Coupling of quantum chemistry models and high-performance algorithms for the global exploration of the energy landscape of atomic and molecular systems
The primary aim of this thesis is to develop efficient methods for characterizing molecular conformations at a quantum level. Various methods devoted to the computation of molecular potential energy are reviewed, as well as the most popular potential energy surfaces (PES) global exploration schemes. In this context, a key contribution of this thesis is the coupling of the robotics-inspired Iterative Global exploration and LOcal Optimization (IGLOO) method, implemented in the MoMA software, with the quantum Density-Functional based Tight-Binding (DFTB) potential, implemented in the deMonNano software. The IGLOO algorithm integrates the motion planning Rapidly-exploring Random Trees (RRT) algorithm with local optimization and structural filtering. A proof of concept has been done through the identification of low-energy conformations of the alanine dipeptide.The IGLOO/DFTB coupling has been applied to the mapping of the PES of three close-sized molecules of the phthalate family (dibutyl phthalate DBP, benzyl butyl phthalate BBP and di-2-ethylhexyl phthalate DEHP), providing detailed insights into their different conformational landscapes. Various geometrical descriptors have been used to analyze their structure-energy relationships. Coulomb interactions, steric hindrance, and dispersive interactions have been found to drive the geometric properties and a strong correlation has been evidenced between the two dihedral angles describing the side-chains orientation of the phthalate molecules. The results demonstrate the method's capability to identify low-energy minima without prior knowledge of the PES.Furthermore, an innovative algorithm for the large-scale generation of molecular structures, including a conformational variety, is presented. It combines molecular graph generation with atom or fragment addition techniques. It is applied to provide an extensive database of 3D structures of hydrogenated amorphous carbon (a-CH) molecules. The analysis of the database generated in this study provides a comprehensive understanding of the relationship between the geometrical and electronic descriptors of a-C:H structures. These properties are compared with those of compact Polycyclic Aromatic Hydrocarbons and linear chains, representing limit cases.Finally, a review is given on methods aiming at identifying saddle points and transition paths between low-energy conformations on the PES. A first step toward the identification of transition paths between low-energy conformations using a motion planning algorithm, known as Transition-based Rapidly-exploring Random Trees (T-RRT), is presented. A similarity measure, designated as the Symmetrized Segment-Path Distance (SSPD), is used to compare the generated trajectories. Subsequently, a clustering technique, namely the Hierarchical Clustering Analysis (HCA), is employed to group similar trajectories in order to identify the common pathways, thereby providing valuable insights into the dynamics of conformational changes. The methodology has been successfully applied to the identification of low-energy paths between two minima of the alanine dipeptide PES.Overall, the research presents significant advancements in the exploration of complex molecular PES at a quantum level including (i) the IGLOO/DFTB coupling (ii) a novel algorithm for 3D structure generation of large-scale molecules and (iii) an original scheme allowing for the identification of multiple transition paths. Correlations between the structural, energetic and electronic properties have been evidenced for the polluting phthalate molecules and astrophysically relevant hydrogenated amorphous carbon (a-CH) molecules. These contributions pave the way for future research, aiming to extend these methods to larger and more complex systems.
