Model Space Diabatization for Quantum Photochemistry

Diabatization is a procedure that transforms multiple adiabatic electronic states to a new representation in which the potential energy surfaces and the couplings between states due to the electronic Hamiltonian operator are smooth, and the couplings due to nuclear momentum are negligible. In this work, we propose a simple and general diabatization strategy, called model space diabatization, that is applicable to multi-configuration quasidegenerateperturbation theory (MC-QDPT) or its extended version (XMC-QDPT). An advantage over previous diabatization schemes is that dynamical correlation calculations are based on standard post-multi-configurational self-consistent field (MCSCF) multi-state methods even though the diabatization is based on state-averaged MCSCF results. The strategy is illustrated here by applications to LiH, LiF, and thioanisole, with the fourfold-way diabatization and XMC-QDPT, and the results illustrate its validity

Electronic structure calculations on extended metal atom chains. Insights on structural, magnetic and transport properties

En aquest treball, es van utilitzar diferents mètodes computacionals per estudiar les propietats de cadenes esteses de metalls de transició (EMACs en anglès). Es va simular la flexibilitat estructural de cadenes de tres àtoms de crom, amb CASSCF/CASPT2 i es van identificar estructures simètriques i asimètriques en un entorn de baixa energia. Basats en aquests resultats, vam realitzar dinàmiques moleculars de primers principis (AIMD) per entendre l'efecte de l'energia tèrmica i com aquesta modifica la proporció d'estructures. També es van estudiar els enllaços metall-metall en compostos de crom, utilitzant el model d'ordre d'enllaç efectiu (EBO) amb els números d'ocupació naturals de la funció d'ona CASSCF. Es van calcular constants d'acoblament magnètic per a compostos bimetàl·lics i EMACs de níquel mitjançant dues estratègies. MC-PT2 amb espai actiu mínim utilitzant orbitals moleculars millorats a partir d'un càlcul d'estats-mitjanats, i es va utilitzar un mètode nou (MCPDFT) per al magnetisme de EMACs grans, que ha mostrat bons resultats en el compost de cinc níquels. Finalment, estudiem propietats del transport d'electrons per dos EMACs de ruteni. Proposem l'ús d'un elèctrode gate metàl·lic per modular els nivells moleculars dels compostos i obtenir espècies redox actives. També utilitzem un mètode químicament més intuïtiu, que proposa crear parells iònics dins de la cel·la.En este trabajo, se utilizaron diferentes métodos computacionales para estudiar las propiedades de cadenas extendidas de metales de transición (EMACs en inglés). Se simuló la flexibilidad estructural de cadenas de tres átomos de cromo, con CASSCF/CASPT2 y se identificaron estructuras simétricas y asimétricas en un entorno de baja energía. Basados en estos resultados, realizamos dinámicas moleculares de primeros principios (AIMD) para entender el efecto de la energía térmica y como ésta modifica la proporción de estructuras. También se estudiaron los enlaces metal-metal en compuestos de cromo, utilizando el modelo de orden de enlace efectivo (EBO) con los números de ocupación naturales de la función de onda CASSCF. Se calcularon constantes de acoplamiento magnético para compuestos bimetálicos y EMACs de níquel mediante dos estrategias. MC-PT2 con espacio activo mínimo utilizando orbitales moleculares mejorados a partir de un cálculo de estados-promediados, y se utilizó un método nuevo (MCPDFT) para el magnetismo de EMACs grandes, que ha mostrado buenos resultados en el compuesto de cinco níqueles. Finalmente, estudiamos propiedades del transporte de electrones para dos EMACs de rutenio. Proponemos el uso de un electrodo gate metálico para modular los niveles moleculares de los compuestos y obtener especies redox activas. También utilizamos un método químicamente más intuitivo, que propone crear pares iónicos dentro de la celda.In this work we use different computational methods in the study of the properties of Extended Metal Atom Chains. The structural flexibility of trichromium chains has been simulated with CASSCF/CASPT2 and symmetric and asymmetric structures were identified in an extremely flat energy landscape. Based on these results, Ab initio molecular dynamic simulations were performed to understand how the thermal energy modifies the proportion of cited structures. In addition, the metal-metal bonding of chromium compounds was characterized using the Effective Bond Order (EBO) model with the natural occupation numbers of the CASSCF wave function. Furthermore, magnetic coupling constants were computed for nickel bimetallic and EMACs compounds, using two different approaches. Minimal active space MC-PT2 was performed with improved molecular orbitals based on state-average calculations, and a recently developed method (MCPDFT) used for the magnetism of large EMACs, showing good results in the five-nickel compound. Finally, the electron transport properties were simulated for two ruthenium EMACs. We propose the use of a metallic gate electrode to modulate the molecular levels of the compounds and achieve redox active species. In addition, another more chemically intuitive approach was tested, that consist of forming an ionic pair in-situ

