The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview

The Generality of the GUGA MRCI Approach in COLUMBUS for Treating Complex Quantum Chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calcu- lations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of dia- batization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully vari- ational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on stan- dard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview

Uncertainty Estimates for Theoretical Atomic and Molecular Data

Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We concentrate on model uncertainties due to approximations to the fundamental many-body quantum mechanical equations and we aim to provide guidelines to estimate uncertainties as a routine part of computations of data for structure and scattering.Comment: 65 pages, 18 Figures, 3 Tables. J. Phys. D: Appl. Phys. Final accepted versio

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions

Development and Validation of the REMP and OO-REMP Hybrid Perturbation Theories

In dieser Arbeit werden die hybriden Störungstheorien REMP und OO-REMP zur Be- rechnung der elektronischen Korrelationsenergie von Atomen und Molekülen eingeführt und validiert. Es handelt sich dabei um quantenchemische Methoden im Formalismus der Rayleigh-Schrödinger-Störungstheorie, für die hier die Energie 2. Ordnung untersucht wird. Basierend auf den Partitionierungen der Møller-Plesset- (MP) und der Anregungsgrader- haltenden Störungstheorie (Retaining the excitation Degree=RE) wird ein ungestörter Hamiltonoperator mit zugehörigem Störoperator definiert, der sich aus einer gewichteten Summe der vorgenannten Methoden zusammensetzt, wodurch die REMP-Methode defi- niert ist. Die neuartige Partitionierung nutzt komplementäre Fehler der zugrunde liegenden Methoden zur internen Fehlerkompensation. In dieser Arbeit werden Energien bis zur 2. Ordnung der Störungstheorie untersucht. Es wird gezeigt, dass die REMP-Partitionierung des elektronischen Hamiltonoperators zu systematisch besseren Ergebnissen führt als jede der Einzelmethoden allein, wobei die Parametrisierung der Mischung universell und praktisch systemunabhängig ist. Dies wird am Beispiel unterschiedlicher Typen von Reaktionsenergien und Gleichgewichtsstrukturen, Schwingungswellenzahlen und elektri- schen Dipolmomenten kleiner Moleküle demonstriert. Es wird außerdem ein variationelles Energiefunktional definiert, das auf der Hybridpartitionierung basiert. Dabei wird die Form der besetzen Molekülorbitale variiert und so optimiert, dass die Gesamtenergie minimal wird. Die Minimierung dieses Funktionals bezüglich aller variationellen Para- meter liefert Ergebnisse, die die der kanonischen Methode systematisch übertreffen. Die vollständig variationelle Methode zeichnet sich zudem durch hervorragende rechnerische Effizienz bei der Vorhersage molekularer Eigeschaften aus. Es wird gezeigt, dass insbeson- dere die vollständig variationelle, orbitaloptimierte Variante (OO-REMP) den Kriterien allgemein anwendbarer Quantenchemiemethoden genügt und hochgenaue Ergebnisse produziert. Die Validierungen legen nahe, dass OO-REMP für single-reference-Systeme für die meisten Thermochmie-Testsätze chemische Genauigkeit erreicht (Root mean square-Fehler ⩽1 kcal mol−1 ). Die neu entwickelten Methoden wurden in ein quelloffenes Quantenchemieprogramm implementiert und stehen nun jedermann zur Verfügung.In this work, the hybrid perturbation theories REMP and OO-REMP for the calculation of electronic correlation energies of atoms and molecules are introduced and validated. These are quantum chemical methods in the framework of Rayleigh-Schrödinger perturbation theory, whose second order energy is investigated here. Based on the partitionings of the Møller-Plesset (MP) and the Retaining the Excitation Degree (RE) perturbation theory, an unperturbed Hamiltonian with a corresponding perturbation operator is defined, which is a weighted sum of the previous methods, thereby defining the REMP method. The novel partitioning has the property to exploit complementary errors of the parent methods for internal error compensation. In this work, energies up to 2nd order in perturbation theory are investigated. It is shown that the REMP partitioning of the electronic Hamiltonian leads to systematically better results than each of the original methods, with the important aspect that the parameterization of the mixture is universal and practically independent of the system considered. This is demonstrated with the example various types of reaction energies and equilibrium structures, vibrational wavenumbers, and electric dipole moments of small molecules. Furthermore, a variational energy functional based on the hybrid partitioning is defined. Here, the shape of the occupied molecular orbitals is varied and optimized such, that the total energy becomes minimal. The minimization of this functional with respect to all variational parameters provides results which systematically surpass those of the canonical method. The fully variational method is furthermore characterized by outstanding computational efficiency regarding the prediction of molecular properties. It is shown that especially the fully variational, orbital-optimized variant suffices the criteria of a generally applicable quantum chemical method and does produce highly accurate results. The validations imply that for single-reference systems OO-REMP reaches chemical accuracy (root mean square error ⩽1 kcal mol−1) for most of the thermodynamic test sets. The newly developed methods were implemented in an open-source quantum chemistry program package and are now available to everyone

