Complete Active Space Self-consistent Field Research Articles

Electronic Structure of Proteins: Exciton Hamiltonian for a Dipeptide

Protein folding has attracted a great deal of interest alongside the increased amount of structural information on proteins. Different spectroscopies, for example, X-ray crystallography and Nuclear Magnetic Resonance (NMR), are often used to study protein structure. Optical spectroscopy despite limited spatial resolution, for example, circular dichroism (CD), has considerable interest, arising from the ability to derive information about secondary structures of a protein from its CD spectrum. The aim of the present work is to explore whether fully ab initio Complete Active Space Self-Consistent Field (CASSCF) calculations of the electronic excited states of dipeptides can help to construct the exciton Hamiltonian for a dipeptide. Exciton theory is an approximate approach allowing the calculation of the CD of proteins. We have treated the problem of finding the exciton Hamiltonian matrix elements as an optimization problem in which the ab initio energies represent the “true” solutions and are used to compute the “error” that will be minimized. We use a Monte Carlo algorithm to conduct optimization. We find many possible solutions, all of which upon diagonalizing the exciton Hamiltonian give energies close to the ab initio energies. Some of the off-diagonal elements are also well-defined, while other distributions of some elements are more variable. More work will be needed to reduce the number of solutions

Reliable Diradical Characterization via Precise Singlet-Triplet Gap Calculations: Application to Thiele, Chichibabin, and Müller Analogous Diradicals.

Accurately calculating the diradical character (y0) of molecular systems remains a significant challenge due to the scarcity of experimental data and the inherent multireference nature of the electronic structure. In this study, various quantum mechanical approaches, including broken symmetry density functional theory (BS-DFT), spin-flip time-dependent density functional theory (SF-TDDFT), mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT), complete active space self-consistent field (CASSCF), complete active space second-order perturbation theory (CASPT2), and multiconfigurational pair-density functional theory (MCPDFT), are employed to compute the singlet-triplet energy gaps (EST) and y0 values in Thiele, Chichibabin, and Müller analogous diradicals. By systematically comparing the results from these computational methods, we identify optimally tuned long-range corrected functional CAM-B3LYP in the BS-DFT framework as a most efficient method for accurately and affordably predicting both EST and y0 values. Additionally, our results demonstrate that (i) MRSF-TDDFT performs much better than SF-TDDFT; (ii) the MCPDFT method is robust in determining EST with minimal dependence on the choice of active space. These findings provide insight into the electronic structure and diradical character of the investigated molecules and highlight effective computational strategies for future studies in this domain. Thus, this work not only advances our understanding of diradical systems but also offers practical guidelines for their computational investigation.

A cross-entropy corrected hybrid multiconfiguration pair-density functional theory for complex molecular systems

Hybrid density functionals, such as B3LYP and PBE0, have achieved remarkable success by substantially improving over their parent methods, namely Hartree-Fock and the generalized gradient approximation, and generally outperforming the second-order Møller-Plesset perturbation theory (MP2) that is more expensive. Here, we extend the linear scheme of hybrid multiconfiguration pair-density functional theory (HMC-PDFT) by incorporating a cross-entropy ingredient to balance the description of static and dynamic correlation effects, leading to a consistent improvement on both exchange and correlation energies. The B3LYP-like translated on-top functional (tB4LYP) developed along this line not only surpasses the accuracy of its parent methods, the complete active space self-consistent field (CASSCF) and the original MC-PDFT functionals (tBLYP and tB3LYP), but also outperforms the widely used complete active space second-order perturbation theory (CASPT2). Remarkably, while remaining satisfactory for general purpose, tB4LYP shows superior accuracy for challenging cases like the Cr2 dissociation and the associated low-lying vibrational energies, the ethylene torsional rotation and the ethyne diabatic colinear dissociations, with the significantly lower computational cost than CASPT2.

Unravelling the electronic structure, bonding, and magnetic properties of inorganic dysprosocene analogues [Dy(E4)2]- (E = N, P, As, CH).

