Structural Basis of Substrate Recognition and Covalent Inhibition of Cdu1 from Chlamydia trachomatis.

Based on the similarity between the active sites of the deubiquitylating and deneddylating enzyme ChlaDub1 (Cdu1) and the evolutionarily related protease adenain, a target-hopping screening approach on a focused set of adenain inhibitors was investigated. The cyanopyrimidine-based inhibitors identified represent the first active-site-directed small-molecule inhibitors of Cdu1. High-resolution crystal structures of Cdu1 in complex with two covalently bound cyanopyrimidines, as well as with its substrate ubiquitin, were obtained. These structural data were complemented by enzymatic assays and covalent docking studies to provide insight into the substrate recognition of Cdu1, active-site pocket flexibility and potential hotspots for ligand interaction. Combined, these data provide a strong basis for future structure-guided medicinal chemistry optimization of this cyanopyrimidine scaffold into more potent and selective Cdu1 inhibitors.

Testing inhomogeneous solvation theory in structure-based ligand discovery.

Binding-site water is often displaced upon ligand recognition, but is commonly neglected in structure-based ligand discovery. Inhomogeneous solvation theory (IST) has become popular for treating this effect, but it has not been tested in controlled experiments at atomic resolution. To do so, we turned to a grid-based version of this method, GIST, readily implemented in molecular docking. Whereas the term only improves docking modestly in retrospective ligand enrichment, it could be added without disrupting performance. We thus turned to prospective docking of large libraries to investigate GIST's impact on ligand discovery, geometry, and water structure in a model cavity site well-suited to exploring these terms. Although top-ranked docked molecules with and without the GIST term often overlapped, many ligands were meaningfully prioritized or deprioritized; some of these were selected for testing. Experimentally, 13/14 molecules prioritized by GIST did bind, whereas none of the molecules that it deprioritized were observed to bind. Nine crystal complexes were determined. In six, the ligand geometry corresponded to that predicted by GIST, for one of these the pose without the GIST term was wrong, and three crystallographic poses differed from both predictions. Notably, in one structure, an ordered water molecule with a high GIST displacement penalty was observed to stay in place. Inclusion of this water-displacement term can substantially improve the hit rates and ligand geometries from docking screens, although the magnitude of its effects can be small and its impact in drug binding sites merits further controlled studies.

An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit.

A new explicitly correlated local coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [DF-LCCSD(T0)-F12x (x = a,b)] is presented. By means of truncating the virtual orbital space to pair-specific local domains (domain approximation) and a simplified treatment of close, weak and distant pairs using LMP2-F12 (pair approximation) the scaling of the computational cost with molecular size is strongly reduced. The basis set incompleteness errors as well as the errors due to the domain approximation are largely eliminated by the explicitly correlated terms. All integrals are computed using efficient density fitting (DF) approximations. The accuracy of the method is investigated for 52 reactions involving medium size molecules. A comparison of DF-LCCSD(T0)-F12x reaction energies with canonical CCSD(T)-F12x calculations shows that the errors introduced by the domain approximation are indeed very small. Care must be taken to keep the errors due to the additional pair approximation equally small, and appropriate distance criteria are recommended. Using these parameters, the root mean square (RMS) deviations of DF-LCCSD(T0)-F12a calculations with triple-ζ basis sets from estimated CCSD(T) complete basis set (CBS) limits and experimental data amount to only 1.5 kJ mol(-1) and 2.9 kJ mol(-1), respectively. For comparison, the RMS deviation of the CCSD(T)/CBS values from the experimental values amounts to 3.0 kJ mol(-1). The potential of the method is demonstrated for five reactions of biochemical or pharmacological interest which include molecules with up to 61 atoms. These calculations show that molecules of this size can now be treated routinely and yield results that are close to the CCSD(T) complete basis set limits.

Local explicitly correlated coupled-cluster methods: efficient removal of the basis set incompleteness and domain errors.

We propose an explicitly correlated local LCCSD-F12 method in which the basis set incompleteness error as well as the error caused by truncating the virtual orbital space to pair-specific local domains are strongly reduced. This is made possible by including explicitly correlated terms that are orthogonalized only to the pair-specific configuration space. Thus, the contributions of excitations outside the domains are implicitly accounted for by the explicitly correlated terms. It is demonstrated for a set of 54 reactions that the reaction energies computed with the new LCCSD-F12 method and triple-zeta basis sets deviate by at most 2.5 kJ/mol from conventional CCSD complete basis set results (RMS: 0.6 kJ/mol). The local approximations should make it possible to achieve linear scaling of the computational cost with molecular size.

Simplified CCSD(T)-F12 methods: theory and benchmarks.

The simple and efficient CCSD(T)-F12x approximations (x = a,b) we proposed in a recent communication [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] are explained in more detail and extended to open-shell systems. Extensive benchmark calculations are presented, which demonstrate great improvements in basis set convergence for a wide variety of applications. These include reaction energies of both open- and closed-shell reactions, atomization energies, electron affinities, ionization potentials, equilibrium geometries, and harmonic vibrational frequencies. For all these quantities, results better than the AV5Z quality are obtained already with AVTZ basis sets, and usually AVDZ treatments reach at least the conventional AVQZ quality. For larger molecules, the additional cost for these improvements is only a few percent of the time for a standard CCSD(T) calculation. For the first time ever, total reaction energies with chemical accuracy are obtained using valence-double-zeta basis sets.