Variational calculations of rotation-vibration spectra for small molecules of astrophysical interest

Variational calculations of rotation-vibration spectra are presented for a range of four- and five-atom molecules of atmospheric and astrophysical importance. Using state-of-the-art electronic structure methods, new nine-dimensional potential energy and dipole moment surfaces are constructed for methyl chloride (CH3Cl), silane (SiH4), and methane (CH4). The respective surfaces are rigorously evaluated against high-resolution spectroscopic data from a variety of experimental sources. The ab initio potential energy surfaces represent some of the most accurate to date, whilst intensity simulations utilizing the dipole moment surfaces show good agreement with experiment. A novel application of rotation-vibration computations is introduced to investigate the sensitivity of spectral lines to a possible space-time variation of the proton-to-electron mass ratio μ. The approach relies on finding the mass dependence of the computed energy levels and is only possible because of the remarkable accuracy of variational calculations. Highly sensitive transitions are uncovered for ammonia (NH3) and the hydronium cation (H3O+) which could lead to a tighter constraint on a varying μ. An advantage of the variational approach is that Einstein A coefficients can be determined to help guide future laboratory and astronomical observations. This thesis demonstrates the current capabilities of variational calculations of rotation-vibration spectra and highlights the challenges faced by the field

Development and Application of Efficient Methods for the Computation of Electronic Spectra of Large Systems

