Denis Usvyat

Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications

A computational technique for solving the MP2 equations for periodic systems using a local‐correlation approach and implemented in the CRYSCOR code is presented. The Hartree‐Fock solution provided by the CRYSTAL program is used as a reference. The motivations for the implementation of the new code are discussed, and the techniques adopted are briefly recalled. With respect to the original formulation (Pisani et al., J Chem Phys 2005, 122, 094113), many new features have been introduced in CRYSCOR to improve its efficiency and robustness. In particular, an adaptation of the density fitting scheme to translationally periodic systems is described, based on Fourier transformation techniques. Three examples of application are provided, concerning the CO2 crystal, proton transfer in ice XI, and the adsorption of methane on MgO (001). The results obtained with the periodic LMP2 method for these systems appear more reliable than the ones obtained using density functional theory.

Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy

Working out how to pack benzene in silico Many organic compounds crystallize in several different energetically similar packing arrangements, or polymorphs. This complicates processes such as drug formulation that rely on reproducible crystallization. Yang et al. have now achieved the long-standing goal of calculating a crystal packing arrangement from first principles to an accuracy that can distinguish polymorphs (see the Perspective by Price). They used benzene as a prototypical test case and applied quantum chemical methods that improve estimates of multibody interactions. The results bode well for future applications of theory to optimization of crystallization protocols. Science, this issue p. 640; see also p. 619 Theoretical calculations of molecular packing in crystals attain sufficient accuracy to distinguish polymorphs. [Also see Perspective by Price] Computation of lattice energies to an accuracy sufficient to distinguish polymorphs is a fundamental bottleneck in crystal structure prediction. For the lattice energy of the prototypical benzene crystal, we combined the quantum chemical advances of the last decade to attain sub-kilojoule per mole accuracy, an order-of-magnitude improvement in certainty over prior calculations that necessitates revision of the experimental extrapolation to 0 kelvin. Our computations reveal the nature of binding by improving on previously inaccessible or inaccurate multibody and many-electron contributions and provide revised estimates of the effects of temperature, vibrations, and relaxation. Our demonstration raises prospects for definitive first-principles resolution of competing polymorphs in molecular crystal structure prediction.

Periodic local Møller–Plesset second order perturbation theory method applied to molecular crystals: Study of solid NH3 and CO2 using extended basis sets

We have calculated the equilibrium geometry, formation energy, and bulk modulus of two molecular bulk crystals, NH(3) and CO(2), at the periodic post-Hartree-Fock correlated level. The dependence of the results on the basis set has been analyzed, by employing basis sets up to aug-cc-pVQZ quality. In the calculations, we used the periodic local Møller-Plesset second order perturbation theory (LMP2), implemented in the CRYSCOR program. Multipolar expansion techniques, as well as density fitting, are employed in this code to reduce the number of and to factorize the required electron repulsion integrals; as a consequence of that, the computational cost for the correlation part of the calculations is comparable to that of the Hartree-Fock. Auxiliary calculations performed on molecular dimers are also reported to verify the accuracy of the LMP2 approach and of the basis sets used. Furthermore, the effect of spin-component scaling has been investigated for the two crystals. One intention of the present paper is also to lay out and specify the computational setup, which is generally applicable for accurate CRYSCOR calculations on molecular crystals.

Second Order Local Møller-Plesset Perturbation Theory for Periodic Systems: the CRYSCOR Code

Abstract This article reviews the periodic LMP2 method and its implementation in the CRYSCOR code. The main steps of the LMP2 calculations and the techniques employed are briefly described. Illustrative single-point calculations for three TiO2 polymorphs: rutile, anatase and brookite in their experimental geometry are performed. It is shown that the method scales linearly with respect to the number of atoms per unit cell, and can be applied to relatively complex periodic systems. The LMP2 method in contrast to DFT positions rutile slightly lower in the energy than anatase. Brookite is found to be the most stable. However, since the energy differences are relatively small, a further investigation of the influence of the domain-sizes, geometry, zero-point vibrations, etc. on the relative stability of these systems is required.

Communication: Improved pair approximations in local coupled-cluster methods

In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.