Theoretical description of electronic excitations in extended systems: beyond the static material model

The theoretical description of bistable materials requires dealing with the interplay of various phenomena, like temperature, environmental effects and electron correlation. We developed a procedure to combine the benefits of the molecular dynamics techniques with the accuracy of the ab initio wave function based methods including various models for the surroundings. The combination of these computational methods involved the making of specific software tools. The proposed procedure has been applied successfully, obtaining good agreements with experimental data, on organic molecules in solvent (cytosine tautomers in water), crystalline materials (NiO, LaMnO3 and TTTA) and inorganic spin-crossover compounds (FeII(bpy)3). We achieved a significant improvement in the description of their absorption spectra: including ligand-to-metal and metal-to-metal charge transfer processes, formally dipole forbidden transitions and the broadening of the spectral bands. Moreover, we observe dramatic changes on the electronic structure by incorporating the environmental effects on the theoretical model.La descripció teòrica de materials biestables requereix el tractament de diversos fenòmens interactuants, com la temperatura, els efectes del medi i la correlació electrònica. S'ha desenvolupat un procediment que combina els beneficis de la dinàmica molecular amb la precisió dels mètodes ab initio basats en la funció d'ona incloent diferents models de l'entorn. La combinació d'aquests mètodes computacionals ha involucrat la creació de programari específic. El procediment proposat ha estat aplicat amb èxit, obtenint bona concordança amb els experiments, a molècules orgàniques en solvent (citosina en aigua), materials cristal•lins (NiO, LaMnO3 i TTTA) i compostos spin-crossover inorgànics (FeII(bpy)3). S'ha assolit una millora significativa en la descripció del seus espectres d'absorció: incloent la transferència de càrrega lligand-metall i metall-metall, les transicions formalment prohibides per dipol i l'eixamplament de les bandes espectrals. A més, s'observen canvis importants en l'estructura electrònica al incorporar els efectes de l'entorn en el model teòric

Where to draw the line: Chasing energy extrapolations, cluster convergence, and molecular trajectories

The adsorption of S on Cu surfaces is studied by density functional theory using both plane-wave and atomic orbital basis sets. Calculations are performed on Cu clusters of increasing sizes, and strong oscillations in the S-Cu binding energy versus cluster size are found. Although expected for small clusters, the oscillations persist even to clusters containing a few hundred atoms. Smearing of the occupancy function in plane-wave DFT, and averaging over clusters of different sizes are presented as possible approaches to approximate bulk results using small to medium sized clusters. Chemically accurate potential energy curves for the lowest lying singlet states of C2 are obtained using the correlation energy extrapolation by intrinsic scaling (CEEIS) method. The potential energies also include complete basis set extrapolation, core-valence correlation, spin-orbit coupling, and scalar relativistic effects. Our calculated ro-vibrational levels show deviations from experiment of between ~10-20 cm-1, demonstrating near spectroscopic accuracy. The correlation energy extrapolation by many-body expansion (CEEMBE) method is presented. Like the CEEIS method, CEEMBE approximates configuration interaction (CI) energies using a linear extrapolation from CI calculations with reduced numbers of virtual orbitals. The method also uses a many-body expansion of the CI energy based on separating the valence orbitals into groups. Tests on ozone and F2 potential energy surfaces show that CI energies can be reproduced to within a few millihartree, and in many cases to within less than 1 millihartree. We also present a hybrid methodology, CEEMBE-h, which adds CEEIS style extrapolations to the CEEMBE procedure. CEEMBE-h reproduces the original CEEMBE energies to within 0.1-0.5 millihartree or less. Nonadiabatic dynamics using spin-flip time-dependent density functional theory (SF-TDDFT) are presented for the penta-2,4-dieniminium cation. We developed an interface between the GAMESS and Newton-X programs for SF-TDDFT dynamics. Time-derivative couplings between SF-TDDFT states are calculated using an approximate wavefunction overlap method. Our comparison with analytical couplings from CASSCF demonstrates that the overlap method for time-derivative couplings is effective for SF-TDDFT. Because of the spin-contamination in SF-TDDFT, the interface includes a state-tracking algorithm to ensure dynamics are propagated on the correct potential energy surface

Too continuous to continue? Multiple electronic surfaces and derivatives

The current document includes six chapters, which are published, accepted, or prepared for submission in various journals. Chapter 2 introduces a study on the triplet surface of O+C2H4. Chapter 3 presents a study on the singlet and triplet surfaces of O+C2H4 with a focus on biradical species. Chapter 4 continues the previous study with a more extensive study on the energetically lowest-lying singlet surface of O+C2H4. Chapters 2-4 rely on a several multireference methods to model ground and excited states and on some single-reference methods. Chapter 5 presents a multireference study on SiCH4 and butadiene with ORMAS energy, first-order nuclear derivative, and first-order nuclear derivative coupling contours, which characterize whether or not the ORMAS approximation effects correct analytical derivatives with seemingly smooth energies over a range of geometries. Chapter 6 presents the interface of NEWTON-X (a dynamics driver program) and GAMESS (an electronic structure suite) along with a dynamics study on CNH4+ that demonstrates the possible effects of the ORMAS approximation on product distributions

