Electronic Structure Theory has led to a variety of developments and applications. In the Nooijen group the focus is on the development and use of Coupled Cluster based approaches. Coupled Cluster is a very strong and accurate approach to the quantum mechanical problem. The research results presented in the thesis testify to the Similarity Transformed Equation of Motion Coupled Cluster (STEOM-CC) for being a very accurate and yet computationally inexpensive approach for excited states. This study reveals new features about STEOM and provides promise regarding future improvement in the methodology. STEOM can be used as the first step in the construction of the Vibronic model, which is a strong tool to move to paradigms beyond the Born-Oppenheimer approximation. Spin-Orbit Coupling (SOC) is a very important ingredient required to study relativistic phenomena and its quantum mechanical implementation for many body systems is not straightforward. The most widely used SOC operator in Chemical Physics is the Breit-Pauli operator, which requires employing non-trivial approximations to the Dirac equation to adapt the theory to many body systems. The integration of electronic structure approaches, Vibronic Coupling, and SOC is essential to study the phenomenon of intersystem crossing (transition between spin states) in fine detail. In this thesis a computational benchmark of STEOM is discussed, while the frameworks of Vibronic Coupling and Spin-Orbit Coupling (SOC) are considered on a theoretical level.

A novel method by which to calculate the near edge X-rayabsorption fine structure region of the X-ray absorption spectrum has been derived and implemented. By means of damped coupled cluster theory at coupled cluster levels CCS, CC2, CCSD and CCSDR(3), the spectra of neon and methane have been investigated. Using methods incorprating double excitations, the important relaxation effects maybe taken into account by simultaneous excitation of the core electron and relaxation of other electrons. An asymmetric Lanczos-chain driven approach has been utilized as a means to partially resolve the excitation space given by the coupled cluster Jacobian. The K-edge of the systems have been considered, and relativistic effects are estimated with use of the Douglas--Kroll scalar relativistic Hamiltonian. Comparisons have been made to results obtained with the four-component static-exchange approach and ionization potentials obtained by the {Delta}SCF-method. The appropriate basis sets by which to describe the core and excited states have been been determined.  The addition of core-polarizing functions and diffuse or Rydberg functions is important for this description. Scalar relativistic effects accounts for an increase in excitation energies due to the contraction of the 1s-orbital, and this increase is seen to be 0.88 eV for neon. The coupled cluster hierachy shows a trend of convergence towards the experimental spectrum, with an 1s -> 3p excitation energy for neon of an accuracy of 0.40 eV at a relativistic CCSDR(3) level of theory. Results obtained at the damped coupled cluster and STEX levels of theory, respectively, are seen to be in agreement, with a mere relative energy shift.

Electronic Structure Theory has led to a variety of developments and applications. In the Nooijen group the focus is on the development and use of Coupled Cluster based approaches. Coupled Cluster is a very strong and accurate approach to the quantum mechanical problem. The research results presented in the thesis testify to the Similarity Transformed Equation of Motion Coupled Cluster (STEOM-CC) for being a very accurate and yet computationally inexpensive approach for excited states. This study reveals new features about STEOM and provides promise regarding future improvement in the methodology. STEOM can be used as the first step in the construction of the Vibronic model, which is a strong tool to move to paradigms beyond the Born-Oppenheimer approximation. Spin-Orbit Coupling (SOC) is a very important ingredient required to study relativistic phenomena and its quantum mechanical implementation for many body systems is not straightforward. The most widely used SOC operator in Chemical Physics is the Breit-Pauli operator, which requires employing non-trivial approximations to the Dirac equation to adapt the theory to many body systems. The integration of electronic structure approaches, Vibronic Coupling, and SOC is essential to study the phenomenon of intersystem crossing (transition between spin states) in fine detail. In this thesis a computational benchmark of STEOM is discussed, while the frameworks of Vibronic Coupling and Spin-Orbit Coupling (SOC) are considered on a theoretical level.

Stuttgart, Univ., Diss., 2008.

University, Diss., 2003--Bonn.

The characteristics of irregular algorithms make a parallel implementation difficult, especially for PC clusters or clusters of SMPs. These characteristics may include an unpredictable access behavior to dynamically changing data structures or strong irregular coupling of computations. Problems are an unknown load distribution and expensive irregular communication patterns for data accesses and redistributions. Thus the parallel implementation of irregular algorithms on distributed memory machines and clusters requires a special organizational mechanism for a dynamic load balance while keeping the communication and administration overhead low. We propose task pool teams for implementing irregular algorithms on clusters of PCs or SMPs. A task pool team combines multithreaded programming using task pools on single nodes with explicit message passing between different nodes. The dynamic load balance mechanism of task pools is generalized to a dynamic load balance scheme for all distributed nodes. We have implemented and compared several versions for task pool teams. As application example, we use the hierarchical radiosity algorithm, which is based on dynamically growing quadtree data structures annotated by varying interaction lists expressing the irregular coupling between the quadtrees. Experiments are performed on a PC cluster and a cluster of SMPs.

We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory. Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0) and at the magnetic ordering wavevectors ±[Q= (4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.

Multireference coupled cluster (MRCC) methods are a highly accurate approach for sys- tems with quasi-degeneracies, where the static correlation plays an important role. How- ever, while canonical MRCC is successful for many systems, it can be used only for small sized systems. Nonetheless, it was shown that large systems can be described by the domain-based local pair natural orbital approach (DLPNO). In our group, we developed DLPNO-MkCCSD, DLPNO-TCCSD and DLPNO-MkCCSD(T) methods, which were able to recover more than 99.7% of the canonical correlation energy, while the computation of systems with more than 2000 basis functions took only a few hours on a single CPU core. Moreover, we also implemented a tailored variant of MRCC which successfully described excited states of cyclobutadiene, while the traditional MRCC under-performed.