Local explicitly correlated second-order perturbation theory for the accurate treatment of large molecules.

A local explicitly correlated LMP2-F12 method is described that can be applied to large molecules. The steep scaling of computer time with molecular size is reduced by the use of local approximations, the scaling with respect to the basis set size per atom is improved by density fitting, and the slow convergence of the correlation energy with orbital basis size is much accelerated by the introduction of terms into the wave function that explicitly depend on the interelectronic distance. The local approximations lead to almost linear scaling of the computational effort with molecular size without much affecting the accuracy. At the same time, the domain error of conventional LMP2 is removed in LMP2-F12. LMP2-F12 calculations on molecules of chemical interest involving up to 80 atoms, 200 correlated electrons, and 2600 contracted Gaussian-type orbitals, as well as several reactions of large biochemical molecules are reported.

Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar.

Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.

A simple and efficient CCSD(T)-F12 approximation.

A new explicitly correlated CCSD(T)-F12 approximation is presented and tested for 23 molecules and 15 chemical reactions. The F12 correction strongly improves the basis set convergence of correlation and reaction energies. Errors of the Hartree-Fock contributions are effectively removed by including MP2 single excitations into the auxiliary basis set. Using aug-cc-pVTZ basis sets the CCSD(T)-F12 calculations are more accurate and two orders of magnitude faster than standard CCSD(T)/aug-cc-pV5Z calculations.

General orbital invariant MP2-F12 theory.

A general form of orbital invariant explicitly correlated second-order closed-shell Moller-Plesset perturbation theory (MP2-F12) is derived, and compact working equations are presented. Many-electron integrals are avoided by resolution of the identity (RI) approximations using the complementary auxiliary basis set approach. A hierarchy of well defined levels of approximation is introduced, differing from the exact theory by the neglect of terms involving matrix elements over the Fock operator. The most accurate method is denoted as MP2-F12/3B. This assumes only that Fock matrix elements between occupied orbitals and orbitals outside the auxiliary basis set are negligible. For the chosen ansatz for the first-order wave function this is exact if the auxiliary basis is complete. In the next lower approximation it is assumed that the occupied orbital space is closed under action of the Fock operator [generalized Brillouin condition (GBC)]; this is equivalent to approximation 2B of Klopper and Samson [J. Chem. Phys. 116, 6397 (2002)]. Further approximations can be introduced by assuming the extended Brillouin condition (EBC) or by neglecting certain terms involving the exchange operator. A new approximation MP2-F12/3C, which is closely related to the MP2-R12/C method recently proposed by Kedzuch et al. [Int. J. Quantum Chem. 105, 929 (2005)] is described. In the limit of a complete RI basis this method is equivalent to MP2-F12/3B. The effect of the various approximations (GBC, EBC, and exchange) is tested by studying the convergence of the correlation energies with respect to the atomic orbital and auxiliary basis sets for 21 molecules. The accuracy of relative energies is demonstrated for 16 chemical reactions. Approximation 3C is found to perform equally well as the computationally more demanding approximation 3B. The reaction energies obtained with smaller basis sets are found to be most accurate if the orbital-variant diagonal Ansatz combined with localized orbitals is used for the first-order wave function. This unexpected result is attributed to geminal basis set superposition errors present in the formally more rigorous orbital invariant methods.

Size-selected methyl lactate clusters: fragmentation and spectroscopic fingerprints of chiral recognition.

A comprehensive experimental study of the OH stretching vibrations of size-selected clusters of enantiopure and racemic methyl lactate is presented. For the size selection, we measured angular dependent mass spectra and time-of-flight distributions at the different fragment masses. In this way the fragmentation of these clusters upon electron impact ionization is obtained. The largest fragment masses of the neutral (MLac)n clusters are the protonated (MLac)n-1H+ ions. The results of a pressure dependent study in an FTIR jet experiment are compared with completely size-selected experiments based on atomic beam deflection and depletion spectroscopy. The size assignments and spectra agree for dimers and trimers. Structures and spectral information for the trimer and the tetramer at density functional and MP2 level are provided. Selective self-aggregation and chiral recognition was observed for homochiral trimers. They exhibit a ring structure bound by OH...OH hydrogen bonds. A spectacular switch in the hydrogen bonding topology was observed for the tetramer. The homochiral enantiomer exhibits cooperative OH...OH bonding, while the heterochiral version shows isolated OH...O=C bonding in a symmetric SRSR arrangement. The crucial ingredients for this identification are the size-selective IR spectra with their different shifts and line patterns which are reproduced by the calculations.

Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor.

The recently introduced MP2-R122*A(loc) and LMP2-R122*A(loc) methods are modified to use a short-range correlation factor expanded as a fixed linear combination of Gaussian geminals. Density fitting is used to reduce the effort for integral evaluation, and local approximations are introduced to improve the scaling of the computational resources with molecular size. The MP2-F122*A(loc) correlation energies converge very rapidly with respect to the atomic orbital basis set size. Already with the aug-cc-pVTZ basis the correlation energies computed for a set of 21 small molecules are found to be within 0.5% of the MP2 basis set limit. Furthermore the short-range correlation factor leads to an improved convergence of the resolution of the identity, and eliminates problems with long-range errors in density fitting caused by the linear r12 factor. The DF-LMP2-F122*A(loc) method is applied to compute second-order correlation energies for molecules with up to 49 atoms and more than 1600 basis functions.