Research

Supported by

Development of Quantum Chemical Methods

Our keen interest lies in advancing quantum chemical methods, with a particular emphasis on simulating excited states. Quantum chemical methods serve as powerful tools for simulating molecular behavior at the smallest level, offering invaluable insights into complex phenomena.

Algebraic Diagrammatic Construction (ADC)

The ADC scheme for the polarization propagator is a Hermitian, wavefunction-based excited state method that allows for the ab initio calculation of excitation energies and excited state properties of molecular systems. For the end user, ADC schemes are so-called “black-box” methods in the sense that they are solely defined by their perturbation theoretical order. Loosely speaking, ADC(n) can be seen as an “MPn for excited states.” Nowadays, ADC(n) schemes are derived via the intermediate state representation (ISR) formalism, which is an equivalent route to the original formulation using propagator theory. A distinct advantage of the ISR approach is that it provides direct access to the excited state wavefunction and allows for the straightforward abstraction and generalization of the ADC scheme. Therefore, working equations for many different ADC flavors can be obtained following the ISR approach, e.g., IP-, EA-, DIP-, and DEA-ADC, providing access to electron-attached or detached excited states. This even includes those flavors for which no propagator can be formulated. Despite ADC being relatively computationally expensive, especially in comparison to time-dependent density functional theory, its distinct advantage is its capability to correctly describe charge-transfer states, doubly excited states, and Rydberg states. So far, we have derived ADC(n) schemes up to fourth order and implemented them in Q-Chem and ADC-connect. Since the complexity of the required matrix elements drastically increases with the growing perturbation theoretical order, the derivation of the ADC(n) working equations becomes effectivelyimpossible to do manually at fourth order. Therefore, we recently developed an automated equation generator that is able to derive and simplify the working equations for ADC schemes of arbitrary order and flavor.

Selected Publications

Molecular Response Properties in the ADC Framework

Molecular response properties indicate how molecules respond when they are exposed to external electric or magnetic fields. These properties have attracted increasing attention in recent years, underlining the growing importance of nonlinear optics across various high-tech fields. The rising interest in this area is due to the fact that comprehending these properties is of central importance for the development of functional materials. In addition, the study of optical processes sheds light on the electronic structure of the investigated system. Especially the study of higher-order response properties, such as static and dynamic hyperpolarizabilities, demands complex theoretical models. The development of efficient methods for calculating these properties represents a major challenge. For this purpose, the ADC framework has been expanded to calculate arbitrary response properties employing its ISR approach. Future endeavors will concentrate on enhancing efficiency and extending this approach to the description of larger molecular systems.

Selected Publications

Quantum Monte Carlo for ADC

Quantum Monte Carlo (QMC) methods are sophisticated stochastic techniques for studying many-electron systems, excelling in parallel computing and addressing many-body effects. In the recent years, QMC has also been used to overcome memory and processing constraints in established post-Hartree-Fock (pHF) methods by integrating them into projector quantum Monte Carlo (PQMC), enhancing efficiency for high-performance computing.

A prominent example in this category is Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which stands out as a highly effective tool for precise results in molecular and periodic systems beyond traditional methods. This innovative approach efficiently utilizes electronic system sparsity, relaxing memory requirements and enabling massively parallelization.

Our recent development, Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC), and its multi-state approach are massively parallel methods for correlated treatment of electronic excited states. QMCADC reformulates second-order ADC schemes within the PQMC framework, akin to FCIQMC. It has been demonstrated that QMCADC is a genuine stochastic solution to ADC and can accurately reproduce vertical excitation energies with a tunable accuracy, promising advancements in studying electronic excitations in larger systems.

Our goal is to establish QMCADC as a viable correlated method for electronic excited state calculations in large systems, surpassing conventional ADC capabilities. Additionally, we plan to adapt other ADC variants, such as ionization potential ADC (IP-ADC) and electron affinity ADC (EA-ADC), to the QMCADC framework, leveraging their similar structure of a Hermitian eigenvalue problem and comparable interaction matrices.