The primary aim of this thesis is to develop efficient methods for characterizing molecular conformations at a quantum level. Various methods devoted to the computation of molecular potential energy are reviewed, as well as the most popular potential energy surfaces (PES) global exploration schemes. In this context, a key contribution of this thesis is the coupling of the robotics-inspired Iterative Global exploration and LOcal Optimization (IGLOO) method, implemented in the MoMA software, with the quantum Density-Functional based Tight-Binding (DFTB) potential, implemented in the deMonNano software. The IGLOO algorithm integrates the motion planning Rapidly-exploring Random Trees (RRT) algorithm with local optimization and structural filtering. A proof of concept has been done through the identification of low-energy conformations of the alanine dipeptide.The IGLOO/DFTB coupling has been applied to the mapping of the PES of three close-sized molecules of the phthalate family (dibutyl phthalate DBP, benzyl butyl phthalate BBP and di-2-ethylhexyl phthalate DEHP), providing detailed insights into their different conformational landscapes. Various geometrical descriptors have been used to analyze their structure-energy relationships. Coulomb interactions, steric hindrance, and dispersive interactions have been found to drive the geometric properties and a strong correlation has been evidenced between the two dihedral angles describing the side-chains orientation of the phthalate molecules. The results demonstrate the method's capability to identify low-energy minima without prior knowledge of the PES.Furthermore, an innovative algorithm for the large-scale generation of molecular structures, including a conformational variety, is presented. It combines molecular graph generation with atom or fragment addition techniques. It is applied to provide an extensive database of 3D structures of hydrogenated amorphous carbon (a-CH) molecules. The analysis of the database generated in this study provides a comprehensive understanding of the relationship between the geometrical and electronic descriptors of a-C:H structures. These properties are compared with those of compact Polycyclic Aromatic Hydrocarbons and linear chains, representing limit cases.Finally, a review is given on methods aiming at identifying saddle points and transition paths between low-energy conformations on the PES. A first step toward the identification of transition paths between low-energy conformations using a motion planning algorithm, known as Transition-based Rapidly-exploring Random Trees (T-RRT), is presented. A similarity measure, designated as the Symmetrized Segment-Path Distance (SSPD), is used to compare the generated trajectories. Subsequently, a clustering technique, namely the Hierarchical Clustering Analysis (HCA), is employed to group similar trajectories in order to identify the common pathways, thereby providing valuable insights into the dynamics of conformational changes. The methodology has been successfully applied to the identification of low-energy paths between two minima of the alanine dipeptide PES.Overall, the research presents significant advancements in the exploration of complex molecular PES at a quantum level including (i) the IGLOO/DFTB coupling (ii) a novel algorithm for 3D structure generation of large-scale molecules and (iii) an original scheme allowing for the identification of multiple transition paths. Correlations between the structural, energetic and electronic properties have been evidenced for the polluting phthalate molecules and astrophysically relevant hydrogenated amorphous carbon (a-CH) molecules. These contributions pave the way for future research, aiming to extend these methods to larger and more complex systems.
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.
A faithful description of chemical processes requires exploring extended regions of the molecular potential energy surface (PES), which remains challenging for strongly correlated systems. Transferable deep-learning variational Monte Carlo (VMC) offers a promising route by efficiently solving the electronic Schrödinger equation jointly across molecular geometries at consistently high accuracy, yet its stochastic nature renders direct exploration of molecular configuration space nontrivial. Here, we present a framework for highly accurate ab initio exploration of PESs that combines transferable deep-learning VMC with a cost-effective estimation of energies, forces, and Hessians. By continuously sampling nuclear configurations during VMC optimization of electronic wave functions, we obtain transferable descriptions that achieve zero-shot chemical accuracy within chemically relevant distributions of molecular geometries. Throughout the subsequent characterization of molecular configuration space, the PES is evaluated only sparsely, with local approximations constructed by estimating VMC energies and forces at sampled geometries and aggregating the resulting noisy data using Gaussian process regression. Our method enables accurate and efficient exploration of complex PES landscapes, including structure relaxation, transition-state searches, and minimum-energy pathways, for both ground and excited states. This opens the door to studying bond breaking, formation, and large structural rearrangements in systems with pronounced multi-reference character.
