Development and Application of Hermitian Methods for Molecular Properties and Excited Electronic States

In many parts of physics, chemistry, biology, or material science, excited electronic states, accessible via the interaction of atoms or molecules with electromagnetic radiation, play an essential role. Experimental spectra, however, generally provide only indirect information on molecular structure and dynamics. Thus, a theoretical description of excitation energies and transition strengths is crucial for a comprehensive understanding of light-induced processes. In this dissertation, the theory, implementation, and application of several Hermitian methods to calculate the properties mentioned above are described. If excitation energies are obtained by diagonalization of a non-Hermitian secular matrix, both left and right eigenvectors need to be calculated to obtain spectral intensities and other properties. In this case, the eigenvectors are not orthogonal to each other, and the energy may become complex. Hermiticity is thus a very desirable property since none of the aforementioned problems occurs. Thus, several approaches based on the algebraic-diagrammatic construction (ADC) scheme, as well as the related unitary coupled-cluster (UCC) method, are presented. Within these methods, one-electron properties such as dipole moments are available via the so-called intermediate state representation (ISR) approach, which corresponds to an expectation value of the respective one-electron operator with the wave function. The ISR formalism is also used to derive explicit working equations for the second-order ADC scheme, which is based on a ground state described by Møller–Plesset (MP) perturbation theory. This implies that ADC inherits all weaknesses from the underlying MP model. For the ADC(2) scheme, merely the first-order MP wave function is required, which contains only doubly-excited determinants for a Hartree–Fock reference. Due to the form of the first-order doubles amplitudes, several cancellations occur in the singles block of the ADC(2) matrix. In order to remedy the breakdown of MP2, the first-order doubles amplitudes from MP are replaced by the ones obtained from a coupled-cluster (CC) calculation, which are formally correct through infinite order. The resulting schemes, referred to as CC-ADC(2), are applied to several sets of small to medium-sized molecular systems, where generally minor improvements in excitation energies compared to the standard ADC(2) scheme can be observed. For the ozone molecule, which is known to be a difficult test case for quantum-chemical methods, the experimental first excitation energy is 1.6 eV; standard ADC(2) is far off with 2.14 eV, and CCD-ADC(2) yields 1.59 eV. Excited-state potential energy curves along the dissociation of the nitrogen molecule calculated with ADC(2) break down at around 2 Å due to the failure of MP2. The CCD-ADC(2) curves remain reasonable up to about 3.5 Å. The CC-ADC(2) methods are successively extended to the calculation of static dipole polarizabilities. It is shown that the correlation amplitudes play a more important role in the modified transition moments than in the ADC secular matrix itself, and consistent improvement is obtained for static polarizabilities with the CC-ADC schemes compared to standard ADC, particularly for aromatic systems like benzene or pyridine, which had proven difficult cases for standard ADC. Specifically, the CC-ADC(2) schemes yield significantly better results than the ADC(3/2) scheme, at a computational cost amounting to only 1% of the latter. The ISR derivation can also be carried out with a CC wave function correct through first order instead of the MP one. However, having converged CCD amplitudes instead of the first-order MP ones, the aforementioned cancellations in the second-order singles block do not occur. Hence, the final matrix elements differ between CCD-ADC(2) and this scheme referred to as CCD-ISR(2). As the expansion of the UCC similarity-transformed Hamiltonian does not truncate naturally, it needs to be truncated manually, usually by using arguments from MP perturbation theory. The UCC2 doubles amplitudes correspond to those from LCCD, but the secular matrix elements depend on the treatment of the similarity-transformed Hamiltonian is treated. By employing the Baker–Campbell–Hausdorff expansion, the second-order singles block is equivalent to CCD-ISR(2), but by employing the Bernoulli expansion, the matrix elements are equivalent to CCD-ADC(2), with differences only in the correlation amplitudes. In a strict perturbation-theoretical framework, all methods turn out to be identical. All different Hermitian second-order methods have been implemented and tested on a set of small molecules, where it turned out that the differences in excitation energies between the methods are small whenever the systems are well described by means of perturbation theory. The Bernoulli UCC scheme is further extended to third order, where excitation energies and oscillator strengths on medium-sized organic molecules as well as ground- and excited-state dipole moments are reported for the first time. While vertical excitation energies of the UCC3 scheme are similar to those obtained with ADC(3), significant improvements can be observed for the dipole moments in the ground and excited states. Furthermore, this UCC scheme is applied to the electron propagator, and ionization potentials of the IP-UCC2 and IP-UCC3 schemes of selected amino acids are reported for the first time. Apart from expectation values, molecular properties can be calculated as derivatives of the energy with respect to a perturbation connected to the observable. The two approaches are only equivalent if the Hellmann–Feynman theorem is fulfilled. By using explicit working equations, the relationship between the two approaches is investigated with a focus on orbital relaxation for all standard quantum-chemical methods, in particular MP and ADC. It is shown that for MP2 the expectation value is very close to the orbital-relaxed property. In contrast, for ADC(1) the expectation value includes no orbital relaxation and for ADC(2) only a small fraction. With ADC(3) eigenvectors, on the other hand, the ISR gets closer to the relaxed values, but only for singly-excited states. Numerical investigations underline all the theoretical predictions