Quantitative wave function analysis for excited states of transition metal complexes

The character of an electronically excited state is one of the most important descriptors employed to discuss the photophysics and photochemistry of transition metal complexes. In transition metal complexes, the interaction between the metal and the different ligands gives rise to a rich variety of excited states, including metal-centered, intra-ligand, metal-to-ligand charge transfer, ligand-to-metal charge transfer, and ligand-to-ligand charge transfer states. Most often, these excited states are identified by considering the most important wave function excitation coefficients and inspecting visually the involved orbitals. This procedure is tedious, subjective, and imprecise. Instead, automatic and quantitative techniques for excited-state characterization are desirable. In this contribution we review the concept of charge transfer numbers---as implemented in the TheoDORE package---and show its wide applicability to characterize the excited states of transition metal complexes. Charge transfer numbers are a formal way to analyze an excited state in terms of electron transitions between groups of atoms based only on the well-defined transition density matrix. Its advantages are many: it can be fully automatized for many excited states, is objective and reproducible, and provides quantitative data useful for the discussion of trends or patterns. We also introduce a formalism for spin-orbit-mixed states and a method for statistical analysis of charge transfer numbers. The potential of this technique is demonstrated for a number of prototypical transition metal complexes containing Ir, Ru, and Re. Topics discussed include orbital delocalization between metal and carbonyl ligands, nonradiative decay through metal-centered states, effect of spin-orbit couplings on state character, and comparison among results obtained from different electronic structure methods.Comment: 47 pages, 19 figures, including supporting information (7 pages, 1 figure

Minimalistic Descriptions of Nondynamical Electron Correlation: From Bond-Breaking to Transition-Metal Catalysis

From a theoretical standpoint, the accurate description of potential energy surfaces for bond breaking and the equilibrium structures of metal-ligand catalysts are distinctly similar problems. Near degeneracies of the bonding and anti-bonding orbitals for the case of bond breaking and of the partially-filled d-orbitals for the case of metal-ligand catalyst systems lead to strong non-dynamical correlation effects. Standard methods of electronic structure theory, as a consequence of the single-reference approximation, are incapable of accurately describing the electronic structure of these seemingly different theoretical problems. The work within highlights the application of multi-reference methods, methods capable of accurately treating these near-degeneracies, for describing the bond-breaking potentials in several small molecular systems and the equilibrium structures of metal-salen catalysts. The central theme of this work is the ability of small, compact reference functions for accurately describing the strong non-dynamical correlation effects in these systems.Ph.D.Committee Chair: C. David Sherrill; Committee Member: Jean-Luc Bredas; Committee Member: Mostafa El-Sayed; Committee Member: Peter J. Ludovice; Committee Member: Thomas Orland

Extension and applications of the GVVPT2 method to the study of transition metals