There are a lot of interesting problems in surface chemistry where quantum chemistry could give great insight, like reaction mechanisms in heterogeneous catalysis, the effect of surface functionalization on semiconductors, or the influence of defects on the reactivity of crystal surfaces. Plane wave based methods applied to crystals cannot handle problems that are localized in nature like surface defects and adsorbates. On the other hand, molecular electronic structure techniques, which describe these effects and the locality of the electronic correlation well, are too computationally expensive to use on these systems. In this work, we introduce translationally-transformed coupled-cluster (TT-CC) theory, a new electronic structure method that incorporates the periodicity of crystals and the locality of electronic correlation. This is accomplished by encoding the periodicity into the amplitudes, instead of using plane waves, in order to be able to use a local basis to reflect the decay of the electronic correlation at sufficiently large distances. This avoids the calculation of redundant amplitudes. Perfectly periodic surfaces are envisioned as reference wavefunctions for localized defects and chemical reactions. The working equations in one dimension are derived starting from the amplitude equations of conventional coupled cluster singles and doubles (CCSD) on an infinite system and rearranging them such that the distance to an anonymous cell is an explicit degree of freedom, L. The formally infinite summations can be truncated by systematically neglecting numerically insignificant amplitudes. The generalization of the amplitude equations to higher dimensions is straightforward, albeit laborious. We show a general strategy to incorporate defects. These will be subjects of future dissertations. We present a proof of principle for 1-dimensional chemical systems of increasing size (He, H2, Be, Ne and N2) using the 6-31G basis set. We compute the energies, with TT-CCSD, at different distances and compared them against the perfectly periodic intensive energy (PPIE) using conventional CCSD. All results, up to L=3, show that the energies of TT-CCSD converge to the PPIE. For neon, TT-CCSD shows an error of -6.2x10-6 Eh per cell against the PPIE at the bonding distance with the potential computational cost of 7 cells using CCSD, as an upper bound. For nitrogen, TT-CCSD shows an error of -2.2x10-9 Eh at 7.5 Å per cell with the same potential cost as upper bound.

Accurate correlated electronic structure methods involve a significant amount of computations and can be only employed to small molecular systems. For example, the coupled-cluster singles, doubles, and perturbative triples model (CCSD(T)), which is known as the ``gold standard" of quantum chemistry for its accuracy, usually can treat molecules with 20-30 atoms. To extend the reach of accurate correlated electronic structure methods to larger molecular systems, we work towards two directions: parallel computing and reduced-cost/scaling approaches. Parallel computing can utilize more computational resources to handle systems that demand more substantial computational efforts. Reduced-cost/scaling approaches, which introduce approximations to the existing electronic structure methods, can significantly reduce the amount of computation and storage requirements. In this work, we introduce a new distributed-memory massively parallel implementation of standard and explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) with canonical bigO{N^6} computational complexity ( C. Peng, J. A. Calvin, F. Pavov{s}evi'c, J. Zhang, and E. F. Valeev, textit{J. Phys. Chem. A} 2016, textbf{120}, 10231.), based on the TiledArray tensor framework. Excellent strong scaling is demonstrated on a multi-core shared-memory computer, a commodity distributed-memory computer, and a national-scale supercomputer. We also present a distributed-memory implementation of the density-fitting (DF) based CCSD(T) method. (C. Peng, J. A. Calvin, and E. F. Valeev, textit{in preparation for submission}) An improved parallel DF-CCSD is presented utilizing lazy evaluation for tensors with more than two unoccupied indices, which makes the DF-CCSD storage requirements always smaller than those of the non-iterative triples correction (T). Excellent strong scaling is observed on both shared-memory and distributed-memory computers equipped with conventional Intel Xeon processors and the Intel Xeon Phi (Knights Landing) processors. With the new implementation, the CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even more massive computations possible on leadership-class computing resources. The inclusion of F12 correction to the CCSD(T) method makes it converge to basis set limit much more rapidly. The large-scale parallel explicitly correlated coupled-cluster program makes the accurate estimation of the coupled-cluster basis set limit for molecules with 20 or more atoms a routine. Thus, it can be used rigorously to test the emerging reduced-scaling coupled-cluster approaches. Moreover, we extend the pair natural orbital (PNO) approach to excited states through the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. (C. Peng, M. C. Clement, and E. F. Valeev, textit{submitted}) We simulate the PNO-EOM-CCSD method using an existing massively parallel canonical EOM-CCSD program. We propose the use of state-averaged PNOs, which are generated from the average of the pair density of excited states, to span the PNO space of all the excited states. The doubles amplitudes in the CIS(D) method are used to compute the state-averaged pair density of excited states. The issue of incorrect states in the state-averaged pair density, caused by an energy reordering of excited states between the CIS(D) and EOM-CCSD, is resolved by simply computing more states than desired. We find that with a truncation threshold of $10^{-7}$, the truncation error for the excitation energy is already below 0.02 eV for the systems tested, while the average number of PNOs is reduced to 50-70 per pair. The accuracy of the PNO-EOM-CCSD method on local, Rydberg and charge transfer states is also investigated. / Ph. D.