Software for the frontiers of quantum chemistry:An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design

Simulation of Vacuum UV Absorption and Electronic Circular Dichroism Spectra of Methyl Oxirane: The Role of Vibrational Effects

SFX Get it!(opens in a new window)|View at Publisher| Export | Download | Add to List | More... Journal of Chemical Theory and Computation Volume 12, Issue 6, 14 June 2016, Pages 2820-2833 Simulation of Vacuum UV Absorption and Electronic Circular Dichroism Spectra of Methyl Oxirane: The Role of Vibrational Effects (Article) Hodecker, M.ab, Biczysko, M.c , Dreuw, A.b, Barone, V.a a Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italy b Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, Germany c International Centre for Quantum and Molecular Structures, College of Sciences, Shanghai University, 99 Shangda Road, Shanghai, China View additional affiliations View references (103) Abstract Vibrationally resolved one-photon absorption and electronic circular dichroism spectra of (R)-methyl oxirane were calculated with different electronic and vibronic models selecting, through an analysis of the convergence of the results, the best compromise between reliability and computational cost. Linear-response TD-DFT/CAM-B3LYP/SNST electronic computations in conjunction with the simple vertical gradient vibronic model were chosen and employed for systematic comparison with the available experimental data. Remarkable agreement between simulated and experimental spectra was achieved for both one-photon absorption and circular dichroism concerning peak positions, relative intensities, and general spectral shapes considering the computational efficiency of the chosen theoretical approach. The significant improvement of the results with respect to smearing of vertical electronic transitions by phenomenological Gaussian functions and the possible inclusion of solvent effects by polarizable continuum models at a negligible additional cost paves the route toward the simulation and analysis of spectral shapes of complex molecular systems in their natural environment. \ua9 2016 American Chemical Society

eChem: A notebook exploration of quantum chemistry

The eChem project features an e-book published as a web page https://doi.org/10.30746/978-91-988114-0-7), collecting a repository of Jupyter notebooks developed for the dual purpose of explaining and exploring the theory underlying computational chemistry in a highly interactive manner as well as providing a tutorial-based presentation of the complex workflows needed to simulate embedded molecular systems of real biochemical and/or technical interest. For students ranging from beginners to advanced users, the eChem book is well suited for self-directed learning, but workshops led by experienced instructors and targeting student bodies with specific needs and interests can readily be formed from its components. This has been done by using eChem as the base for a workshop directed towards graduate students learning the theory and practises of quantum chemistry, resulting in very positive assessment of the interactive nature of this framework. The members of the eChem team are engaged in both education and research and as a mirroring activity, we develop the open-source software upon which this e-book is predominantly based. The overarching vision and goal of our work is to provide a science- and education-enabling software platform for quantum molecular modeling on contemporary and future high-performance computing systems, and to document the resulting development and workflows in the eChem book

Metabolomic Profiles for Primary Progressive Multiple Sclerosis Stratification and Disease Course Monitoring

Primary progressive multiple sclerosis (PPMS) shows a highly variable disease progression with poor prognosis and a characteristic accumulation of disabilities in patients. These hallmarks of PPMS make it difficult to diagnose and currently impossible to efficiently treat. This study aimed to identify plasma metabolite profiles that allow diagnosis of PPMS and its differentiation from the relapsing-remitting subtype (RRMS), primary neurodegenerative disease (Parkinson’s disease, PD), and healthy controls (HCs) and that significantly change during the disease course and could serve as surrogate markers of multiple sclerosis (MS)-associated neurodegeneration over time. We applied untargeted high-resolution metabolomics to plasma samples to identify PPMS-specific signatures, validated our findings in independent sex- and age-matched PPMS and HC cohorts and built discriminatory models by partial least square discriminant analysis (PLS-DA). This signature was compared to sex- and age-matched RRMS patients, to patients with PD and HC. Finally, we investigated these metabolites in a longitudinal cohort of PPMS patients over a 24-month period. PLS-DA yielded predictive models for classification along with a set of 20 PPMS-specific informative metabolite markers. These metabolites suggest disease-specific alterations in glycerophospholipid and linoleic acid pathways. Notably, the glycerophospholipid LysoPC(20:0) significantly decreased during the observation period. These findings show potential for diagnosis and disease course monitoring, and might serve as biomarkers to assess treatment efficacy in future clinical trials for neuroprotective MS therapies

