Roger D. Amos

Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds

A comparative study has been performed on the electronic spectra of a number of unsaturated organic molecules, using on the one hand density functional linear response theory and on the other multiconfigurational second-order perturbation theory, in order to establish the accuracy that the density functional based methods can give for excitation energies and energy surfaces for excited states. The following molecules are included in the study: tetrazine; the five-membered ring systems cyclopentadiene, furan, pyrrole, and thiophene; acetone; and a dipeptide. The results show that DFT valence excited states have errors that vary between 0 and 1 eV, while Rydberg states are accurate to about 0.2eV in most cases. The use of an asymptotically corrected exchange-correlation potential was essential for the latter result. However, transitions which involve a considerable charge transfer have much larger errors. The results show in some cases a surprisingly strong interaction between valence and Rydberg excited st...

GEOMETRIC DERIVATIVES OF EXCITATION ENERGIES USING SCF AND DFT

Abstract There is increasing interest in using the methods of time-dependent density functional theory to calculate electronic excitation energies. We have implemented an analytic gradient method to find the geometric derivatives of the excitation energies. When added to the gradient for the ground state, this yields the excited-state energy derivatives. This enables the efficient generation and searching of excited-state potential energy surfaces to obtain excited-state geometries and other properties. The initial implementation is for SCF methods and for the local density approximation. Some examples of excited-state geometry optimizations are given.

Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals

Abstract Density functional theory (DFT) is having increasing success in predicting excitation energies using the methods of time-dependent DFT. As a result, it should be possible to generate potential energy surfaces for excited states by adding the excitation energy, as a function of geometry, to the ground-state energy. It is easier to find stationary points such as minima and transition states if the gradient of the energy is known. The present Letter extends earlier work on the gradients on excited-state surfaces using SCF and LDA (local density approximation) methods, to use gradient-corrected and hybrid functionals. Some examples of geometry optimisations are given.

The analytic configuration interaction gradient method: Application to the cyclic and open isomers of the S3 molecule

The theory for the ab initio evaluation of potential energy gradients at the configuration interaction level of accuracy is presented, with special attention to the treatment of the various types of orbitals (frozen core, active, frozen virtual) which may arise. The new method has been used for a study of the D3h and C2v geometries of S3. SCF and CISD calculations predict the D3h structure to be lower than the C2v by 9.3 and 2.3 kcal/mol, respectively, whereas CASSCF and MRCISD predict the C2v structure to be the lowest by 8.9 and 8.2 kcal/mol, respectively, using good basis sets. These calculations support the prediction of Carlsen and Schaefer that both forms should be observable experimentally.

The elimination of singularities in derivative calculations

Abstract The evaluation of gradients and second derivatives of the electronic energy of a molecule is discussed for two methods which include electron correlation effects - configuration interaction and perturbation theory. It is shown that numerically stable procedures can be devised using the fact that the energy is invariant to certain orbital rotations amongst occupied and amongst virtual orbitals. Some details are given on the implementation of this procedure for closed-shell second-order perturbation theory second derivatives.

The harmonic frequencies of benzene

Abstract We report calculations for the harmonic frequencies of C6H6 and C6D6. Our most sophisticated quantum chemistry values are obtained with the MP2 method and a TZ2P+f basis set (288 basis functions), which are the largest such calculations reported on benzene to date. Using the SCF density, we also calculate the frequencies using the exchange and correlation expressions of density functional theory. We compare our calculated harmonic frequencies with those deduced from experiment by Goodman, Ozkabak and Thakur. The density functional frequencies appear to be more reliable predictions than the MP2 frequencies and they are obtained at significantly less cost.

On the necessity of f basis functions for bending frequencies

The calculation of out‐of‐plane bending vibrations for π‐bonded systems appears to be extraordinarily sensitive to the choice of a one‐particle basis set. Ab initio predictions are reported for acetylene, an extreme example, at the self‐consistent field (SCF), singles and doubles configuration interaction (CISD), nth order Mo/ller–Plesset perturbation theory (MPn,n=2–4), coupled‐pair functional (CPF), and singles and doubles coupled cluster (CCSD) levels of theory. It is found that the addition of a set of f  basis functions to the carbon atom changes the value of the SCF πg frequency by +45 cm−1, and the value of all correlated πg frequencies by more than +100 cm−1. Evidence is presented that this behavior is present in other π‐bonded systems. It is concluded that basis sets consisting of triple zeta plus two sets of polarization functions plus one set of f functions (TZ2P+f ) can predict highly accurate (∼1% average error) harmonic frequencies with the MP2, CPF, and CCSD methods, for a large number of m...

Electric and magnetic properties of CO, HF, HCI, and CH3F

Electric multiple moments polarizabilities and magnetizabilities of CO, HF, HCI, and CH3F are calculated using SCF wavefunctions and coupled Hartree-Fock perturbation method. The A and G tensors are also calculated and discussed in relation to electric-induced differential scattering and electric-field-gradient-induced birefringence in these gases.

Higher analytic derivatives. IV. Anharmonic effects in the benzene spectrum

This is the fourth in a series of papers on the ab initio calculation of the third and fourth derivatives of the energy of a molecule. In this paper we examine anharmonic effects in the infrared and Raman spectra of benzene. The following spectroscopic properties have been calculated; ab initio anharmonic corrections (ω−ν) and estimates of the harmonic frequencies ω for all 30 vibrational modes of C6H6 and C6D6, a complete set of anharmonic constants x and g for C6H6, intensities for the infrared spectrum of C6H6 up to 6148 cm−1, and anharmonic corrections to the Raman scattering factors for the fundamental modes of C6H6. In addition, we have improved on previous calculations of the equilibrium geometry of benzene, using Mo/ller–Plesset perturbation theory and a triple zeta plus double polarization (TZ2P) basis. We have also calculated a zero‐point vibrationally averaged geometry which is in good agreement with the experimental R0 value. All these calculations are based on a Hartree–Fock quartic potential...

Kohn—Sham bond lengths and frequencies calculated with accurate quadrature and large basis sets

Abstract We report calculations of bond lengths and frequencies using Kohn—Sham theory, defined as replacing the exchange term in the Hathree—Fock self-consistent field procedure by potentials of density functional theory. Several functionals are tested including the local density approximation to the exchange energy. Beckes non-local correction to the exchange, the Vosko—Wilk—Nusair functional for correlation with Perdews non-local correction to the correlation energy and the Lee—Yang—Parr correlation functional. High accuracy quadrature is used, which enables the gradient of the energy to be calculated straightforwardly. The results are compared to Hartree—Fock theory and to hydrid DFT methods based on the Hartree—Fock density. On average, bond lengths from the hybrid method are much better than SCF bond lengths, and often better than those from second-order Moller—Plesset theory. The Kohn—Sham bond lengths are rather long, but improve as the basis set is increased, and for large basis sets bond lengths, dipole moments and frequencies appear on to be a significant improvement over SCF theory.