Selected Publications

Excitonic Renormalization

Fragmentation schemes were explored in many different flavors throughout the history of quantum chemistry. Prominent examples are symmetry-adapted perturbation-theory (SAPT), block correlated (BC) and active space decomposition (ASD) methods, as well as the very successful density-matrix renormalization-group (DMRG). However, BC and ASD methods require explicit orthogonalization for all fragments, SAPT requires tedious derivation for global anti-symmetry and lacks cooperative effects at low orders of perturbation theory, while DMRG lacks in its description of dynamical correlation.

A different strategy, proposed by Dutoi and Liu, is based on separating local and long-range correlation making use of a biorthogonal framework and the so-called fluctuation operator basis, shown in Figure 3. The approach allows for methods and basis sets of choice for each fragment separately, allowing for tailored treatment of local correlation. The resulting densities can be truncated to the “relevant” state space. The Hamiltonian is then build from the correlated densities of the single fragments and integrals in the atomic orbital basis between multiple fragments. This Hamiltonian provides a comparably small state space, which already includes intra-fragment correlation, as well as a second quantized formulation. Deriving a CCSD approach within this framework results in a formal scaling of N^3 with the system size and N^4 with the number of states per fragment, which is massively truncated.

The approach still has three major issues though, which we are working on. The first and most crucial one is, that the full overlap matrix between pairs of fragments has to be build up from the determinants in a brute force numerical approach, which takes one back to FCI cost. For this problem we came up with a solution, that scales N5 in CPU time and memory and recovers most of the FCI accuracy.

Selected Publications

Machine Learning for Orbital Free Density Functional Theory

Orbital-free density functional theory (OF-DFT) holds the promise of enabling cost-effective quantum mechanical calculations for exceptionally large systems, surpassing the capabilities of traditional QM methods. However, its potential has been hindered by the challenge of accurately computing kinetic energy solely as a functional of the electron density.

We set out to learn the kinetic energy functional from ground truth obtained from more expensive quantum mechanical methods such as Kohn-Sham DFT. We aim to develop a machine learning approach characterized by broad applicability and high accuracy, with a focus on generalization over molecular composition and geometry. The model must accurately handle a wide range of densities since it will be employed within an optimization algorithm to determine the ground state density. This introduces an additional challenge in generating training data for diverse densities, the majority of which do not originate from classical ground states.

Furthermore, we hope to ensure its accuracy and generalizability by incorporating known physical constraints into the model, such as the invariance of the kinetic energy with respect to translations and rotations of the molecule.

Selected Publications

Computational Investigation of Structure-Property Relations in Organic Chemistry

The development of novel organic functional materials is of great interest for application as organic semiconductors and photoactive compounds. To guide this development, we are investigating the molecular and spectroscopic properties of organic compounds at the electronic structure level and how they relate to molecular structure.

Organic Functional Materials

The development of novel organic functional materials is of great interest for application as organic semiconductors and photoactive compounds. N-heteropolycycles have proven to be promising candidates for organic electron-transporting (n-channel) semiconductors, because of the change of their electronic properties through the introduction of nitrogen atoms into the π-conjugated backbone of polycyclic aromatic hydrocarbons. One objective is to gain a deeper insight into the molecular and spectroscopic properties of N-heteropolycycles at the electronic structure level and how they relate to molecular structure, with the ultimate goal of enabling the design of novel compounds with tailored properties. In cooperation with experimental groups various N-heteropolycycles are investigated regarding project-specific questions and properties.

Selected Publications

Molecular Solar Thermals/Photoswitches

In general, molecular photoswitches are systems that upon excitation by light undergo chemical changes forming a new meta-stable state storing the absorbed energy. Their properties, such as absorption behavior, energy storage, energy release behavior, quantum efficiencies, stability and more are challenging to predict. Therefore, we apply self-developed and existing state-of-the-art quantum chemical methods for the investigation of such systems. With the gained insights we aim to guide synthesis efforts and assist spectroscopic investigations. Especially for the application within molecular solar thermal (MOST) storage systems, this interdisciplinary approach is necessary. These compounds are single molecules capable of storing solar energy and converting it to heat on demand. We are determined to make a strong contribution to renewable energy generation as well as energy storage development.

Selected Publications

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