Ian L. Alberts

Geometrical structures and vibrational frequencies of the energetically low‐lying isomers of SiC3

The ground state of the SiC3 molecule is found to be a closed‐shell cyclic C2v symmetry structure which can be described as a four‐membered ring with a transannular (cross ring) carbon–carbon bond, r(C–C)=1.469 A. Theoretical studies with a triple‐zeta plus double‐polarization function (TZ2P) basis set in conjunction with the configuration‐interaction technique at the TZ2P self‐consistent‐field optimized geometries predict this rhomboidal structure to be 4.1 kcal/mol more stable than the linear triplet Si–C–C–C isomer. A second closed‐shell rhomboidal C2v symmetry structure with carbon–silicon transannular bonding, r(Si–C)=1.880 A, was located and characterized as a local minimum lying 4.3 kcal/mol above the ground‐state rhomboidal structure at this level of theory. Higher‐level theoretical methods, including contributions from triple excitations, with larger basis sets will be required to obtain a more definitive set of relative energies.

Interpretation of excited state Hartree-Fock analytic derivative anomalies for NO2 and HCO2 using the molecular orbital Hessian

A simple procedure utilizing the molecular orbital (MO) Hessian, the second derivative of the Hartree–Fock (HF) energy with respect to MO coefficient perturbations, has been proposed in the interpretation of anomalous analytic HF energy derivatives. The nature of the anomalous analytic self‐consistent field (SCF) harmonic vibrational frequencies and infrared (ir) intensities of the 2B2 and 2A2 excited states of NO2 and HCO2 have been studied in detail. By suitable partitioning of the HF second energy derivative expression, an association between the abnormal force constants, the dipole moment derivatives, and specific solutions to the SCF coupled perturbed HF equations is established. This connection to unstable wave functions can now be used with the MO Hessian to predict these anomalies at the HF level. In addition, appropriate small complete active space SCF (CASSCF) methods have been utilized to overcome the inherent shortcomings of the HF wave functions, and determine more realistic values for the fo...

Stationary points on the potential energy surfaces of (C2H2)2, (C2H2)3, and (C2H4)2

Minima on the potential energy surfaces of (C2H2)2, (C2H2)3, and (C2H4)2 have been located by ab initio methods, using the Mo/ller–Plesset second‐order (MP2) procedure, with a DZP basis set. For (C2H2)2, a T‐shaped structure is predicted and for (C2H2)3, a C3h structure. For (C2H4)2 there are two candidates, a T‐shaped structure and a staggered‐parallel structure, and it is difficult to distinguish between them. Other stationary points have been located on the surfaces, but they are all found to be transition states, by the method of analytic second derivatives. Existing experimental data is insufficient to decide unequivocally as to the geometry of the minima. These calculations appear to resolve these questions and there is no contradiction with the data.

Use of the molecular orbital Hessian for self-consistent-field (SCF) wavefunctions

Abstract The molecular orbital (MO) Hessian for the self-consistent-field (SCF) wavefunction is defined as the second derivative of the electronic energy of the system with respect to changes in the MO coefficients. The lowest eigenvalue of the MO Hessian is widely used to determine the stability of SCF wavefunctions. The present study extends the use of the MO Hessian in several directions: prediction of low-lying excited states, qualification of basis sets, identification of MOs involved in chemical reactions, warning of a variational collapse, relative stability of wavefunctions, as well as absolute stability of wavefunctions. An SCF instability index is defined as the number of negative eigenvalues of the MO Hessian, since it is possible that an SCF wavefunction has more than one negative eigenvalue of the corresponding MO Hessian. The MO Hessian is analyzed for the ground and excited states of H 2 O, H 2 CO and NO 2 at equilibrium geometries and/or at transition states for dissociation and for conformational change. Examples are given of stationary values of the electronic energy with respect to orbital rotations representing local minima, maxima and points of inflection. The relevance of the eigenvalues of the MO Hessian to the physical and chemical properties of the system under consideration is discussed.

