The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds

We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 {\AA} for RHF and MP2, respectively.Comment: Revised manuscrip

Threading a path to exascale with chemical scissors and integral compressors in a singular manner

Research presented in this dissertation aims at enabling (correlated) fragmentation methods to explore biochemistry and catalysis effects of macrosystems at high levels of accuracy using exascale computing resources. The target is the second-order MollerPlesset perturbation theory (MP2), and MP2 in the FMO framework (FMO/MP2). First, the 2-electron integral bottleneck is addressed by using the resolution-of-the-identity (RI) approximation to reduce the memory storage and the computational cost of the integral transformation from the atomic orbital (AO) to the molecular orbital (MO) basis. The RI approximation is also combined with the singular value decomposition (SVD) to introduce a flexible compression factor that fully controls the accuracy of the integral compression. The RIMP2 energy and analytic energy gradient are implemented in the GAMESS electronic structure program and are parallelized with an efficient hybrid distributed/shared memory model with the support of the MPI and OpenMP APIs. Both the RI-MP2 energy and gradient are interfaced to the FMO framework for large system calculations

Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum.

We develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons

Diagrammatic Coupled Cluster Monte Carlo

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -- diagCCMC -- allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.Comment: 31 pages, 6 figure

First Order Static Excitation Potential: Scheme for Excitation Energies and Transition Moments

We present an approximation scheme for the calculation of the principal excitation energies and transition moments of finite many-body systems. The scheme is derived from a first order approximation to the self energy of a recently proposed extended particle-hole Green's function. A hermitian eigenvalue problem is encountered of the same size as the well-known Random Phase Approximation (RPA). We find that it yields a size consistent description of the excitation properties and removes an inconsistent treatment of the ground state correlation by the RPA. By presenting a hermitian eigenvalue problem the new scheme avoids the instabilities of the RPA and should be well suited for large scale numerical calculations. These and additional properties of the new approximation scheme are illuminated by a very simple exactly solvable model.Comment: 15 pages revtex, 1 eps figure included, corrections in Eq. (A1) and Sec. II

Assessment of random-phase approximation and second order M{\o}ller-Plesset perturbation theory for many-body interactions in solid ethane, ethylene, and acetylene

The relative energies of different phases or polymorphs of molecular solids can be small, less than a kiloJoule/mol. Reliable description of such energy differences requires high quality treatment of electron correlations, typically beyond that achievable by routinely applicable density functional theory approximations (DFT). At the same time, high-level wave function theory is currently too computationally expensive. Methods employing intermediate level of approximations, such as M{\o}ller-Plesset (MP) perturbation theory and the random-phase approximation (RPA) are potentially useful. However, their development and application for molecular solids has been impeded by the scarcity of necessary benchmark data for these systems. In this work we employ the coupled-clusters method with singles, doubles and perturbative triples (CCSD(T)) to obtain a reference-quality many-body expansion of the binding energy of four crystalline hydrocarbons with a varying $\pi$-electron character: ethane, ethene, and cubic and orthorhombic forms of acetylene. The binding energy is resolved into explicit dimer, trimer, and tetramer contributions, which facilitates the analysis of errors in the approximate approaches. With the newly generated benchmark data we test the accuracy of MP2 and non-self-consistent RPA. We find that both of the methods poorly describe the non-additive many-body interactions in closely packed clusters. Using different DFT input states for RPA leads to similar total binding energies, but the many-body components strongly depend on the choice of the exchange-correlation functional

Development of efficient and low-scaling methods to compute molecular properties at MP2 and double-hybrid DFT levels

This thesis introduces new methods to compute molecular properties at the level of second-order Møller-Plesset perturbation theory (MP2) and double-hybrid density functional theory, building on a reformulation in atomic orbitals and exploiting the rank deficiency of the (pseudo-)density matrices, thus reducing the scaling behavior with respect to the size of the basis set. By furthermore employing the resolution-of-the-identity approximation, low-scaling and efficient MP2 energy gradients are presented, where significant two-electron integrals are screened using a distance-including integral estimation technique. With this, the forces and the hyperfine coupling constants of systems larger than previously computable at the MP2-level are obtained. In the second part of this thesis, the locality of the spin density in many molecular systems is exploited in the computation of the hyperfine coupling constants, leading to further speed-ups and allowing for a thorough investigation of the effect of the protein environment on the hyperfine coupling within the core region of a pyruvate formate lyase. With this efficient method, studying the effect of nuclear motion on the accuracy of the computed hyperfine coupling constants is possible. The study presented in this thesis demonstrates that both electron correlation and vibrational motion are crucial for an accurate theoretical description. When calculating magnetic properties, the dependence on the choice of gauge origins needs to be considered. This effect is studied systematically, and in detail, in a fourth project of this thesis for the computation of electronic g-tensors, for which it was previously assumed that the computation is largely independent of the choice of the gauge-origin. The study clearly contradicts this assumption and motivates the use of gauge including atomic orbitals in future work on electronic g-tensors. In a last part, this work transfers the algorithmic developments on the computation of analytic gradients to the computation of nuclear magnetic resonance (NMR) shieldings at the MP2-level. Though a sublinear scaling ansatz to compute the NMR shielding tensor per nucleus is available, the lack of an efficient implementation and the large dependency on the size of the basis sets prohibits the accurate computation of the shielding tensor of medium- to large-sized molecules. Furthermore, while this ansatz in theory scales linearly when all nuclei in a system are computed, it is inefficient due to the dependence of the rate-determining steps on the nuclear magnetic moments. This thesis therefore presents a new all-nuclei ansatz and introduces the methodology for the efficient computation of the energy gradients developed in this thesis, highlighting significant computational savings

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory—a linear-scaling, massively parallel framework—as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models