Henrik Koch

Reduced scaling in electronic structure calculations using Cholesky decompositions

We demonstrate that substantial computational savings are attainable in electronic structure calculations using a Cholesky decomposition of the two-electron integral matrix. In most cases, the computational effort involved calculating the Cholesky decomposition is less than the construction of one Fock matrix using a direct O(N2) procedure.

The benzene-argon complex: A ground and excited state ab initio study

Equilibrium dissociation energies De of the benzene–argon van der Waals complex are calculated in the ground state S0 and in the excited state S1 using integral-direct coupled cluster methods. The results confirm previous investigations of S0, showing that high quality correlation consistent basis sets and connected triple excitations are imperative for a good description of the van der Waals complex. We estimate the CCSD(T) dissociation energy De=389±2 cm−1 for the ground state S0. Using the CCSD linear response approach the frequency shift (redshift) δνe=19 cm−1 is obtained. Accurate spectroscopic structural data and frequency shifts δν0 for the 601 band of the S1←S0 transition are available for most of the benzene–rare gas atom complexes. However, the experimental determination of absolute dissociation energies of these complexes is connected with much larger uncertainties. The theoretical result agrees very well with the experimentally available redshift, showing that integral-direct coupled cluster m...

Atomic integral driven second order polarization propagator calculations of the excitation spectra of naphthalene and anthracene

An atomic integral direct implementation of the second order polarization propagator approximation (SOPPA) for the calculation of electronic excitation energies and oscillator strengths is presented. The SOPPA equations are solved iteratively using an integral direct approach and, contrary to previous implementations, the new algorithm does not require two-electron integrals in the molecular orbital basis. The linear transformation of trial vectors are calculated directly from integrals in the atomic orbital basis. In addition, the eigenvalue solver is designed to work efficiently with only three trial vectors per eigenvalue. Both of these modifications dramatically reduce the amount of disk space required, thus, increasing the range of applicability of the SOPPA method. Calculations of the lowest singlet excitation energies and corresponding dipole oscillator strengths for naphthalene and anthracene employing basis sets of 238 and 329 atomic orbitals, respectively, are presented. The overall agreement of...

GAUGE INVARIANT COUPLED CLUSTER RESPONSE THEORY

We introduce a time-dependent coupled cluster based Lagrangian that includes orbital rotation. This Lagrangian is shown to give gauge invariant response properties for one-electron operators in the limit of a complete one-electron basis. The pole structure of the linear response function is compatible with that of the exact response function and the notorious problem of unphysical second-order poles in the Brueckner coupled cluster response theory is not present in this model. The total energy of the model is identical to the coupled cluster model using optimized orbitals recently revived by Sherrill et al. [J. Chem. Phys. 109, 4171 (1998)]. The model provides a straightforward approach for calculating magnetic response properties in a gauge invariant manner using coupled cluster type wave functions.

Ground state benzene–argon intermolecular potential energy surface

A highly accurate ab initio intermolecular potential energy surface for the benzene–argon van der Waals complex is evaluated using the coupled cluster singles and doubles model including connected triple excitations [CCSD(T)] model with an augmented correlation consistent polarized valence double zeta basis set extended with midbond functions. The vibrational energy levels obtained by full three-dimensional dynamical calculations are in excellent agreement with the available experimental data.

The helium-, neon-, and argon-cyclopropane van der waals complexes: Ab initio ground state intermolecular potential energy surfaces and intermolecular dynamics

Using the coupled cluster singles and doubles including connected triples model and the augmented correlation consistent polarized valence double zeta basis set extended with a set of 3s3p2d1f1g midbond functions, ab initio helium–, neon–, and argon–cyclopropane ground state intermolecular potential energies are evaluated and fitted to an analytic function including up to four-body interactions. These are the first ab initio potential energy surfaces available for these complexes and are characterized by an absolute minimum of −73.3 cm−1 at a distance on the cyclopropane C3-axis of 3.291 A, −125.3 cm−1 at 3.435 A, and −301.1 cm−1 at 3.696 A for helium, neon, and argon, respectively. The bound van der Waals states are calculated. Two types of tunneling motion cause splittings of these levels: a C3 tunneling between the three equivalent local minima placed in the cyclopropane plane, and a C2 tunneling motion of the rare gas atom between the global minima above and below the cyclopropane plane.

