LiO) = 1.7737 A. This anomalous lowering of spatial symmetry from C2v to Cs, makes the two oxygen atoms inequivalent, and thus it becomes necessary to avert the symmetry dilemma in the reference wavefunction to provide unequivocal evidence for a C2v geometrical structure of X 2A2 LiO2 which is consistent with the ionic model. This task is achieved with the CASSCF-π and CISD-π wavefunctions, the latter yielding d(OO) = 1.3405 A, r(LiO) = 1.7937 A, ω1(a1) = 1263 cm−1, ω2(a1) = 740 cm−1, and ω3(b2) = 519 cm−1 at the C2v equilibrium geometry. Final proposals of d(OO) = 1.335 A, r(LiO) = 1.76 A, and D0(LiO2) = 62 kcal/mol are made for X 2A2 LiO2, as indicated by appurtenant studies of X 2ΠgO2−1 and X 2Π LiO. Improved predictions are thereby provided for gas-phase LiO, viz., re = 1.694 A ωe = 814 cm−1, ν0 = 798 cm−1, and D0(LiO) = 86 kcal/mol. The A 2B2 state of LiO2 is also predicted to have a C2v geometrical structure, d(OO) = 1.3497 A and r(LiO) = 1.8612 A being obtained at the TZP CISD level, and a final adiabatic excitation energy of Te = 16.7 kcal/mol is determined. A large differential correlation energy effect is found to be important in obtaining an accurate relative energy for the 2Π, C2∞v, LiOO linear structure, which is found to be a shallow minimum 22.2 kcal/mol above the X 2A2, C2v state with TZP CISD bond lengths of d(OO) = 1.3149 A and r(LiO) = 1.6341 A. Finally, 2Π LiO2 is connected to the X 2A2 and A 2B2 minima via two transition states of 2A″ and 2A′ symmetry, respectively, with interconversion barriers near 1.4 and 1.1 kcal/mol.

The H+5 potential energy hypersurface: Characterization of ten distinct energetically low‐lying stationary points

Ab initio molecular electronic structure theory has been used in an attempt to characterize the low‐lying stationary points on the H+5 potential energy hypersurface. Three distinct levels of theory have been used: the self‐consistent‐field (SCF) method, configuration interaction (CI) including all single and double excitations, and full configuration interaction. Four different basis sets were used: double zeta (DZ), double zeta plus polarization (DZP), an extended basis set designated H (6s2p/4s2p), and a second extended basis set designated H (8s3p/6s3p). The higher levels of theory are in agreement that the only minimum for H+5 is a C2v structure, with three other stationary points (of D2d, C2v, and D2h symmetries) lying less than 1 kcal/mol higher in energy. The predicted dissociation energy D0 is 5.5 kcal/mol, which is estimated to be about 1 kcal/mol less than the exact D0. Furthermore, there are six other stationary points lying less than 8 kcal/mol above the minimum. Vibrational frequencies, dipol...

The effects of triple and quadruple excitations in configuration interaction procedures for the quantum mechanical prediction of molecular properties

The importance of including triple and quadruple excitations (relative to a single Hartree–Fock determinant) in ab initio electronic structure configuration interaction (CI) theory is investigated for several small molecules [HF, N2, CO, H2O, NH3, (3B1) CH2, and (1A1) CH2]. Specifically the effects of these high order electron correlations on equilibrium molecular geometries, dipole moments, harmonic vibrational frequencies, and infrared intensities are reported. Triple and quadruple excitations are generally found to affect the dipole moment, in an absolute sense, only slightly. In some cases, infrared intensities show a medium to large dependence on higher excitations. Molecular geometries, and subsequently the harmonic vibrational frequencies, however, are significantly more dependent upon these higher excitations. Quadruple excitations are found to be significantly more important than triple excitations for all closed shell systems except for CO, where the relative importance of triples to quadruples ...

Analytic energy third derivatives for open-shell self-consistent-field wavefunctions

Abstract A theoretical formalism and its implementation are described for the analytic evaluation of energy third derivatives for open-shell, single-configuration Hartree-Fock wavefunctions. Cubic force constants and vibration-rotation interaction constants for the electronically excited states of methylene and formaldehyde are predicted using a wide range of basis sets, from minimum basis through triple zeta plus double polarization.

How bent can a benzene be? The molecular structure, infrared spectrum and energetics of [6]paracyclophane

Abstract Ab initio molecular quantum mechanical methods have been applied to the [6] paracyclophane molecule (C 12 H 16 ), prepared by M. Jones and co-workers in 1974. The complete molecular structure has been predicted via the self-consistent-field (SCF) method, using both minimum and double-zeta [C(9s5p/4s2p), H(4s/2s)] basis sets. The critical geometrical parameter is the deviation φ of the benzene ring from planarity, and φ is predicted to be 17.2° and 18.6°, respectively, with the minimum and double-zeta (DZ) basis sets. The DZ angle agrees well with the experimental values, 19.4° and 20.7° , taken from crystal structures of substituted [6] paracyclophanes. These bending angles φ are 5.2° (minimum basis) and 5.1° (DZ basis) less than the analogous theoretical predictions for the less stable [5] paracyclophane. DZ SCF harmonic vibrational frequencies and infrared intensities are presented and compared with analogous predictions for benzene. The vertical excitation energies for the lowest triplet and first excited singlet states of [6] paracyclophane are also investigated. Finally the resonance energy is predicted from a suitable homodesmotic reaction and compared to the analogous result for benzene. The question of whether [6] paracyclophane is aromatic is discussed from several different perspectives.

Analytic energy second derivatives for paired-excited multi-configuration self-consistent-field wavefunctions. Application of the PE MCSCF model to H2O, CH2, HCN, HCCH, H2CO, NH3, CH4, and C2H4

Abstract A method to analytically evaluate second derivatives for both the generalized valence bond (GVB) and paired-excited multiconfigurationself-consistent-field (PE MCSCF) wavefunctions is presented. Harmonic vibrational frequencies, infrared intensities, and electric polarizabilities, all of which have been evaluated with several basis sets, are reported for H2O, CH2(3B1), CH2 (1A1), HCN, C2H2, H2CO (1A1), H2CO (3A″), NH3, CH4, and C2H4 in order to demonstrate the importance of these techniques. This work presents the most detailed examination to date of the reliability of the PE MCSCF approach to the correlation problem.

[5]Paracyclophane: molecular structure and implications for aromaticity

Abstract The structure of [5]paracyclophane was optimized at the STO-3G SCF level. The dihedral angle φ, which is zero for benzene, is 22.4°. This value is significantly less than previously reported values obtained via molecular mechanics modeling techniques or MNDO calculations. Although our ab initio structure predicts a larger C-C bond alternation in the benzene ring (C-C bond lengths vary from 1.365 to 1.415 A), the smaller angle φ indicates that the title compound is more stable and probably possesses more “aromatic character” than previous theoretical studies concluded. A discussion concerning the ambiguity of “aromatic character” is presented.

The molecular structures and energetics of [7]paracyclophane and [8]paracyclophane. an investigation of the boundaries of aromaticity

Abstract The equilibrium geometries of the [ n ] paracyclophanes ( n = 7,8) have been predicted via ab initio molecular quantum mechanics. Self-consistent-field (SCF) theory has been used in conjunction with minimum (MBS) and double-zeta (DZ) basis sets. Together with earlier theoretical studies of [5]paracyclophane and [6]paracyclophane, this research comprises a fairly complete study of the structures of small paracyclophanes for which some experimental data exists.