The ground and low-lying excited electronic states of molecules of the first ( 2 Sc , 2 Cr , 2 Mn , and 2 Ni ) and second ( 2 Y , 2 Mo , and 2 Tc ) row of transition elements have been investigated for the first time with the generalized Van Vleck second order multireference perturbation theory (GVVPT2) method, a variant of MRPT. All potential energy curves (PECs) obtained in these studies were smooth and continuous; that is, they are free from wiggles or inflexion points. In order to account for relativistic effects, which become important in heavy elements, the GVVPT2 method was extended to include scalar relativistic effects through the spin-free exact two component (sf-X2C) method and used in the studies of all molecules of second row transition elements and some of those of the first row considered in this present work. GVVPT2 studies of triatomic lithium and beryllium were also done as a first step to studies of small clusters of transition metals. The spectroscopic constants (bond lengths, harmonic frequencies, bond energies, and adiabatic transition energies) obtained for all PECs at the GVVPT2 level were in good agreement with experimental data, where available, and with results from previous studies using other high level ab initio methods. Optimized geometries of the triatomics were also in good agreement with previous findings. The studies included electronic states (e.g., the g 1 g 1 2 Σ and 3 Σ states of 2 Y as well as the g 5 1 Σ and g 9 1 Σ states of 2 Tc ) not previously discussed in the literature. As a first step to applying GVVPT2 to the study of relatively larger systems, the present work includes the results of efforts on improving DFT-in-DFT embedding theory. New equations were determined which involved an additional constraint of orthogonality of the orbitals of one subsystem to those of the complementary subsystem as warranted by formal arguments based on the formulation of DFT-in-DFT embedding. A computer program was realized using the new embedding equations and test calculations performed. Analyses of electron density deformations in embedding theory, in comparison with conventional Kohn-Sham (KS)-DFT densities, were performed using the new embedding program and a computer code that was also written to compute electron densities of molecules in real space, given reduced one particle density matrices. The results revealed that whereas the current formulation of DFT-in-DFT embedding theory generally underestimates electron density, at the interface between subsystems in comparison with conventional KS-DFT calculations of the supermolecule, the new DFT-in-DFT embedding scheme with the external orthogonality constraint was found to remedy the situation. Worthy of special note in this new embedding protocol is the fact that the nonadditive kinetic potential ( T v ), thought to be a major cause of weaknesses in DFT-in-DFT embedding and to which many previous research efforts have been devoted, can be set exactly to zero. The present work therefore realized, for the first time, a new DFT-in-DFT embedding theory that neither relies on kinetic functionals nor requires a supermolecular DFT calculation. Test calculations using the new embedding theory and supermolecular basis set expansion of KS orbitals reproduced conventional KS-DFT energies to at least the 7th decimal place (and even exactly at many geometries). A new way of expanding KS orbitals was also employed in the new embedding protocol, which is intermediate between the usual supermolecular and monomer basis expansions, referred to as the “extended monomer expansion”. The monomer basis expansion scheme was inadequate for the new DFT-in-DFT embedding protocol. Test calculations found this novel, computationally cheaper, extended monomer approach to give results quite close to those from supermolecular basis expansions

Extension and applications of the GVVPT2 method to the study of transition metals

The ground and low-lying excited electronic states of molecules of the first ( 2 Sc , 2 Cr , 2 Mn , and 2 Ni ) and second ( 2 Y , 2 Mo , and 2 Tc ) row of transition elements have been investigated for the first time with the generalized Van Vleck second order multireference perturbation theory (GVVPT2) method, a variant of MRPT. All potential energy curves (PECs) obtained in these studies were smooth and continuous; that is, they are free from wiggles or inflexion points. In order to account for relativistic effects, which become important in heavy elements, the GVVPT2 method was extended to include scalar relativistic effects through the spin-free exact two component (sf-X2C) method and used in the studies of all molecules of second row transition elements and some of those of the first row considered in this present work. GVVPT2 studies of triatomic lithium and beryllium were also done as a first step to studies of small clusters of transition metals. The spectroscopic constants (bond lengths, harmonic frequencies, bond energies, and adiabatic transition energies) obtained for all PECs at the GVVPT2 level were in good agreement with experimental data, where available, and with results from previous studies using other high level ab initio methods. Optimized geometries of the triatomics were also in good agreement with previous findings. The studies included electronic states (e.g., the g 1 g 1 2 Σ and 3 Σ states of 2 Y as well as the g 5 1 Σ and g 9 1 Σ states of 2 Tc ) not previously discussed in the literature. As a first step to applying GVVPT2 to the study of relatively larger systems, the present work includes the results of efforts on improving DFT-in-DFT embedding theory. New equations were determined which involved an additional constraint of orthogonality of the orbitals of one subsystem to those of the complementary subsystem as warranted by formal arguments based on the formulation of DFT-in-DFT embedding. A computer program was realized using the new embedding equations and test calculations performed. Analyses of electron density deformations in embedding theory, in comparison with conventional Kohn-Sham (KS)-DFT densities, were performed using the new embedding program and a computer code that was also written to compute electron densities of molecules in real space, given reduced one particle density matrices. The results revealed that whereas the current formulation of DFT-in-DFT embedding theory generally underestimates electron density, at the interface between subsystems in comparison with conventional KS-DFT calculations of the supermolecule, the new DFT-in-DFT embedding scheme with the external orthogonality constraint was found to remedy the situation. Worthy of special note in this new embedding protocol is the fact that the nonadditive kinetic potential ( T v ), thought to be a major cause of weaknesses in DFT-in-DFT embedding and to which many previous research efforts have been devoted, can be set exactly to zero. The present work therefore realized, for the first time, a new DFT-in-DFT embedding theory that neither relies on kinetic functionals nor requires a supermolecular DFT calculation. Test calculations using the new embedding theory and supermolecular basis set expansion of KS orbitals reproduced conventional KS-DFT energies to at least the 7th decimal place (and even exactly at many geometries). A new way of expanding KS orbitals was also employed in the new embedding protocol, which is intermediate between the usual supermolecular and monomer basis expansions, referred to as the “extended monomer expansion”. The monomer basis expansion scheme was inadequate for the new DFT-in-DFT embedding protocol. Test calculations found this novel, computationally cheaper, extended monomer approach to give results quite close to those from supermolecular basis expansions