Efficient and accurate treatment of weak pairs in local CCSD(T) calculations. II. Beyond the ring approximation

In order to arrive at linear scaling of the computational cost with molecular size, local coupled cluster methods discriminate pairs of local molecular orbitals according to the spatial separation R of the latter. Only strong pairs are treated at the full coupled cluster level, whereas for weak pairs a lower level of theory (usually Møller-Plesset perturbation theory of second order, MP2) is used. Yet an MP2 treatment of weak pairs is inadequate in certain situations (for example, for describing π-stacking), which calls for an improved but still inexpensive method for dealing with the weak pairs. In a previous contribution, we proposed as a substituent for MP2 the LrCCD3 method, which is based on ring coupled cluster doubles (ring-CCD) and includes all third-order diagrams with energy contributions decaying not quicker than R(-6). In the present work, we explore a still more accurate method, which is based on the same principles. It turned out to be essential to abandon the restriction to ring-CCD, i.e., to include further CCD diagrams beyond the ring approximation. The occurring intermediates turn out to be formally very similar to LMP2 density matrices, such that an efficient evaluation of these non-ring CCD diagrams is possible. Furthermore, a computationally cheap a posteriori estimate for the fourth-order singles contribution to the weak pair energy, which also exhibits a decay behavior of R(-6), is introduced. The resulting method, denoted as LCCD[S]-R(-6), indeed provides a substantial improvement in accuracy over the previous LrCCD3 method at a relatively modest additional computational cost.

Linear-scaling explicitly correlated treatment of solids: periodic local MP2-F12 method.

Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.

Efficient and accurate treatment of weak pairs in local CCSD(T) calculations

Local coupled cluster theory is based on (i) a restriction of the list of pairs (or triples) of occupied molecular orbitals, and (ii) a truncation of the virtual space to orbital pair (or triple) specific subspaces. The latter is motivated by an exponential decay of the contributions to the pair energy with respect to the distance between related local occupied and virtual orbitals; the former only by a polynomial R(-6) decay with respect to the distance R between the two occupied orbitals of the pair. Consequently, the restriction of the pair list is more critical, and contributions of pairs should not be neglected unless the corresponding interorbital distance is really large. In local coupled cluster theory pairs are usually discriminated on the basis of the interorbital distance, or the size of the 2nd order Møller-Plesset perturbation theory (MP2) estimate of the pair energy. Only strong pairs are treated at the full coupled cluster level, while weak pairs are treated just at the level of MP2. Yet MP2 might be problematic in certain cases, for example, π-stacking is badly described by MP2, etc. We propose to substitute the MP2 treatment of weak pairs by an approach based on ring-CCD by including third-order diagrams with R(-6) decay behavior. Such an approach is clearly superior; it provides higher accuracy, while the computational cost is not significantly higher than that of a MP2 based treatment of weak pairs.

Periodic quantum mechanical simulation of the He-MgO(100) interaction potential

He-atom scattering is a well established and valuable tool for investigating surface structure. The correct interpretation of the experimental data requires an accurate description of the He-surface interaction potential. A quantum-mechanical treatment of the interaction potential is presented using the current dominant methodologies for computing ground state energies (Hartree-Fock, local and hybrid-exchange density functional theory) and also a novel post-Hartree-Fock ab initio technique for periodic systems (a local implementation of Mo̸ller-Plesset perturbation theory at second order). The predicted adsorption well depth and long range behavior of the interaction are compared with that deduced from experimental data in order to assess the accuracy of the interaction potential.

Incrementally Corrected Periodic Local MP2 Calculations: I. The Cohesive Energy of Molecular Crystals

A method for accurate calculations of the cohesive energy of molecular crystals is presented. The cohesive energy is evaluated as a sum of several components. The major contribution is captured by periodic Hartree-Fock (HF) coupled with the local Møller-Plesset perturbation theory of second order (LMP2) with a triple-ζ basis set. Post-MP2 corrections and corrections for the basis set incompleteness are calculated from inexpensive incremental calculations with finite clusters. This is an essential improvement with respect to the periodic LMP2 method and allows for results of benchmark quality for crystalline systems. The proposed technique is superior to the standard incremental scheme as concerns the cluster size and basis set convergence of the results. In contrast to the total energy or electron correlation energy, which are evaluated in standard incremental calculations, post-MP2 and basis set corrections are rather insensitive to approximations and converge quickly both in terms of the order of the increments and the number of terms at a given order. Evaluation of the incremental corrections within the sub-kJ/mol precision requires computing very few of the most compact two-center and three-center non-embedded clusters, making the whole correction scheme computationally inexpensive. This method as well as alternative routes to compute the cohesive energy via the incremental scheme are tested on two molecular crystals: carbon dioxide (CO2) and hydrogen cyanide (HCN).