Strong electron correlation is ubiquitous in chemistry and physics. The importance of strong correlation in diverse chemical systems and the failure of traditional electronic structure methods to capture it motivate the current work. We highlight the role of electron pairing in strong correlation and introduce conceptually appealing wavefunction ansätze that can accurately describe strong pairing interactions. Our work builds the foundations of a new generation of quantum chemistry methods which would expand the space of many-electron systems that are accurately understood.
Strong electron correlation is ubiquitous in chemistry and physics. The importance of strong correlation in diverse chemical systems and the failure of traditional electronic structure methods to capture it motivate the current work. We highlight the role of electron pairing in strong correlation and introduce conceptually appealing wavefunction ansätze that can accurately describe strong pairing interactions. Our work builds the foundations of a new generation of quantum chemistry methods which would expand the space of many-electron systems that are accurately understood.
Geminal wavefunctions, introduced in the late 1950s, have long been recognized for their ability to compactly capture strong electron correlation. Despite their promise, they were historically overshadowed by more computationally efficient methods. Advances in both computational resources and theoretical frameworks have renewed interest in geminal-based approaches, particularly as researchers seek accurate yet tractable wavefunctions for complex electronic systems. Recent developments highlight their versatility: from serving as efficient starting points for correlated wavefunctions, to hybrid formulations that blend geminal concepts with coupled-cluster theory, to emerging applications in quantum algorithms where orbital-pairing provides a natural structure. In this mini-review, we summarize key advances in geminal wavefunction theory, with a focus on their modern resurgence, new methodological innovations, and potential directions for electronic structure theory and quantum computation.
Accurately predicting the effects of correlations caused by strong interactions between electrons represents one of the key unsolved challenges in quantum chemistry. This thesis details theoretical developments addressing two aspects of this challenge. First, advances in Canonical Transformation (CT) theory address the task of describing weak interactions between the chemically active valence electrons and the chemically inert core electrons when the valence electrons are strongly correlated. Second, new methodologies for Jastrow factor wavefunctions are explored in an attempt to describe strong interactions amongst the valence electrons. In its original form, CT theory suffered from poorly understood numerical instabilities in strongly interacting systems and poor accuracy relative to coupled cluster theory in weakly interacting systems. Here the numeric issues are identified as consequences of CT theory's central approximation and shown to be similar to the intruder states of many-body perturbation theory. It is demonstrated that these instabilities can be avoided by placing particular restrictions on the theory's degrees of freedom. In weakly interacting systems, we show that using a quadratic, rather than linear, commutator approximation improves accuracy, and that the accuracy in any system can be improved by making use of the system's 3-body reduced density matrix. These improvements are demonstrated in a variety of systems, including N2 , H2 O, NiO, and free base porphin. Jastrow factor wavefunctions have traditionally been handled using quan- tum Monte Carlo techniques such as variational Monte Carlo (VMC). Here we explore how VMC can be made to accommodate the unconventionally large numbers of variational parameters present in many-body Jastrow factors and show that the stochastic reconfiguration algorithm can be thus improved by employing the method of conjugate gradients to solve its central linear equation. In addition to extending the reach of VMC, we have also developed nonstochastic methods for working with Jastrow factor wavefunctions that do not rely on random sampling. These methods, similar in design to those used with the coupled cluster wavefunction, produce energies very close to those of VMC in applications to the Heisenberg, spinless Hubbard, and full Hubbard model Hamiltonians.
Our overarching goal is the development of wavefunction-based quantum chemistry methods that give good results for both weakly- and strongly-correlated systems, that preserve as many fundamental properties of the exact wavefunction as possible, and that are computationally affordable and black-box for the end user. Many of our contributions in this area are based on the archetypal quantum chemistry method, coupled-cluster theory, and they have resulted from our efforts to understand and remedy the failure of symmetry-adapted coupled-cluster theory in the presence of strong correlation. In this thesis, we recount these investigations and discuss the key insights and results that they have produced. We describe in detail the novel wavefunction approaches we have devised, as well as the approximations and considerations one must make in order to arrive at useful equations. We believe that this work could be important for the continued development of affordable methods capable of accurately describing a wide variety of quantum chemical systems.
Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems.
Precise prediction and control of chemical reactions and material propertiesthe central goal of precision chemistrytruly rely on accurate and efficient theoretical modeling of chemical systems. In recent years, significant progress has been made in theoretical and computational chemistry. Especially, interdisciplinary studies in the direction of the two emerging computational frontiers, artificial intelligence and quantum computation, are revolutionizing this field. Expressive neural networks can be used to represent many-electron wave functions with high accuracy, capturing strong correlations with a favorable computational cost compared to other methods. Leveraging quantum computation in quantum chemistry is also expected to deliver a quantum advantage in problems including electronic structure calculations. With artificial intelligence and quantum computation, we expect to establish a unified, high-precision, and scalable computational foundation for generating accurate quantum chemical data essential for precision chemistry.
A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements in numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement seen previously. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.