Metabolomic Profiles for Primary Progressive Multiple Sclerosis Stratification and Disease Course Monitoring

Primary progressive multiple sclerosis (PPMS) shows a highly variable disease progression with poor prognosis and a characteristic accumulation of disabilities in patients. These hallmarks of PPMS make it difficult to diagnose and currently impossible to efficiently treat. This study aimed to identify plasma metabolite profiles that allow diagnosis of PPMS and its differentiation from the relapsing-remitting subtype (RRMS), primary neurodegenerative disease (Parkinson’s disease, PD), and healthy controls (HCs) and that significantly change during the disease course and could serve as surrogate markers of multiple sclerosis (MS)-associated neurodegeneration over time. We applied untargeted high-resolution metabolomics to plasma samples to identify PPMS-specific signatures, validated our findings in independent sex- and age-matched PPMS and HC cohorts and built discriminatory models by partial least square discriminant analysis (PLS-DA). This signature was compared to sex- and age-matched RRMS patients, to patients with PD and HC. Finally, we investigated these metabolites in a longitudinal cohort of PPMS patients over a 24-month period. PLS-DA yielded predictive models for classification along with a set of 20 PPMS-specific informative metabolite markers. These metabolites suggest disease-specific alterations in glycerophospholipid and linoleic acid pathways. Notably, the glycerophospholipid LysoPC(20:0) significantly decreased during the observation period. These findings show potential for diagnosis and disease course monitoring, and might serve as biomarkers to assess treatment efficacy in future clinical trials for neuroprotective MS therapies

Data_Sheet_1_Metabolomic Profiles for Primary Progressive Multiple Sclerosis Stratification and Disease Course Monitoring.docx

<p>Primary progressive multiple sclerosis (PPMS) shows a highly variable disease progression with poor prognosis and a characteristic accumulation of disabilities in patients. These hallmarks of PPMS make it difficult to diagnose and currently impossible to efficiently treat. This study aimed to identify plasma metabolite profiles that allow diagnosis of PPMS and its differentiation from the relapsing-remitting subtype (RRMS), primary neurodegenerative disease (Parkinson’s disease, PD), and healthy controls (HCs) and that significantly change during the disease course and could serve as surrogate markers of multiple sclerosis (MS)-associated neurodegeneration over time. We applied untargeted high-resolution metabolomics to plasma samples to identify PPMS-specific signatures, validated our findings in independent sex- and age-matched PPMS and HC cohorts and built discriminatory models by partial least square discriminant analysis (PLS-DA). This signature was compared to sex- and age-matched RRMS patients, to patients with PD and HC. Finally, we investigated these metabolites in a longitudinal cohort of PPMS patients over a 24-month period. PLS-DA yielded predictive models for classification along with a set of 20 PPMS-specific informative metabolite markers. These metabolites suggest disease-specific alterations in glycerophospholipid and linoleic acid pathways. Notably, the glycerophospholipid LysoPC(20:0) significantly decreased during the observation period. These findings show potential for diagnosis and disease course monitoring, and might serve as biomarkers to assess treatment efficacy in future clinical trials for neuroprotective MS therapies.</p

Data_Sheet_3_Metabolomic Profiles for Primary Progressive Multiple Sclerosis Stratification and Disease Course Monitoring.xlsx

<p>Primary progressive multiple sclerosis (PPMS) shows a highly variable disease progression with poor prognosis and a characteristic accumulation of disabilities in patients. These hallmarks of PPMS make it difficult to diagnose and currently impossible to efficiently treat. This study aimed to identify plasma metabolite profiles that allow diagnosis of PPMS and its differentiation from the relapsing-remitting subtype (RRMS), primary neurodegenerative disease (Parkinson’s disease, PD), and healthy controls (HCs) and that significantly change during the disease course and could serve as surrogate markers of multiple sclerosis (MS)-associated neurodegeneration over time. We applied untargeted high-resolution metabolomics to plasma samples to identify PPMS-specific signatures, validated our findings in independent sex- and age-matched PPMS and HC cohorts and built discriminatory models by partial least square discriminant analysis (PLS-DA). This signature was compared to sex- and age-matched RRMS patients, to patients with PD and HC. Finally, we investigated these metabolites in a longitudinal cohort of PPMS patients over a 24-month period. PLS-DA yielded predictive models for classification along with a set of 20 PPMS-specific informative metabolite markers. These metabolites suggest disease-specific alterations in glycerophospholipid and linoleic acid pathways. Notably, the glycerophospholipid LysoPC(20:0) significantly decreased during the observation period. These findings show potential for diagnosis and disease course monitoring, and might serve as biomarkers to assess treatment efficacy in future clinical trials for neuroprotective MS therapies.</p