Organometallic sandwich complexes of Dy(III) ion are ubiquitous for designing high-temperature single-ion magnets with blocking temperatures close to the liquid nitrogen boiling point. Magnetic bistability at the molecular level makes them potential candidates for nano-scale information storage materials. In the present contribution, we have thoroughly investigated the electronic structure, bonding, covalency, and magnetic anisotropy of inorganic dysprosocene complexes with a general formula of [Dy(E4)2]- (where E = N, P, As, CH) using state-of-the-art scalar relativistic density functional theory (SR-DFT), and a multiconfigurational complete active space self-consistent field (CASSCF) method with the N-electron valence perturbation theory (NEVPT2). Geometry optimization calculations predict stabilization of the [Dy(E4)2]- complexes with a linear geometry and D4h local symmetry Dy(III) ion in [Dy(N4)2]- (1) and [Dy(P4)2]- (2) complexes, while a bent geometry has been observed for the [Dy(As4)2]- (3), [Dy(P2(CH)2)2]- (4), and [Dy(As2(CH)2)2]- (5) complexes. Energy decomposition analysis (EDA) and natural bonding orbital (NBO) calculations reveal sizable 5d-ligand covalency followed by 6s/6p and weak 4f-ligand covalency in complexes 1-5. Both the natural localized molecular orbitals (NLMOs) at the DFT level and ab initio-based ligand field theory (AILFT) at the NEVPT2 level of theory predict an increase in the Dy-ligand covalency as we move from N to As. Spin-Hamiltonian parameter analysis of complexes 1-5 reveals stabilization of the mJ |±15/2〉 as the ground state with highly axial g values (gxx ∼ gyy ∼ 0 and gzz ∼ 20) and the barrier height of 2902, 1214, 1104, 1845, and 1509 K for 1-5, respectively. The Orbach effective demagnetization barrier (Ueff) for complexes 1-5 ranges between 2416-1175 K, with a record Ueff value of 2416 K observed for 1. In addition, we have explored the role of heavy element effects on the magnetic anisotropy by turning off the spin-orbit coupling of the pnictogens (N, P, and As), and our calculations clearly predict that heavy atoms in the first coordination sphere help in increasing the barrier height for magnetic relaxation. Heavy elements like P and As significantly enhance the SOC contributions, thereby providing a platform for designing and optimizing Dy(III) complexes with tailored magnetic behaviors.

Extended Active Space Ab Initio Ligand Field Theory: Applications to Transition-Metal Ions.

Ligand field theory (LFT) is one of the cornerstones of coordination chemistry since it provides a conceptual framework in which a great many properties of d- and f-element compounds can be discussed. While LFT serves as a powerful qualitative guide, it is not a tool for quantitative predictions on individual compounds since it incorporates semiempirical parameters that must be fitted to experiment. One way to connect the realms of first-principles electronic structure theory that has emerged as particularly powerful over the past decade is the ab initio ligand field theory (AILFT). The original formulation of this method involved the extraction of LFT parameters by fitting the ligand field Hamiltonian to a complete active space self-consistent field (CASSCF) Hamiltonian. The extraction was shown to be unique provided that the active space consists of 5/7 metal d/f-based molecular orbitals (MOs). Subsequent improvements have involved incorporating dynamical correlation using second-order N-electron valence state perturbation theory (NEVPT2) or second-order dynamical correlation dressed complete active space (DCDCAS). However, the limitation of past approaches is that the method requires a minimal space of 5/7 metal d- or f-based molecular orbitals. This leads to a number of limitations: (1) neglect of radial or semicore correlation would arise from the effect of a second d-shell or an sp-shell in the active space, (2) a more balanced description of metal-ligand bond covalency is lacking because the bonding ligand-based counterparts of the metal d/f orbitals are not in the active space. This usually leads to an exaggerated ionicity of the M-L bonds. In this work, we present an extended active space AILFT (esAILFT) that circumvents these limitations and is, in principle, applicable to arbitrary active spaces, as long as these contain the 5/7 metal d/f-based MOs as a subset. esAILFT was implemented in a development version of the ORCA software package. In order to help with the application of the new method, various criteria for active space extension were explored for 3d, 4d, and 5d transition-metal ions with varying charge. An interpretation of the trends in the Racah B parameter for these ions is also presented as a demonstration of the capabilities of esAILFT.

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe-2S] Systems: A Benchmark Study of the [Fe2S2(SCH3)4]2-,3-,4-, [Fe2S2(SCys)4]2-, [Fe2S2(S-p-tol)4]2-, and [Fe2S2(S-o-xyl)4]2- Complexes.

