The accuracy of large-scale ab initio calculations is always desired, but they are unfortunately not usually practical in many fields, such as studies of heterogeneous catalysis, photosynthesis, and functional mechanisms of biomolecules. DFT serves as a prevailing method for large calculations due to its compromise between cost and accuracy, but it has a number of failure cases, like bond breaking. On the other hand, the simple theoretical nature of force-field simulations, which often work well, reminds us that large systems are not necessarily exponentially complicated. A recurring theme in the electronic structure of large systems is therefore the use of fragment-based approaches. Existing fragment approaches typically treat the most powerful electron correlations perturbatively, on the same footing with dispersion forces (if at all). In our approach, electrons are not treated individually in the global calculation, but subunits will be chosen. (e.g., amino acid residues or individual water molecules). The most important local states are selected to account for inter-subunit interactions. Most familiar wavefunction methods (SCF, PT, coupled-cluster) can be applied directly to this internally correlated Hamiltonian, and the Hamiltonian itself is systematically improvable to exactitude. Furthermore, different parts of a system can be treated at different accuracy. Our initial investigations focus on the correlation structure of groups of harmonic oscillators, where the coupling inside of groups is stronger than between groups. This mimics discrete molecules while providing us with exact analytical solutions for comparison. Correlations between grouped oscillators will be characterized by both numerical and analytical methods, in order to shed light on building an algorithm for real molecules and systems.
The accuracy of large-scale ab initio calculations is always desired, but they are unfortunately not usually practical in many fields, such as studies of heterogeneous catalysis, photosynthesis, and functional mechanisms of biomolecules. DFT serves as a prevailing method for large calculations due to its compromise between cost and accuracy, but it has a number of failure cases, like bond breaking. On the other hand, the simple theoretical nature of force-field simulations, which often work well, reminds us that large systems are not necessarily exponentially complicated. A recurring theme in the electronic structure of large systems is therefore the use of fragment-based approaches. Existing fragment approaches typically treat the most powerful electron correlations perturbatively, on the same footing with dispersion forces (if at all). In our approach, electrons are not treated individually in the global calculation, but subunits will be chosen. (e.g., amino acid residues or individual water molecules). The most important local states are selected to account for inter-subunit interactions. Most familiar wavefunction methods (SCF, PT, coupled-cluster) can be applied directly to this internally correlated Hamiltonian, and the Hamiltonian itself is systematically improvable to exactitude. Furthermore, different parts of a system can be treated at different accuracy. Our initial investigations focus on the correlation structure of groups of harmonic oscillators, where the coupling inside of groups is stronger than between groups. This mimics discrete molecules while providing us with exact analytical solutions for comparison. Correlations between grouped oscillators will be characterized by both numerical and analytical methods, in order to shed light on building an algorithm for real molecules and systems.
Conspectus Ab initio modeling of matter has become a pillar of chemical research: with ever-increasing computational power, simulations can be used to accurately predict, for example, chemical reaction rates, electronic and mechanical properties of materials, and dynamical properties of liquids. Many competing quantum mechanical methods have been developed over the years that vary in computational cost, accuracy, and scalability: density functional theory (DFT), the workhorse of solid-state electronic structure calculations, features a good compromise between accuracy and speed. However, approximate exchange-correlation functionals limit DFT's ability to treat certain phenomena or states of matter, such as charge-transfer processes or strongly correlated materials. Furthermore, conventional DFT is purely a ground-state theory: electronic excitations are beyond its scope. Excitations in molecules are routinely calculated using time-dependent DFT linear response; however applications to condensed matter are still limited. By contrast, many-electron wavefunction methods aim for a very accurate treatment of electronic exchange and correlation. Unfortunately, the associated computational cost renders treatment of more than a handful of heavy atoms challenging. On the other side of the accuracy spectrum, parametrized approaches like tight-binding can treat millions of atoms. In view of the different (dis-)advantages of each method, the simulation of complex systems seems to force a compromise: one is limited to the most accurate method that can still handle the problem size. For many interesting problems, however, compromise proves insufficient. A possible solution is to break up the system into manageable subsystems that may be treated by different computational methods. The interaction between subsystems may be handled by an embedding formalism. In this Account, we review embedded correlated wavefunction (CW) approaches and some applications. We first discuss our density functional embedding theory, which is formally exact. We show how to determine the embedding potential, which replaces the interaction between subsystems, at the DFT level. CW calculations are performed using a fixed embedding potential, that is, a non-self-consistent embedding scheme. We demonstrate this embedding theory for two challenging electron transfer phenomena: (1) initial oxidation of an aluminum surface and (2) hot-electron-mediated dissociation of hydrogen molecules on a gold surface. In both cases, the interaction between gas molecules and metal surfaces were treated by sophisticated CW techniques, with the remainder of the extended metal surface being treated by DFT. Our embedding approach overcomes the limitations of conventional Kohn-Sham DFT in describing charge transfer, multiconfigurational character, and excited states. From these embedding simulations, we gained important insights into fundamental processes that are crucial aspects of fuel cell catalysis (i.e., O2 reduction at metal surfaces) and plasmon-mediated photocatalysis by metal nanoparticles. Moreover, our findings agree very well with experimental observations, while offering new views into the chemistry. We finally discuss our recently formulated potential-functional embedding theory that provides a seamless, first-principles way to include back-action onto the environment from the embedded region.
