George Vacek

The balance between theoretical method and basis set quality: A systematic study of equilibrium geometries, dipole moments, harmonic vibrational frequencies, and infrared intensities

Analytic gradient methods have been used to predict the equilibrium geometries, dipole moments, harmonic vibrational frequencies, and infrared (IR) intensities of HCN, HNC, CO2, CH4, NH4+, HCCH, H2O, H2CO, NH3, and FCCH at the self‐consistent‐field (SCF), the single and double excitations configuration interaction (CISD), the single and double excitations coupled‐cluster (CCSD), and the single, double, and perturbative triple excitations coupled‐cluster [CCSD(T)] levels of theory. All studies were performed using a triple zeta plus double polarization (TZ2P) basis set and a TZ2P basis set augmented with one set of higher angular momentum functions [TZ (2df,2pd)]. The predicted equilibrium geometries, dipole moments, harmonic vibrational frequencies, and IR intensities were compared to available experimental values. The geometries were predicted accurately at the highest levels of theory. Most of the dipole moments were found to agree favorably with experiment. With the TZ2P basis set, the average absolute...

A systematic theoretical study of the harmonic vibrational frequencies for polyatomic molecules: The single, double, and perturbative triple excitation coupled‐cluster [CCSD(T)] method

Analytic gradient methods have been used to predict the harmonic vibrational frequencies and the infrared (IR) intensities of HCN, HNC, CO2, CH4, NH4+, C2H2, H2O, H2CO, and NH3 at the single, double, and perturbative triple excitation coupled‐cluster [CCSD(T)] level of theory. All studies were performed using a double zeta plus polarization (DZ+P) basis set with a contraction scheme of (9s5p1d/4s2p1d) for C, N, and O and (4s1p/2s1p) for H. The results of previous studies using the same basis set with self‐consistent field (SCF), single and double excitation configuration interaction (CISD), and the single and double excitation coupled‐cluster (CCSD) methods are included to allow a detailed comparison. The theoretical harmonic frequencies of all nine molecules are compared to the 28 (out of a total of 35 possible) known experimental harmonic vibrational frequencies. IR intensities are also compared to known experimental values. The absolute average error in frequencies for the CCSD(T) method with respect t...

Isomerization reactions on the lowest potential energy hypersurface of triplet vinylidene and triplet acetylene

Triplet vinylidene, first predicted to have a sizeable barrier to unimolecular rearrangement in 1978 by theory, has now been observed under three different sets of experimental conditions. In order to quantitatively characterize the potential energy hypersurface of triplet vinylidene and triplet acetylene, high‐level ab initio quantum mechanical methods have been employed. Basis sets as large as triple zeta plus two sets of polarization functions augmented with higher angular momentum functions [TZ(2df,2pd)] have been utilized in conjunction with correlated methods as sophisticated as the coupled cluster approach including all single, double, and perturbative triple excitations [CCSD(T)]. Of particular interest are predictions of the zero‐point vibrational energy corrected barriers for rearrangement of a 3B2 vinylidene to b 3Bu trans‐bent acetylene and of cis‐bent a 3B2 acetylene to trans‐bent b 3Bu acetylene. At the highest level of theory used here, TZ(2df,2pd) CCSD(T), these are predicted to be 47....

Low-lying triplet electronic states of acetylene:cis 3 B 2 and3 A 2,trans 3 B u and3 A u

SummaryAb initio molecular electronic structure theory has been used in conjunction with flexible basis sets to investigate the equilibrium properties of the four low-lying triplet electronic states of acetylene. Self-consistent-field (SCF) and configuration interaction with single and double excitations (CISD) levels of theory were employed with basis sets ranging from double zeta plus polarization (DZP) to quadruple zeta plus triple polarization with higher angular momentum polarization functions [QZ(3df, 3pd)]. Complete geometry optimizations of the equilibrium structures and vibrational analyses for the3B2,3Bu,3Au, and3A2 states as well as the ground1Σg+ state of acetylene were carried out at the SCF and CISD levels of theory. With the DZP basis set, configuration interaction with single, double, and triple excitations (CISDT) wavefunctions were also used to optimize geometries. At the CISD optimized geometries the total energies were determined using the correlated wavefunctions with higher excitations. Those wavefunctions include the triple zeta plus double polarization (TZ2P)-CISDT, coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)] methods. Although the energy ordering of3B2<3Bu<3Au<3A2 remained unchanged, the excitation energies of these four triplet states relative to the1Σg+ ground state is increased by about 7.5 kcal/mol in comparison with previous theoretical work. At the highest level of theory, CCSD(T) with the QZ(3df, 3pd) basis set, the classical excitation energies of the four triplet states relative to the ground state were predicted to be 88.0(3.82; 30,790), 96.0(4.16; 33,590), 102.4(4.44; 35,830), and 109(4.76; 38,420) kcal/mol(eV; cm−1), respectively. For the first two triplet states, including the zero-point vibrational energies (ZPVE) the energy differences were 86.6(3.75; 30,270) and 94.8(4.11; 33,170) kcal/mol(eV; cm−1), respectively. The classical energy separation between the3B2 and3A2 states was predicted to be 7630 cm−1. Including the estimated ZPVE correction of 50 cm−1 this energy difference became 7680 cm−1, which is in very good agreement with the experimental value of 7388 cm−1. Thetrans triplet states have never been observed in the laboratory, and it is hoped that these quantitative theoretical predictions will assist in their experimental identification.