Iron-sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Using a [2Fe-2S] model complex with FeII and FeIII oxidation states, which leads to different charges, i.e., [Fe2S2(SMe)4]2-,3-,4-, we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree-Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe2S2(SCys)4]2-, [Fe2S2(S-o-tol)4]2-, and [Fe2S2(S-o-xyl)4]2-, via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the FeIII/FeIII → FeII/FeIII (4.27 eV) and FeII/FIII → FeII/FII (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

Effect of Oriented External Electric Field in Altering Magnetic Exchange and Magnetic Anisotropy in Lanthanide-Radical Complexes.

Magnetic exchange coupling (J) is one of the important spin Hamiltonian parameters that control the magnetic characteristics of single-molecule magnets (SMMs). While numerous chemical methodologies have been proposed to modify ligands and control the J value, and magneto-structural correlations have been developed accordingly, altering this parameter through non-chemical means remains a challenging task. This study explores the impact of an Oriented-External Electric Field (OEEF) on over twenty lanthanide-radical complexes using Density Functional Theory (DFT) and ab initio Complete Active Space Self-Consistent Field (CASSCF) methods. Five complexes - [{(Me3Si)2N]2Gd(THF)}2(μ-η2:η2-N2)] (1), [Gd(Hbpz3)2(dtbsq)] (2), [Gd(hfac)3(IM-2py)] (3), [Gd(hfac)3(NITBzImH)] (4), and [Gd(hfac)3{2Py-NO}(H2O)] (5) - were selected for detailed analysis, revealing significant OEEF effects on magnetic exchange interactions and structural parameters. Various parameters such as bond distances, bond angles, and torsional angles were examined as a function of OEEF to establish guiding principles for molecule selection. In complexes 1, 2, and 3, OEEF influenced torsional angles and altered exchange interactions. Complex 4 demonstrated enhanced ferromagnetic coupling under OEEF, reaching a maximum J value of +5.3 cm-1. Complex 5 reveals switching the sign of JGd-rad exchange interaction from antiferromagnetic to ferromagnetic under OEEF, highlighting the potential of electric fields in designing materials with tuneable magnetic properties. These findings offer valuable insights for future research and applications in advanced materials and molecular electronics.

Theoretical Study on One- and Two-Photon Absorption Properties of π-Stacked Multimer Models of Phenalenyl Radicals

Effects of the number of monomers (N) on the two-photon absorption (TPA) properties of π-stacked multimer models consisting of phenalenyl radicals were investigated theoretically. We conducted spectral simulations for the π-stacked N-mer models (N = 2, 4, and 6) with different stacking distances (d1) and their alternation patterns (d2/d1). Excitation energies and transition dipole moments were calculated at the extended multi-configurational quasi-degenerate second-order perturbation theory (XMC-QDPT2) level based on the complete active space self-consistent field (CASSCF) wavefunctions with the active space orbitals constructed from the singly occupied molecular orbitals (SOMOs) of monomers. The TPA cross-section value per dimer unit at the first peak, originating from the electronic transition along the stacking direction, was predicted to increase significantly as the d2/d1 approaches one, as the d1 decreases, and as the N increases from 2 to 6. These tendencies are similar to the calculation results for the static hyperpolarizabilities.

Ground and Excited States from Ensemble Variational Principles

The extension of the Rayleigh-Ritz variational principle to ensemble states ρw≡∑kwk|Ψk⟩⟨Ψk| with fixed weights wk lies ultimately at the heart of several recent methodological developments for targeting excitation energies by variational means. Prominent examples are density and density matrix functional theory, Monte Carlo sampling, state-average complete active space self-consistent field methods and variational quantum eigensolvers. In order to provide a sound basis for all these methods and to improve their current implementations, we prove the validity of the underlying critical hypothesis: Whenever the ensemble energy is well-converged, the same holds true for the ensemble state ρw as well as the individual eigenstates |Ψk⟩ and eigenenergies Ek. To be more specific, we derive linear bounds d−ΔEw≤ΔQ≤d+ΔEw on the errors ΔQ of these sought-after quantities. A subsequent analytical analysis and numerical illustration proves the tightness of our universal inequalities. Our results and particularly the explicit form of d±≡d±(Q)(w,E) provide valuable insights into the optimal choice of the auxiliary weights wk in practical applications.

Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and applications.

The increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH3) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.

Theoretical spin-orbit laser cooling for AlZn molecule.

A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.