The effect of intermolecular interactions on the electric properties of helium and argon. I. Ab initio calculation of the interaction induced polarizability and hyperpolarizability in He2 and Ar2

The frequency-dependent interaction induced polarizabilities and second hyperpolarizabilities are calculated for He2 at the coupled cluster singles and doubles and full configuration interaction levels and for Ar2 at the coupled cluster singles and doubles level. The frequency-dependence is approximated by a power series to second-order in the frequency arguments using Cauchy moments and hyperpolarizability dispersion coefficients. Using large correlation consistent basis sets, results close to the basis set limit are obtained. The computed curves for the interaction induced (hyper-) polarizabilities are tabulated for a range of internuclear distances. The data are employed in a companion paper to make for the first time a direct comparison between the experimentally determined pressure dependence of an ESHG hyperpolarizability and ab initio calculated hyperpolarizability second virial coefficients.

Gauge invariant coupled cluster response theory using optimized nonorthogonal orbitals

Using the time-dependent Lagrangian response approach, the recently revived orbital optimized coupled cluster (OCC) model is reformulated using nonorthogonal orbital rotations in a manner that conserves the commutativity of the cluster excitation operators. The gauge invariance and the simple pole structure of the OCC linear response function are retained, while the dimension of the eigenvalue problem is reduced by a factor of 2. Restricting the cluster operator to double excitations, we have carried out the first implementation of gauge invariant coupled cluster response theory. Test calculations of the excitation energy, and length and velocity gauge oscillator strengths are presented for the lowest electric dipole allowed transitions of the CH + molecular ion and the Ne atom. Additionally, the excitation energies to the four lowest-lying states of water are calculated.

The vibrational and temperature dependence of the indirect nuclear spin–spin coupling constants of the oxonium (H3O+) and hydroxyl (OH−) ions

Abstract The indirect nuclear spin–spin coupling constants of the gas phase oxonium (H 3 O + ) and hydroxyl (OH − ) ions, their temperature dependence and isotope shifts are predicted by ab initio calculations. The coupling constants are calculated as a function of the symmetric stretching and the inversional coordinates of H 3 O + and as a function of the bond length of OH − at the uncorrelated level of the random phase approximation (RPA), at the correlated levels of the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes – SOPPA(CCSD) – and of the multiconfigurational random phase approximation (MCRPA) with a large complete active space wavefunction. Effective ro-vibrational state dependent coupling constants are obtained from these functions and the corresponding ro-vibrational wavefunctions. The effective coupling constants for several states are then used to determine the temperature dependence of the coupling constants. The results are compared with the coupling constants of H 2 O and the nuclear magnetic shielding constants of H 3 O + and OH − .

The effect of intermolecular interactions on the electric properties of helium and argon. II. The dielectric, refractivity, Kerr, and hyperpolarizability second virial coefficients

The dielectric, refractivity, Kerr, and hyperpolarizability second virial coefficients for the helium and argon gases are evaluated for a wide range of temperatures using a semiclassical approach and the high quality frequency-dependent interaction induced electric polarizabilities and second hyperpolarizabilities of the previous paper. For helium and argon we obtain satisfactory agreement with most of the experimental data for the dielectric and the refractivity second virial coefficients. Our results confirm that the helium gas second Kerr virial coefficient is very small at temperatures beyond 70 K. For argon we obtain a very good agreement with a recent experimental determination at 632.8 nm, whereas we suggest that previous experimental results for 458 nm might be inaccurate. The ESHG results indicate a possible disagreement between a recent experimental determination and the semiclassical ansatz for the second hyperpolarizability virial coefficients.