Quantum chemistry models atoms and molecules using quantum mechanics, with the electronic structure problem at its core. This problem, which determines the energy and properties of electrons in a molecule, is exponentially hard to solve exactly on classical computers. To approximate solutions, effective models introduce layers of simplifications. However, these approximations can fail for strongly correlated systems, necessitating alternative approaches. Quantum computers, capable of processing quantum information natively, offer a promising path to simulate molecular systems beyond classical reach, with potential applications in catalysis, materials science, and photochemistry. Despite rapid advancements in quantum hardware, practical quantum computations remain challenging due to limited resources. This thesis optimizes quantum resource usage in computational chemistry, introducing novel embedding techniques and exploring applications beyond ground-state energies. Chapter 1 establishes the foundation by reviewing quantum chemistry methods, from Hartree-Fock and Density Functional Theory (DFT) to active space approaches. It also provides an introduction to quantum computing for chemistry, focusing on near-term algorithms. The following chapters present novel methods aimed at reducing quantum resource requirements and tackling problems classical methods struggle with. Chapter 2 introduces a technique to reduce the λ-norm of the electronic structure Hamiltonian, a key measure of quantum resource demand. By transforming molecular orbitals, this method enhances sampling efficiency in Noisy Intermediate-Scale Quantum (NISQ) algorithms and reduces runtime in Fault-Tolerant Quantum Computing (FTQC). Localized orbitals outperform canonical ones, and an orbital-optimization scheme is proposed to minimize the λ-norm. Benchmarks on hydrogen chains, FeMoco, and Ruthenium complexes demonstrate its effectiveness. Chapter 3 presents the FragPT2 framework for simulating large systems with multiple interacting fragments. This method embeds each fragment in the mean field of others and applies multi-reference perturbation theory to capture inter-fragment correlations such as dispersion and charge transfer efficiently. The approach reduces computational overhead and enables scalable simulations, as shown in applications to \ce{N2} dimers, aromatic dimers, and butadiene. Chapter 4 focuses on photochemical systems, where multiple electronic states must be treated equally. The state-averaged orbital-optimized variational quantum eigensolver (SAOOVQE) is extended with analytical energy gradients and non-adiabatic couplings, enabling geometry optimizations and simulations of non-adiabatic dynamics on quantum hardware. This is demonstrated by locating the conical intersection in formaldimine, highlighting SAOOVQE’s potential for studying photoisomerization in biomolecules. Building on this, Chapter 5 develops a quantum algorithm to detect conical intersections, where the Born-Oppenheimer approximation breaks down. These intersections are characterized by a discrete Berry phase (0 or π), representing their topological nature. The algorithm extracts this phase as a single bit of information, ensuring resilience to noise. Analytical proof and numerical validation using a toy molecular model illustrate its effectiveness for studying light-perception biochemistry and related photochemical processes. Finally, Chapter 6 explores machine learning density functionals trained on noisy quantum data. While DFT is computationally efficient, its accuracy depends on approximated exchange-correlation functionals. This work proposes a neural network-based approach to learn the exact functional from quantum data, showing that training on noisy outputs from NISQ devices can mitigate sampling errors. Applications to the Fermi-Hubbard model and other systems demonstrate its potential to generalize and provide accurate results under noise. This thesis advances quantum computational chemistry by optimizing quantum resource usage, developing new embedding strategies, and expanding the scope of quantum simulations beyond ground-state properties. These contributions pave the way for practical quantum algorithms that could revolutionize molecular simulations in the near future.
