László Füsti-Molnár

Importance of Dispersion and Electron Correlation in ab Initio Protein Folding

Dispersion is well-known to be important in biological systems, but the effect of electron correlation in such systems remains unclear. In order to assess the relationship between the structure of a protein and its electron correlation energy, we employed both full system Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) calculations in conjunction with the Polarizable Continuum Model (PCM) on the native structures of two proteins and their corresponding computer-generated decoy sets. Because of the expense of the MP2 calculation, we have utilized the fragment molecular orbital method (FMO) in this study. We show that the sum of the Hartree-Fock (HF) energy and force field (LJ6)-derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order Møller-Plesset perturbation (MP2) theory. In one of the two examples studied, the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discrimination capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly. Furthermore, when we randomly scrambled the Lennard-Jones parameters, the correlation between the MP2 energy and the sum of the HF energy and dispersive energy (HF+LJ6) significantly drops, which indicates that the choice of Lennard-Jones parameters is important.

Fast and accurate Coulomb calculation with Gaussian functions

Coulomb interaction is one of the major time-consuming components in a density functional theory (DFT) calculation. In the last decade, dramatic progresses have been made to improve the efficiency of Coulomb calculation, including continuous fast multipole method (CFMM) and J-engine method, all developed first inside Q-Chem. The most recent development is the advent of Fourier transform Coulomb method developed by Fusti-Molnar and Pulay, and an improved version of the method has been recently implemented in Q-Chem. It replaces the least efficient part of the previous Coulomb methods with an accurate numerical integration scheme that scales in O(N2) instead of O(N4) with the basis size. The result is a much smaller slope in the linear scaling with respect to the molecular size and we will demonstrate through a series of benchmark calculations that it speeds up the calculation of Coulomb energy by several folds over the efficient existing code, i.e., the combination of CFMM and J-engine, without loss of accuracy. Furthermore, we will show that it is complementary to the latter and together the three methods offer the best performance for Coulomb part of DFT calculations, making the DFT calculations affordable for very large systems involving thousands of basis functions.

New developments in the Fourier transform Coulomb method: Efficient and accurate localization of the filtered core functions and implementation of the Coulomb energy forces

A new linear scaling approach for the solution of Coulomb problem called the Fourier transform Coulomb (FTC) method has been published recently. Two further developments will be presented in this article. First, an efficient and accurate technique to localize the so-called filtered core functions is introduced, which considerably improves the scaling property of the method and speeds up the most time consuming computational steps by one and two orders of magnitude. An efficient scheme to implement the Coulomb forces is also presented using the localization technique. Besides these methodological developments, detailed results are shown for the scaling property of the computational cost, which is linear in both system and in basis set size. Huge speed ups are achieved compared to the analytical integral evaluation based technique in line with traditional ab initio accuracy requirements. Additionally, ongoing and further possible improvements for every main computational step are also discussed in detail.

Efficient computation of the exchange-correlation contribution in the density functional theory through multiresolution

A new algorithm is presented to improve the efficiency of the computation of exchange-correlation contributions, a major time-consuming step in a density functional theory (DFT) calculation. The new method, called multiresolution exchange correlation (mrXC), takes advantage of the variation in resolution among the Gaussian basis functions and shifts the calculation associated with low-resolution (smooth) basis function pairs to an even-spaced cubic grid. The cubic grid is much less dense in the vicinity of the nuclei than the atom-centered grid and the computation on the former is shown to be much more efficient than on the latter. MrXC does not alter the formalism of the current standard algorithm based on the atom-centered grid (ACG), but instead employs two fast and accurate transformations between the ACG and the cubic grid. Preliminary results with local density approximation have shown that mrXC yields three to five times improvement in efficiency with negligible error. The extension to DFT functionals with generalized gradient approximation is also briefly discussed.

Accurate benchmark calculations on the gas-phase basicities of small molecules.

Accurate benchmark calculations of gas-phase basicities of small molecules are presented and compared with available experimental results. The optimized geometries and thermochemical analyses were obtained from MP2/aug-cc-pVTZ calculations. Two different ab initio electron-correlated methods MP2 and CCSD(T) were employed for subsequent gas-phase basicity calculations, and the single-point energies were extrapolated to the complete basis set (CBS) limit. The overall accuracy for different ab initio methods is compared, and the accuracy in descending order is CCSD(T)_CBS > CCSD(T)/aug-cc-pVDZ > (MP2/aug-cc-pVQZ approximately MP2_CBS) > HF/aug-cc-pVQZ. The best root-mean-squared-error obtained was 1.0 kcal mol(-1) at the CCSD(T)_CBS//MP2/aug-cc-pVTZ level for a test set of 41 molecules. Clearly, accurate calculations for the electron correlation energy are important for the theoretical prediction of molecular gas-phase basicities. However, conformational effects were also found to be relevant in several instances when more complicated molecules were examined.

Photodissociation of HOBr. Part II. Calculation of photodissociation cross-sections and photofragment quantum state distributions for the first two UV absorption bands

Total absorption cross-sections and product rotational quantum state distributions are computed from first principles for the first two ultraviolet absorption bands of the HOBr molecule corresponding to excitation to the 11A″ and 21A′ states. The dynamical calculations are based on ab initio potential energy surfaces and transition dipole moment surfaces. The theory of triatomic photodissociation is presented in detail, in a manner which is clearer than previously available, and an important correction is made to the theoretical formulae. The theory takes proper account of angular momentum coupling and of the parity of all of the constituent wavefunctions. It is applicable to any initial (or final) angular momentum. The computed absorption bands agree reasonably well with available experimental results but highlight shortcomings of the electronic structure calculations on which these dynamical calculations are based. Predictions are made for the effect of excitation of initial vibrational states on the absorption line shapes.

Photodissociation of HOBr. I. Ab initio potential energy surfaces for the three lowest electronic states and calculation of rotational–vibrational energy levels and wave functions

Potential energy surfaces are presented for the three lowest lying singlet electronic states of HOBr. The surfaces are computed using the recently developed multireference averaged quadratic coupled clusters method and a TZ2P orbital basis set. They provide the basic data needed to compute the dynamics of the HOBr+hν→OH+Br photodissociation process, which plays a key role in the bromine chemistry of the stratosphere. A pseudopotential is used for the core electrons of the Br atom; this is shown not to introduce any errors in the shape of the surfaces through direct comparison with sample all-electron calculations. Transition dipole moment surfaces for the two excitation processes (1 1A″←X 1A′ and 2 1A′←X 1A′) are also presented. These are computed using a multireference singles and doubles configuration interaction method. A grid based method is developed to compute the vibrational–rotational states of the molecule and spectroscopic constants extracted from the computed molecular energy level spacings a...

An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring.