Filip Pawłowski

The Dalton quantum chemistry program system

Dalton is a powerful general‐purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self‐consistent‐field, Møller–Plesset, configuration‐interaction, and coupled‐cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic‐structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge‐origin‐invariant manner. Frequency‐dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one‐, two‐, and three‐photon processes. Environmental effects may be included using various dielectric‐medium and quantum‐mechanics/molecular‐mechanics models. Large molecules may be studied using linear‐scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants

rotation interaction constants a r . The vibration‐rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree‐Fock vibration‐rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD~T! energy. The most accurate vibration‐rotation interaction constants are those calculated at the CCSD~T!/cc-pVQZ level. The equilibrium bond distances determined from these interaction constants have relative errors of 0.02%‐0.06%, surpassing the accuracy obtainable either by purely experimental techniques ~except for the smallest systems such as diatomics! or by ab initio methods.

Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory

We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Linear scaling implementation of molecular electronic self-consistent field theory.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.

Accuracy of spectroscopic constants of diatomic molecules from ab initio calculations

The basis-set convergence of cc-pVXZ basis sets is investigated for the MP2 and CCSD equilibrium bond distances and harmonic frequencies of BH, HF, CO, N2, and F2 by comparing with explicitly correlated R12 results. The convergence is, in general, smooth but slow—for example, for harmonic frequencies at the quadruple-zeta level, the basis-set error is typically 7 cm−1; at the sixtuple-zeta level, it is about 2 cm−1. For most constants, the convergence can be accelerated by using a two-point linear extrapolation procedure. Equilibrium bond distances, harmonic frequencies, anharmonic contributions, vibration-rotation interaction constants, and rotational constants for the vibrational ground state have been calculated for the same set of molecules using standard wave function and basis-set levels of ab initio theory. The accuracy of the calculated constants has been established by carrying out a statistical analysis of the deviations with respect to experiment. The largest errors for bond distances and harmo...

Calculation of frequency-dependent polarizabilities using the approximate coupled-cluster triples model CC3

CC3 is a member of the coupled-cluster model hierarchy CCS, CC2, CCSD, CC3, and CCSDT which is especially designed to describe frequency-dependent properties. CCS is the coupled-cluster singles model, in CCSD doubles are added and in CC2 the doubles of the CCSD model are approximated using the same strategy as for triples when CCSDT is approximated to give CC3. Excitation energies have been calculated successfully using this hierarchy. The error in the excitation energies is reduced by about a factor 3 at each level for the models CCS, CC2, CCSD, and CC3, and the CC3 excitation energies closely approximate the ones of the CCSDT model. 14 Calculation of frequency-dependent polarizabilities and hyperpolarizabilities have shown similar systematic improvements to the excitation energies. 15‐17

High-order correlation effects on dynamic hyperpolarizabilities and their geometric derivatives: A comparison with density functional results

Second harmonic generation hyperpolarizabilities and their geometric derivatives have been calculated for HF, HCl, CO, and LiF, using the coupled cluster hierarchies, CCS, CC2, CCSD, CC3, and large correlation-consistent basis sets. The full configuration interaction results have been used to test the accuracy of the coupled cluster results. The CCS and CC2 methods do not improve on the Hartree-Fock results while CCSD is robust and gives significant improvements compared to CCS and CC2. The effects of triples in CC3 are in some cases substantial. Higher order correlation effects are significant for LiF. Including core-valence correlation effects is required only if high accuracy is desired. The coupled cluster results have been used as benchmarks for the results obtained by means of density functional theory using various exchange-correlation functionals. For the hyperpolarizability B3LYP was found to perform best, i.e., to give the results closest to the CC3 ones, while for the geometric derivatives none of the considered functionals was able to give a consistent description for all the considered molecules.

Interaction between LiH molecule and Li atom from state-of-the-art electronic structure calculations.

State-of-the-art ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born-Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupled-cluster method with single, double, and noniterative triple excitations [UCCSD(T)-F12] for the core-core and core-valence correlation and full configuration interaction for the valence-valence correlation. The potential energy surface has a global minimum 8743 cm(-1) deep if the Li-H bond length is held fixed at the monomer equilibrium distance or 8825 cm(-1) deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlation-consistent polarized valence X-tuple-zeta basis sets, with X ranging from 2 to 5, and a very large set of bond functions. Using simple two-point extrapolations based on the single-power laws X(-2) and X(-3) for the orbital basis sets, we were able to reproduce the CCSD(T)-F12 results for the characteristic points of the potential with an error of 0.49% at worst. The contribution beyond the CCSD(T)-F12 model, obtained from full configuration interaction calculations for the valence-valence correlation, was shown to be very small, and the error bars on the potential were estimated. At linear LiH-Li geometries, the ground-state potential shows an avoided crossing with an ion-pair potential. The energy difference between the ground-state and excited-state potentials at the avoided crossing is only 94 cm(-1). Using both adiabatic and diabatic pictures, we analyze the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the Li-H bond is allowed to vary, a seam of conical intersections appears at C(2v) geometries. At the linear LiH-Li geometry, the conical intersection is at a Li-H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li-H distances that are well outside the classical turning points of the ground-state potential of LiH. This suggests that the conical intersection will have little impact on the dynamics of Li-LiH collisions at ultralow temperatures. Finally, the reaction channels for the exchange and insertion reactions are also analyzed and found to be unimportant for the dynamics.

Rovibrational dynamics of the strontium molecule in the AΣu+1, c3Πu, and aΣu+3 manifold from state-of-the-art ab initio calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A(1)Σ(u)(+), c(3)Π(u), and a(3)Σ(u)(+) manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X(1)Σ(g)(+) to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0(u)(+) state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Knöckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A(1)Σ(u)(+)←X(1)Σ(g (+) transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the (1)S(0) + (3)P(1) dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.