Molecular line lists for the singlet states in gaseous YN at high temperature

ABSTRACT Our aim in this study is to investigate the electronic structure of the gaseous YN molecule and provide an accurate molecular line list of spectroscopic transitions between the five lowest singlet states. The calculations were done by using large basis set for yttrium aug-cc-pVQZ-PP with relativistic effective core potentials at the spin-free level. We first used the method of complete active space self-consistent field, which was followed by the multireference singles and doubles configuration interaction. Potential energy curves and permanent and transition dipole moments were calculated at the internuclear distance range of 1.3–2.96 Å. For each state, we calculated the spectroscopic constants (Te, ωe, ωexe, ωeye, Be, αe, Re). The calculated values of the spectroscopic constants are in excellent agreement with the experimental constants available, with a relative difference of less than 5 cm−1. We further calculated the transition intensities of allowed transitions, and we provided the absorption spectra up to a temperature of 4000 K. The computed molecular line list contains 2.6 million transitions calculated between almost 18 186 vibro-rotational energy levels. It covers the frequency range between 0 and 30 000 cm−1. The effect of temperature on the spectra of hot YN was investigated with partition functions calculated between 298 and 4000 K. This study should help in identifying the singlet state spectrum of the hot YN molecule, which is possibly found in the atmospheres of cool stars and hot rocky super-Earths.

Implementation of frozen density embedding in CP2K and OpenMolcas: CASSCF wavefunctions embedded in a Gaussian and plane wave DFT environment.

Most chemical processes happen at a local scale where only a subset of molecular orbitals is directly involved and only a subset of covalent bonds may be rearranged. To model such reactions, Density Functional Theory (DFT) is often inadequate, and the use of computationally more expensive correlated wavefunction (WF) methods is required for accurate results. Mixed-resolution approaches backed by quantum embedding theory have been used extensively to approach this imbalance. Based on the frozen density embedding freeze-and-thaw algorithm, we describe an approach to embed complete active space self-consistent field simulations run in the OpenMolcas code in a DFT environment calculated in CP2K without requiring any external tools. This makes it possible to study a local, active part of a chemical system in a larger and relatively static environment with a computational cost balanced between the accuracy of a WF method and the efficiency of DFT, which we test on environment-subsystem pairs. Finally, we apply the implementation to an oxygen molecule leaving an aluminum (111) surface and a ruthenium(IV) oxide (110) surface.

Advancing Our Understanding of the Excited States of the Tantalum Anion.

Our study provides a comprehensive theoretical examination of the energy levels associated with the neutral tantalum atom and its ions in various charge states (Ta, Ta+, and Ta-), employing the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, and relativistic infinite order two-component (IOTC) method with multiconfiguration complete active space self-consistent field (CASSCF) followed by the second-order single-state multireference perturbation (CASPT2) methods. The effect of spin-orbit (SO) coupling is introduced via the restricted active space state interaction (RASSI) method, utilizing atomic mean field SO integrals (AMFI). Through IOTC CASSCF/CASPT2 RASSI calculations, we determined the electron affinity (EA) of the tantalum atom to be 0.321 eV, which stands among the most accurate theoretical values achieved to date. This result closely aligns with the experimental measurement of 0.329 eV. Our investigation highlights potential discrepancies between the predicted symmetry of the excited states of the tantalum anion and experimental observations. Additionally, we calculated the bonding energies for transitions from Ta- to Ta and identified four potential bound or quasi-bound states in the tantalum anion.

Fundamental Invariant Neural Network (FI-NN) Potential Energy Surface for the OH + CH3OH Reaction with Analytical Forces.

The hydrogen abstraction reaction of OH + CH3OH plays a great role in combustion and atmospheric and interstellar chemistry and has been extensively studied theoretically and experimentally. Theoretically, the numerical gradients with respect to the Cartesian coordinates of atoms in molecular simulations on our recent potential energy surface (PES) for the title reaction trained using the permutationally invariant polynomial neural network (PIP-NN) approach hinder the extensive calculation because of the unaffordable computation cost. To address this issue, we in this work report a new full-dimensional accurate analytical PES for the title reaction using the fundamental invariant neural network (FI-NN) approach based on 140,192 points of the quality UCCSD(T)-F12a/AVTZ. Besides, the spin-orbit (SO) corrections of OH in the entrance channel were determined at the level of complete active space self-consistent field with the AVTZ basis set. As a compromise between computational cost and efficiency, the Δ-machine learning approach was employed to construct the SO-corrected PES. Based on this new FI-NN PES with analytical forces, thermal rate coefficients and various dynamic properties, including the integral cross sections, the differential cross sections, and the product energy partitioning, were determined by running a total of 5.5 million trajectories. The use of analytical gradients of the FI-NN PES accelerated simulations and about 99% of computation cost was saved, compared to that for the PIP-NN PES with numerical gradients. Such a significant acceleration is achieved mainly by replacing PIPs with FIs.