In this thesis, an efficient procedure to compute electronic excitation spectra of molecular systems is presented, focusing particularly on the computation of electronic circular dichroism (ECD) spectra. ECD spectroscopy is commonly used to distinguish between the two enantiomers of a chiral compound. Due to a strong sensitivity to the three-dimensional structure, reliable simulation of ECD spectra of solvated molecules by quantum chemical methods requires the knowledge of the relevant conformers along with the corresponding ECD signals (i.e., the individual transition intensities and energies) and Boltzmann populations. The latter point can be addressed by an established thermochemical protocol. It combines electronic energies computed in gas phase by dispersion-corrected density functional theory (DFT-D) with nuclear ro-vibrational and solvation contributions to yield the free energies in solution. This model is applied to study the association of two intermolecular frustrated Lewis pairs (FLPs). Though this case study does not aim at computing an ECD spectrum, it provides insight on whether such a scheme could also be suited to rank conformers in solution. Comparison to high-level reference methods and partially available experimental data suggests that the largest uncertainty can be attributed to the implicit solvation model. The errors for different dimer arrangements, however, appear to be within the order of 1 kcal mol-1, which is encouraging for the pursued computation of conformer free energies. In combination with a quadruple-ζ basis set, hybrid DFT-D methods like the PW6B95-D3 are almost converged with respect to a complete basis and provide satisfactory results for the electronic energy contribution. Hence, they are recommended choices for the final electronic structure level to rank different conformers in routine calculations. The major part of this thesis deals with the development and application of cost-efficient excited state methods. The current state-of-the-art to compute ECD spectra for systems with roughly 100 atoms is the time-dependent density functional theory (TD-DFT) approach. Based on the latter, the simplified TD-DFT (sTD-DFT) method is developed. The excited state treatment is accelerated by at least three orders of magnitude, resulting from semiempirically approximated two-electron integrals and a significant reduction of the involved matrix dimensions. The introduced approximations are in line with the ones in the previously presented simplified Tamm-Dancoff approximated TD-DFT (sTDA-DFT). It is shown that the sTD-DFT and the sTDA-DFT approaches provide roughly the same accuracy for vertical excitation energies, as well as absorption and ECD spectra, as their parental schemes, i.e., TD-DFT and Tamm-Dancoff approximated TD-DFT (TDA-DFT), respectively. Thus, sTD-DFT is an efficient approach that is suitable for the computation of ECD spectra. Furthermore, sTD-DFT calculations conducted on "snapshots" from molecular dynamics (MD) simulations offer an appealing way to effectively incorporate vibronic effects without a quantum mechanical (QM) treatment of the nuclei. Such a treatment is exemplified for [16]helicene (102 atoms) and a di-substituted derivative (164 atoms). While the feasibility of applying sTDA-DFT to very large systems is demonstrated for two palladium(II) metallosupramolecular spheres (822 and 1644 atoms, respectively), it is also shown that this method produces ECD spectra of incorrect sign in the origin-independent dipole velocity formalism for extended π-systems. This behavior is due to the Tamm-Dancoff approximation (TDA) and, therefore, it is also present in TDA-DFT and the related configuration interaction singles (CIS) approach. Based on the insights obtained from this study, the A+B/2 correction is developed, which corrects the (simplified) TDA eigenvectors affording origin-independent dipole velocity ECD spectra of roughly (s)TD-DFT quality, while retaining the lower computational cost of the (s)TDA excited state treatment. Combination with a newly developed, purpose-specific extended tight-binding procedure for the ground state yields the ultra-fast sTDA-xTB approach. Due to different adjustments of the atomic orbital basis and the tight-binding Hamiltonian, the method is on a par with TDA-PBE0/def2-SV(P) for vertical excitation energies. The entire computation of an ECD spectrum ( The last part of this thesis reports on another purpose-specific extended tight-binding scheme, GFN-xTB, which provides molecular geometries, harmonic vibrational frequencies, and non-covalent interaction energies with comparable or better accuracy than existing semiempirical methods. Since parameters are available for all elements with Z ≤ 86, the method offers great potential to sample the conformational space of almost arbitrary molecules with up to a few hundred atoms. In combination with the ultra-fast sTDA-xTB approach, ECD spectra can be computed in an almost "black box" manner, e.g., by computing spectra on MD snapshots. Together with the established thermochemistry protocol mentioned above, the newly developed architecture sets the stage for a fully automatic multi-level ECD procedure to be developed in the near future.Diese Dissertation stellt einen effizienten Ansatz zur Berechnung von elektronischen Anregungsspektren molekularer Systeme vor, wobei der besondere Fokus auf der Berechnung von elektronischen Circulardichroismus-(ECD-)Spektren liegt. Die ECD-Spektroskopie wird typischerweise verwendet, um zwischen den beiden Enantiomeren einer chiralen Verbindung zu unterscheiden. Aufgrund der hohen Sensibilität für die räumliche