Accurate prediction of molecular structures and properties is vital for chemistry; materials science, and drug discovery, yet classical electronic-structure methods often fail for strongly correlated systems, large basis sets, and complex potential-energy landscapes. Quantum technology encompassing quantum computing, quantum machine learning, and hybrid quantum classical strategies offers a fundamentally new paradigm by encoding many-electron wave functions directly on qubits and exploiting superposition and entanglement to explore exponentially large Hilbert spaces. This review synthesizes recent algorithmic and hardware advances relevant to molecular modelling, including the Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), quantum unitary coupled-cluster (q-UCC) families, equation-of-motion and subspace methods for excited states, tensor-network hybrids, and quantum kernel and variational QML approaches. We examine noise-aware hybrid workflows, error-mitigation techniques, symmetry-preserving ansätze, and operator-factorization methods that reduce measurement and gate overhead. Representative applications are discussed: ground- and excited-state energy prediction, potential-energy surface mapping, geometry and transition-state optimization, spectroscopic property estimation (IR, UV–Vis, NMR, EPR), and reaction-dynamics scenarios where non-adiabatic effects and conical intersections dominate. Resource estimates and scaling analyses clarify current NISQ limitations qubit counts, circuit depth, shot complexity and delineate the roadmap to fault-tolerant QPE for chemical accuracy. We compare quantum approaches with classical baselines (DFT, CCSD (T), multireference methods), identifying domains where quantum methods already show promise (strong correlation, multi-reference dissociation, spin-state ordering) and where classical methods remain competitive. Finally, we highlight near-term industrial opportunities in drug design, catalysis, CO2 capture, and energy materials, and outline critical research directions: algorithmic reductions in measurement/precision cost, hardware improvements in fidelity and connectivity, scalable ansatz design, and integrated software stacks for reproducible hybrid simulations. Together, these developments indicate that while practical, large-scale quantum advantage for general chemistry remains future work, quantum technologies are rapidly maturing into powerful tools for targeted molecular problems that are intractable with existing classical techniques.
Strongly correlated electronic systems underpin a wide range of emerging quantum technologies, including solid-state defects for quantum information processing, molecular magnets, spin qubits, and quantum sensing platforms. Predictive computational design of these materials requires electronic structure methods capable of simultaneously describing strong electron correlation, excited-state phenomena, spin-dependent interactions, and environmental effects. While multireference wave function methods provide the necessary accuracy, their computational cost severely limits their application to realistic molecular and condensed-phase systems. This dissertation addresses this challenge through the development and application of quantum embedding and fragmentation methodologies that extend multireference electronic structure theory to increasingly complex quantum materials. The first part of this dissertation develops embedding-based approaches for describing optical properties of strongly correlated defects in extended solids. Complete Active Space Density Matrix Embedding Theory (CAS-DMET) and NEVPT2-DMET are applied to oxygen vacancy defects in magnesium oxide, where a systematic double-extrapolation protocol is introduced to approach both the non-embedding and thermodynamic limits. This framework enables quantitatively reliable calculations of absorption and emission energies while significantly reducing the computational cost of conventional multireference treatments of periodic systems. The second part extends embedding methodologies to the description of spin-dependent electronic structure. Density Matrix Embedding Pair-Density Functional Theory (DME-PDFT) is developed to recover dynamic electron correlation beyond the embedded active space, providing an efficient route for studying transition metal complexes and other strongly correlated molecular systems. Building upon these developments, CAS-DMET is further extended to investigate spin-phonon relaxation in molecular magnets and molecular crystals, demonstrating that quantum embedding can accurately describe spin dynamics and decoherence processes while substantially reducing computational cost. Beyond classical electronic structure calculations, this dissertation explores fragmentation strategies for hybrid quantum-classical algorithms through the development of efficient methodologies within the Localized Active Space Unitary Selective Coupled Cluster (LAS-USCC) framework. These developments improve the scalability of quantum chemistry algorithms for large active spaces and establish connections between embedding concepts and emerging quantum computing approaches. Finally, electronic structure calculations based on time-dependent density functional theory are employed to investigate fluorescent protein chromophores as potential biocompatible quantum sensors. These studies demonstrate how first-principles calculations can provide insight into spin-dependent properties in biologically relevant systems and expand the scope of computational approaches for quantum materials beyond traditional inorganic and molecular platforms. Collectively, the work presented in this dissertation establishes embedding and fragmentation as versatile frameworks for accurately describing the optical and spin properties of strongly correlated quantum systems across multiple length scales. By combining multireference electronic structure methods with physically motivated subsystem decompositions,these approaches bridge the gap between chemical accuracy and computational scalability, providing practical computational tools for the study and design of quantum materials relevant to quantum information science, molecular spintronics, and quantum sensing.
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He-H2+ complex for reference surfaces at three different levels of quantum chemistry and using recent comprehensive Feshbach resonance(FR) measurements. In all cases, the positions and intensities of peaks in the collision cross-section are improved. We find these observables to be mainly sensitive to the long-range part of the PES.
The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) to represent parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided, and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.