Strong correlation poses a difficult problem for electronic structure theory, with computational cost scaling quickly with system size. Fragment embedding is an attractive approach to this problem. By dividing a large complicated system into smaller manageable fragments "embedded" in an approximate description of the rest of the system, we can hope to ameliorate the steep cost of correlated calculations. While appealing, these methods often converge slowly with fragment size because of small errors at the boundary between fragment and bath. We describe a new electronic embedding method, dubbed "Bootstrap Embedding," a self-consistent wavefunction-in-wavefunction embedding theory that uses overlapping fragments to improve the description of fragment edges. We apply this method to the one dimensional Hubbard model and a translationally asymmetric variant, and find that it performs very well for energies and populations. We find Bootstrap Embedding converges rapidly with embedded fragment size, overcoming the surface-area-to-volume-ratio error typical of many embedding methods. We anticipate that this method may lead to a low-scaling, high accuracy treatment of electron correlation in large molecular systems.
Computational chemistry has made remarkable progress in the last couple of decades due to the availability of better and more powerful computers. However, there is definitely more room for improvement. There are problems in material science and biology that require 102 to 104 atoms to be considered and the importance of such systems cannot be over-emphasized. Addressing such systems with ab-initio methods is still a quantum chemist’s dream. ¨ Brute force solutions of the Schrodinger equation are not possible for reasonably interesting and important systems due to the large number of Slater determinants that have to be stored in a computer’s memory. Thus electronic structure theorists have made chemically and mathematically intuitive approximations to simplify the problems. A particularly difficult class of systems that is very interesting to the theoretical and experimental chemists is the strongly correlated systems. High Tc superconductors, nanotubes, graphene sheets, transition metal complexes and photosynthetic materials all fall under this category. These systems are too large to be treated by traditional quantum chemical methods. Another reason why such systems have not been studied sufficiently by ab-initio method is that they comprise of complicated strong electron-electron correlation (and therefore the name strongly correlated), thus, making them impossible to be qualitatively defined by a molecular orbital picture, which has been a quantum chemist’s fa- vorite tool for a long time now. Therefore, in this thesis, we have tried to develop, improve and apply methods for treating such strongly correlated systems. The thesis is broadly divided into two parts. In the first part, we discuss the orbital optimized DMRG method developed to treat static correlation in large strongly correlated systems. In the next part we discuss the two methods that can treat dynamic correlation in such complicated systems.
The workhorse method of computational materials science is undeniably density functional theory in the Kohn-Sham framework of approximate exchange and correlation energy functionals. However, the need for highly accurate predictions of ground and excited state properties in materials science motivates the further development and exploration of alternative as well as complementary techniques. Among these alternative approaches, quantum chemical wavefunction based theories and in particular coupled cluster theory hold the promise to fill a gap in the toolbox of computational materials scientists. Coupled cluster (CC) theory provides a compelling framework of approximate infinite-order perturbation theory in the form of an exponential of cluster operators describing the true quantum many-body effects of the electronic wave function at a computational cost that, despite being significantly more expensive than DFT, scales polynomially with system size. The hierarchy of size-extensive approximate methods established in the framework of CC theory achieves systematic improvability for many materials properties. This is in contrast to currently available density functionals that often suffer from uncontrolled approximations that limit the accuracy in the prediction of materials properties. In this tutorial-style review we will introduce basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the connection between coupled cluster theory and the random-phase approximation to bridge the gap between traditional quantum chemistry and many-body Green’s function theories that are widely-used in the field of solid state physics. We will discuss various approaches to improve the computational performance without compromising accuracy. These approaches include large-scale parallel design as well as techniques that reduce the prefactor of the computational complexity. A central part of this article discusses the convergence of calculated properties to the thermodynamic limit which is of significant importance for reliable predictions of materials properties and constitutes an additional challenge compared to calculations of large molecules. Furthermore we mention technical aspects of computer code implementations of periodic coupled cluster theories in different numerical frameworks of the one-electron orbital basis; the projector-augmented-wave formalism using a plane wave basis set and the numeric atom-centered-orbital with resolution-of-identity.
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as the full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size. Downfolding and embedding approaches mitigate this cost but typically require prior selection of a correlated subspace, which can be difficult to determine in heterogeneous or extended systems. Here, we introduce a stochastic cluster expansion framework for efficiently recovering the total correlation energy of large systems with near-DMRG accuracy and without the need to select an active space a priori . By combining correlation contributions from randomly sampled environment orbitals with an exactly treated subspace of interest, the method reproduces total energies for nonreacting and reactive systems while drastically reducing computational cost. The approach also provides a quantitative diagnostic for molecule–solvent correlation, guiding principled embedding decisions. This framework enables systematically improvable many-body calculations in extended systems, opening the door to high-accuracy studies of chemical processes in condensed phase environments.