Struktur des Moleküls wird zur zuverlässigen Simulation von ECD-Spektren die Kenntnis der relevanten Konformere inklusive ihrer Boltzmann-Populationen und der jeweiligen ECD-Signale (d.h. deren energetische Lage und Intensitäten) benötigt. Die Populationen können mithilfe eines literaturbekannten Thermochemieprotokolls unter Verwendung der dispersionskorrigierten Dichtefunktionaltheorie (DFT-D) näherungsweise berechnet werden. In der vorliegenden Arbeit wird dieses Modell verwendet, um die Komplexbildung von zwei intermolekularen frustrierten Lewispaaren (FLPs) zu untersuchen. Obwohl diese Fallstudie keine Berechnung eines ECD-Spektrums zum Ziel hat, geben die gewonnenen Erkenntnisse durchaus Aufschluss darüber, ob sich der gewählte Ansatz auch dazu eignet, die Populationen verschiedener Konformere zu bestimmen. Der Vergleich mit hochwertigen Vergleichsrechnungen auf der einen und mit zum Teil verfügbaren experimentellen Daten auf der anderen Seite legt nahe, dass der größte Unsicherheitsfaktor in den Solvatationsbeiträgen vorliegt, welche mithilfe eines impliziten Lösungsmittelmodells bestimmt werden. Allerdings liegen deren geschätzte Fehler für unterschiedliche räumliche Anordnungen des Komplexes, d.h. bei einer gleichbleibenden Systemgröße von ca. 50-100 Atomen, lediglich bei etwa 1 kcal mol-1. Für die Berechnung von freien konformellen Enthalpien ist mit ähnlich großen Fehlern zu rechnen. Kombiniert mit Quadruple-ζ-Basissätzen weisen Hybrid-DFT-Methoden bereits nahezu konvergierte elektronische Energien auf und können bei gleichzeitiger Verwendung einer Dispersionskorrektur relativ genaue Gasphasenenergiebeiträge (so z.B. PW6B95-D3) zu den freien Enthalpien in Lösung beitragen. Der Großteil dieser Dissertation beschäftigt sich mit der Entwicklung und Anwendung von kosteneffizienten Methoden zur Berechnung angeregter Zustände. Die gegenwärtig am häufigsten verwendete Methode zur Berechnung von ECD-Spektren ist die zeitabhängige Dichtefunktionaltheorie (TD-DFT). Von dieser ausgehend wird die vereinfachte TD-DFT Methode (sTD-DFT) entwickelt. Aufgrund der semiempirischen Näherung der Zweielektronenintegrale und der deutlichen Reduzierung der relevanten Matrixdimensionen wird die Berechnung der angeregten Zustände um mindestens drei Größenordnungen beschleunigt. Diese Näherungen sind konsistent zu jenen, die bereits in dem vereinfachten Tamm-Dancoff-genäherten TD-DFT (sTDA-DFT) Ansatz eigeführt wurden. Im Vergleich zu den Ausgangsmethoden, also TD-DFT und seiner Tamm-Dancoff-Näherung (TDA-DFT), ist weder eine signifikante Beeinträchtigung der senkrechten Anregungsenergien noch eine Verschlechterung der Absorptions- und ECD-Intensitäten bemerkbar. Insbesondere die sTD-DFT Methode eignet sich zur effizienten und zuverlässigen Berechnung von ECD-Spektren. Die Effizienz der sTD-DFT Methode ermöglicht unter anderem die Berechnung von Spektren auf Nichtminimumsstrukturen, die aus einer Molekulardynamik-(MD)-Simulation stammen. Somit können vibronische Effekte näherungsweise erfasst werden, ohne dass ein quantenmechanischer (QM) Ansatz für die Kerne verwendet werden muss. Exemplarisch wird dieses Verfahren für das [16]Helicen (102 Atome) und einem disubstituierten Derivat (164 Atome) angewandt. Die Anwendbarkeit der sTDA-DFT Methode auf sehr große Systeme wird am Beispiel von zwei Palladium(II)-metallosupramolekularen Komplexen (822 und 1644 Atome) verdeutlicht, doch zeigt eine weitere Studie, dass Tamm-Dancoff-genäherte (TDA) Methoden für die ECD Spektren von ausgedehnten, delokalisierten π-Systemen im Impulsformalismus das falsche Vorzeichen liefern. Gleiches gilt für den verwandten Konfigurationswechselwirkungs-Ansatz mit Einfachanregungen (CIS). Basierend auf den Erkenntnissen dieser Studie ist es gelungen, die sogenannte A+B/2-Näherung zu entwickeln, welche die entsprechenden Fehler in den TDA Eigenvektoren behebt, ohne die Kosten der Methode sichtlich zu erhöhen. Durch die Kombination des so korrigierten vereinfachten TDA-Ansatzes mit einer speziell optimierten semiempirischen Tight-Binding-Methode für den Grundzustand wird die äußerst schnelle sTDA-xTB-Methode erhalten. Aufgrund verschiedener Modifikationen der Atomorbitalbasis und des Tight-Binding-Potentials erreicht diese Methode eine ähnliche Genauigkeit für senkrechte Anregungsenergien wie z.B. eine DFT-basierende Rechnung auf TDA-PBE0/def2-SV(P) Niveau. Die beachtliche Effizienz der Methode wird im Vergleich zum bereits effizienten sTD-BHLYP/def2-SV(P) Ansatz für das [16]Helicen (alle Anregungen bis 9 eV) deutlich: Während letzterer Ansatz etwas mehr als eine Stunde Rechenzeit benötigt, ist das ECD-Spektrum mit sTDA-xTB bereits nach 10 s verfügbar. Da die Parametrisierung nahezu das gesamte Periodensystem abdeckt, werden Standardrechnungen von Spektren großer Systeme (mit ca. 1000 Atomen) ermöglicht, selbst wenn mehrere Konformere berücksichtigt werden. Im letzten Teil der Arbeit wird eine weitere spezialisierte Tight-Binding-Methode vorgestellt (GFN-xTB), die wiederum auf die Berechnung von Geometrien, harmonischen Frequenzen und nichtkovalenten Wechselwirkungen ausgelegt ist und hierfür bessere Ergebnisse liefert als vergleichbare semiempirische Methoden. Die Verfügbarkeit von Parametern für alle Elemente mit Z ≤ 86 ermöglicht das Absuchen des konformellen Raums für unterschiedliche Systeme mit wenigen hundert Atomen. Zusammen mit sTDA-xTB sind in kürzester Zeit Berechnungen von Sprektren z.B. entlang von MD-Trajektorien möglich. Vereint mit den bereits existierenden Thermochemieprotokollen sind somit die ersten Voraussetzungen für eine völlig automatische Prozedur zur Berechnung von ECD-Spektren geschaffen worden