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins.

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions.

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

Combined Multireference-Multiscale Approach to the Description of Photosynthetic Reaction Centers.

A first-principles description of the primary photochemical processes that drive photosynthesis and sustain life on our planet remains one of the grand challenges of modern science. Recent research established that explicit incorporation of protein electrostatics in excited-state calculations of photosynthetic pigments, achieved for example with quantum-mechanics/molecular-mechanics (QM/MM) approaches, is essential for a meaningful description of the properties and function of pigment-protein complexes. Although time-dependent density functional theory has been used productively so far in QM/MM approaches for the study of such systems, this methodology has limitations. Here we pursue for the first time a QM/MM description of the reaction center in the principal enzyme of oxygenic photosynthesis, Photosystem II, using multireference wave function theory for the high-level QM region. We identify best practices and establish guidelines regarding the rational choice of active space and appropriate state-averaging for the efficient and reliable use of complete active space self-consistent field (CASSCF) and the N-electron valence state perturbation theory (NEVPT2) in the prediction of low-lying excited states of chlorophyll and pheophytin pigments. Given that the Gouterman orbitals are inadequate as a minimal active space, we define specific minimal and extended active spaces for the NEVPT2 description of electronic states that fall within the Q and B bands. Subsequently, we apply our multireference-QM/MM protocol to the description of all pigments in the reaction center of Photosystem II. The calculations reproduce the electrochromic shifts induced by the protein matrix and the ordering of site energies consistent with the identity of the primary donor (ChlD1) and the experimentally known asymmetric and directional electron transfer. The optimized protocol sets the stage for future multireference treatments of multiple pigments, and hence for multireference studies of charge separation, while it is transferable to the study of any photoactive embedded tetrapyrrole system.

Experimental molecular structures in the gas phase at the upper size limit: The case of Si6Tip6.

Currently, the largest (ramax = 19.9Å) and by far the most complicated (234 atoms, C1 symmetry, 696 independent geometrical parameters, and 27 261 interatomic terms) experimental molecular structure of a cage-type Si6Tip6 (Tip = 2,4,6-iPr3C6H2) isomer has been investigated in the gas phase by the electron diffraction method (Tav = 645K) supplemented with theoretical simulations. A detailed analysis of the current possibilities for experimentally investigating large molecular structures is performed. A series of density functional theory approximations and the role of dispersion interactions have been benchmarked using the obtained data. Based on the refined geometry of Si6Tip6, various quantum-chemical methods have been applied for the investigation of the electronic structure of its Si6 core. In particular, natural bond orbital, quantum theory of atoms in molecules, interacting quantum atoms, fractional occupation number weighted density, and complete active space self-consistent field (CASSCF) methods were utilized. The diradical character of the molecule has been assessed by the UHF and CASSCF approximations. The problem of bonding between the hemispheroidal silicon atoms has been investigated.

The Photophysics and Photochemistry of Phenylalanine, Tyrosine, and Tryptophan: A CASSCF/CASPT2 Study.

Among all amino acids, the three aromatic systems including phenylalanine, tyrosine, and tryptophan are known to manifest UV light absorption at the higher wavelengths. Their fluorescent properties are important for protein detection and determination of the spatial structure. Based on ab initio quantum chemical calculations, the absorption spectra in the 0-12 eV UV range of these aromatic amino acids were interpreted, and the photochemistry of the lowest-lying excited states was studied. For that, molecular ground-state geometries were determined using both the coupled-cluster single and double (CCSD) and complete active space self-consistent field (CASSCF) methods. The vertical electronic transition energies, associated oscillator strengths, and electric dipole moments of the lowest excited states were computed at the CASPT2//CASSCF level. The decay mechanisms of the lowest-energy excited states were investigated by performing minimum energy path (MEPs) computations. The results showed that the CCSD and CASSCF computations yielded similar structures. The lowest-energy S1 state in phenylalanine and tyrosine, and S1 and S2 in tryptophan are mainly described by the π → π* excitation localized in the aromatic ring. Upon light absorption, the main photoresponse of the molecules is driven by the benzene, phenol, and indole chromophoric units.