THE A 1AU STATE AND THE T2 POTENTIAL SURFACE OF ACETYLENE : IMPLICATIONS FOR TRIPLET PERTURBATIONS IN THE FLUORESCENCE SPECTRA OF THE A STATE

The cis–trans isomerization reaction on the T2 surface of acetylene and the lowest excited singlet state of acetylene, A 1Au, are investigated by ab initio electronic structure theory. We report optimized geometries, dipole moments, and harmonic vibrational frequencies of stationary points and adiabatic energy differences between them using basis sets as large as triple‐ζ plus double polarization with higher angular momentum functions, TZ(2df,2pd), and theoretical methods up to coupled‐cluster singles and doubles with a perturbative triples correction [CCSD(T)] and the equation‐of‐motion coupled‐cluster method (EOM‐CCSD). Our theoretical predictions should aid the interpretation of observations from a series of recent spectroscopic studies involving excited electronic states of acetylene. In particular, the present theoretical results rule out several possible explanations for the anomalous sudden increase in detectable Zeeman anticrossings reported by Dupre et al. [Chem. Phys. 152, 293 (1991)].

The X̃ AlOH–X̃ HAlO isomerization potential energy hypersurface

Ab initio molecular electronic structure theory has been used to study the AlOH–HAlO unimolecular isomerization reaction on the singlet ground state potential energy surface. Electron correlation effects were included via configuration interaction and coupled‐cluster methods. Basis sets as complete as triple zeta plus two sets of polarization functions and a set of higher angular momentum functions [TZ(2df,2pd)] were employed. The classical barrier for hydrogen migration from X HAlO to X AlOH is predicted to be 38.4 kcal mol−1 using the TZ(2df,2pd) basis set with the coupled‐cluster method including all single and double excitations with the effect of connected triple excitations included perturbatively [CCSD(T)]. After correction for zero‐point vibrational energies (ZPVEs), an activation energy of 36.6 kcal mol−1 is obtained. The ΔE for isomerization is −42.2 (−40.5 with ZPVE correction) kcal mol−1 at the same level of theory. The dipole moments of HAlO and AlOH in their equilibrium geometries are 4.52...

Comparative energy derivative analyses of the HBO–BOH and AlOH–HAlO potential energy hypersurfaces

A study of first and second derivatives of the orbital, electronic, nuclear, and total energies for closed‐shell self‐consistent‐field (SCF) wave functions has been applied to the ground state HBO–BOH and AlOH–HAlO potential energy hypersurfaces. At the stationary points, these energy derivative quantities are uniquely transformed from the Cartesian to the normal coordinate system. Using the four equilibrium and four transition state structures on the two potential energy hypersurfaces, it is demonstrated that the energy derivative method may be used as a powerful quantitative model in understanding and interpreting various chemical phenomena including structures and reactivities. Specifically, the inversion (bending through linear geometry) motions for the bent BOH and AlOH molecules are found to be electronically favorable processes. The isomerization reaction between the linear HBO and bent BOH is seen to be electronically unfavorable, whereas the corresponding reaction between the bent AlOH and linear...

Molecular geometries of disilane, silylgermane and digermane. Is there a discrepancy between experiment and theory?

Abstract Equilibrium geometries of the staggered conformers of disilane, silylgermane, and digermane were located at the CCSD(T), CCSD, CISD, MP2, DFT, and HF levels of theory, using a number of valence double- and triple-zeta basis sets augmented by polarization functions. Contrary to doubts expressed by Oberhammer, Lobreyer and Sundermeyer (OLS), the correlated levels of theory, used in conjunction with valence triple-zeta basis sets augmented by f-polarization functions on heavy atoms, are capable of reproducing all experimental parameters that are well established. The present results described a microwave HGeH bond angle in Ge 2 H 6 that is 2° larger than the somewhat questionable experimental value. The theoretical data presented suggest that the assumptions by OLS of intrinsically related GeH and SiH bond lengths and of equal HSiH and HGeH angles in H 3 SiGeH 3 are not justified.

Does oxirene exist? A theoretical inquiry involving the coupled-cluster method

Abstract The oxirene isomer of C 2 H 2 O has been characterized at three levels of ab initio quantum-mechanical theory. At all three levels, oxirene is shown to be a genuine minimum on the respective C 2 H 2 O potential energy hypersurfaces. However, the steep decrease in the predicted ring-deformation vibrational frequency (to 262 cm − with the double-zeta-plus-polarization basis set, single-and double-excitation coupled-cluster method) as a function of level of theory leaves open the possibility that oxirene may be a transition state for the degenerate rearrangement of ketene.

First and second energy derivative analyses of the vinylidene and acetylene triplet state potential energy hypersurfaces

First and second derivatives of the orbital, electronic, nuclear, and total energies for the self‐consistent‐field (SCF) wave function have been used to study the triplet state of the CCH2 and HCCH molecules. The diagonal elements of the Lagrangian matrix for the general open‐shell SCF wave function are used as the ‘‘orbital’’ energies. The first and second derivatives of the orbital energies in terms of the normal coordinates are determined by the finite difference method, while the corresponding derivatives of the electronic, nuclear, and total SCF energies are obtained via analytic derivative techniques. It is demonstrated that the derivatives of the energies with respect to the normal coordinates provide useful chemical information for the triplet state potential energy hypersurfaces of the CCH2 and HCCH molecules. Specifically, the isomerization reactions from a 3B2 vinylidene to b 3Bu acetylene and from a 3B2 acetylene to b 3Bu acetylene are found to be electronically stable processes and their ...