Computational strategies for the accurate thermochemistry and kinetics of gas-phase reactions

This PhD thesis focuses on the theoretical and computational modeling of gas phase chemical reactions, with a particular emphasis on astrophysical and atmospherical ones. The ability to accurately determine the rate coefficients of key elementary reactions is deeply connected to the accurate determination of geometrical parameters, vibrational frequencies and, even more importantly, electronic energies and zeropoint energy corrections of reactants, transition states, intermediates and products involved in the chemical reaction, together with a suitable choice of the statistical approach for the rate computation (i.e. the proper transition state theory model). The main factor limiting the accuracy of this process is the computational time requested to reach meaningful results (i.e. reaching subchemical accuracy below 1 kJ mol−1), which increases dramatically with the the size of the system under investigation. For small-sized systems, several nonempirical procedures have been developed and presented in the literature. However, for larger systems the well-known model chemistries are far from being parameter-free since they include some empirical parameters and employ geometries which are not fully reliable for transition states and noncovalent complexes possibly ruling the entrance channels. Based on these premises, this dissertation has been focused on the development of new “cheap” composite schemes, entirely based on the frozen core coupled cluster ansatz including single, double, and (perturbative) triple excitation calculations in conjunction with a triple-zeta quality basis set, including the contributions due to the extrapolation to the complete basis set limit and core-valence effects using second-order Møller- Plesset perturbation theory. For the first time the “cheap” scheme has been extended to explicitly-correlated methods, which have an improved performance with respect to their conventional counterparts. Benchmarks with different sets of state of the art energy barriers, interaction energies and geometrical parameters spanning a wide range of values show that, in the absence of strong multireference contributions, the proposed models outperforms the most well-known model chemistries, reaching a subchemical accuracy without any empirical parameter and with affordable computer times. Besides the composite schemes development efforts, a robust protocol for disclosing the thermochemistry and kinetics of reactions of atmospheric and astrophysical interest, rooted in the so-called ab initio-transition-state-theory-based master equation approach have been thoroughly investigated and validated