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

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

In this work, the automated generator environment for ORCA (ORCA‐AGE) is described. It is a powerful toolchain for the automatic implementation of wavefunction‐based quantum chemical methods. ORCA‐AGE consists of three main modules: (1) generation of “raw” equations from a second quantized Ansatz for the wavefunction, (2) factorization and optimization of equations, and (3) generation of actual computer code. We generate code for the ORCA package, making use of the powerful functionality for wavefunction‐based correlation calculations that is already present in the code. The equation generation makes use of the most elementary commutation relations and hence is extremely general. Consequently, code can be generated for single reference as well as multireference approaches and spin‐independent as well as spin‐dependent operators. The performance of the generated code is demonstrated through comparison with efficient hand‐optimized code for some well‐understood standard configuration interaction and coupled cluster methods. In general, the speed of the generated code is no more than 30% slower than the hand‐optimized code, thus allowing for routine application of canonical ab initio methods to molecules with about 500–1000 basis functions. Using the toolchain, complicated methods, especially those surpassing human ability for handling complexity, can be efficiently and reliably implemented in very short times. This enables the developer to shift the attention from debugging code to the physical content of the chosen wavefunction Ansatz. Automatic code generation also has the desirable property that any improvement in the toolchain immediately applies to all generated code

Development of Relativistic Electronic Structure Methods for Accurate Calculations of Molecules Containing Heavy Elements

The dissertation focuses on an efficient implementation of relativistic spin-orbit coupled-cluster methods (SO-CC) widely applicable to molecules containing heavy elements. SO-CC methods have high computational time and storage requirements with a bottleneck associated with the storage and processing of large molecular orbital (MO) integral matrices. These high computational requirements limit the application of SO-CC methods to relatively small molecules compared with their non-relativistic counterparts. Inspired by atomic orbital (AO)-based algorithms in non-relativistic methods, AO-based algorithms have been developed to enhance the computational efficiency of SO-CC methods in the framework of the exact two-component (X2C) theory, with the following advances: 1. The AO-based scheme avoids the evaluation and storage of large MO integral matrices. 2. It lowers the formal floating-point operation count of the computationally significant "ladder term" by a factor of four. 3. It allows the use of sparsity in the AO integral matrix to further reduce the storage requirements and formal operation count. This dissertation develops the formulation and implementation of the AO-based algorithms for SO-CC methods, leveraging the spin-free nature of AO two-electron integrals and sparsity in the AO integral matrix to eliminate the storage bottleneck and reduce the formal operation count. This implementation has been parallelized using shared memory (OpenMP)-based parallelization. In addition, the development of an automatic expression generation library, named AutoGen, and its application to the derivation of working equations in unitary coupled-cluster (UCC) singles and doubles-based third-order polarization propagator theory (UCC3) is discussed in the dissertation. Derivation and implementation of working equations has become a limiting factor in developing several classes of quantum chemistry methods. The number of tensor contraction expressions reaches hundreds and even thousands in many methods including the UCC-based methods. Derivation and implementation of such a large number of expressions is time-consuming and error-prone. The Python-based library developed is driven by string-based manipulation of creation and annihilation operators to bring them to normal order using Wick's theorem. Working equations can be extracted in a simple object form, allowing easy extension and integration with other software packages