Mo/ller–Plesset third order calculations with large basis sets

The value of the Mo/ller–Plesset third order calculations is examined. An efficient method for the evaluation of the gradient of the MP3 energy is reported, and it has been programmed for both restricted and unrestricted Hartree–Fock wave functions. Large basis set calculations (TZ2P or better) are reported for the optimization of geometries and the determination of harmonic frequencies (which are obtained by finite differences of analytic gradients). The molecules selected are NH2, PH2, AsH2, H2O, NH3, H2CO, HCN, and C2H2. For the closed shell systems, the RMP3 predictions for bond lengths are inferior (≈0.006 A) to RMP2 predictions (≈0.003 A) for single bonds, and for multiple bonds the RMP3 bond lengths are too short by approximately the same amount (≈0.01 A) that RMP2 are too long. For the open shell systems, the UMP3 geometrical parameters show only a marginal improvement over UMP2, except for PH2 where the bond length error is reduced to 0.003 A. The results for harmonic frequencies show a similar c...

The second stable conformer of 1,3-butadiene. Geometry optimizations with configuration interaction and coupled cluster methods

Abstract The structures of s -cis and gauche butadiene have been determined using methods that include the effects of dynamical electron correlation. Optimized geometries, energies and harmonic vibrational frequencies are presented and discussed at the various levels of theory employed. The information yielded by the highest theoretical level used leads to a prediction that the gauche conformer is a minimum on the potential energy surface, lying 0.8 kcal/mol below the s -cis conformer which is predicted to be a transition state. This barrier to planarity is reduced to 0.5 kcal/mol with inclusion of zero-point vibrational energy effects. It is postulated that the gauche structure is favoured since the reduction in steric interactions in this conformation overcomes any loss of conjugation relative to the planar structure. Isoprene and dimethyl-butadiene have also been shown to display these effects in a more pronounced manner.

The structure and harmonic vibrational frequencies of the weakly bound complexes formed by HF with CO, CO2 and N2O

The structure and harmonic vibrational frequencies of several weakly bound complexes formed by HF are reported. Theab initio MP2 approach is used with large basis sets for the optimisation of geometries and the determination of harmonic frequencies. CO⋯HF and OC⋯HF are examined; both are found to be minima, with the latter being the dominant structure. The linear OCO⋯HF andT shaped OCO⋯FH are studied, but only the linear structure is a minimum. N2O⋯HF has two minima on the surface corresponding to bent NNO⋯HF and linear ONN⋯HF structures.

A study of nitrosyl fluoride

Abstract A CI gradient study of the ground-state potential surface of the FNO molecule is presented. The geometries, the relative stabilities of the two isomers, FNO and FON, and the activation barrier of the isomerization reaction have been evaluated. The spectroscopic vibration-rotation interaction constants of FNO have been computed and compared with experiment.

The boron—carbon triple bond (B̄C): Some theoretical predictions

Abstract The structures of the organoboron anions HBCH and HBCBH2 have been determined using ab initio methods that include the effects of dynamical electron correlation. Optimized geometries, electric dipole moments and harmonic vibrational frequencies are presented and discussed at the various levels of theory employed. The dependence of these molecular properties on the inclusion of diffuse functions in the basis set is investigated. The BC bond lengths predicted at the highest consistent theoretical level, CISD/TZ2P, are 1.319 A for HBCH and 1.338 and 1.467 A for HBCBH2. It may be argued that the prototypical HBCH anion contains a formal BC triple bond, while the larger HBCBH2 anion incorporates a weaker BC triple bond and a very strong CB single bond. It is postulated that the partial bonding character in the diboro anion may be understood in terms of resonance structures and hyperconjugate interactions involving orbital overlap.

The electronic spectra of SNS. Low-lying doublet states

The present study aims to characterize the electronically low‐lying doublet states of the SNS molecule in detail. From an analysis of the eigenvalues and eigenvectors of the molecular orbital (MO) Hessian at the self‐consistent‐field (SCF) level, the corresponding rotations amongst the high‐lying occupied and low‐lying unoccupied molecular orbitals highlight nine low‐lying doublet states worthy of study. Three bent (2A1, 2B2, and 2A2), three ring (2B1, 2A2, and 2A1), and three linear (2Πu and two 2Πg) structural isomers with doublet electronic states have been investigated at the SCF, configuration interaction with single and double excitations (CISD), and complete active space (CAS) SCF levels of theory with five different basis sets, double zeta (DZ) through triple zeta plus double polarization (TZ+2P). At the SCF level of theory, the stability of the wave functions and the energetics of the above mentioned doublet states are discussed in terms of the molecular orbital (MO) Hessian. The MO Hessian is of...