Complete Active Space Self-consistent Field Research Articles

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.

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.

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.

Theoretical investigation of the electronic structure of the Rhodium Halides molecules RhF and RhCl with dipole moment calculation

The current study involves an ab initio exploration of the ground and low-lying excited electronic states of the rhodium halide molecules RhF and RhCl using the complete active space self-consistent field (CASSCF) with multireference configuration interaction (MRCI+Q) method including single and double excitations and with Davidson corrections. We investigated the potential energy curves, the transition and permanent electric dipole moments, the electronic energy relative to the ground state Te, the harmonic frequency ωe, the internuclear distance Re, and the rotational constant Be corresponding to each of the bounded states. Our findings demonstrate good agreement with the available experimental data. Notably, this work represents the inaugural theoretical investigation of the excited states of RhF and RhCl molecules, identifying the ground state of both to be X3Π, as observed in the sole two experimental investigations.

Theoretical study of the substituent effects on the ESIPT mechanism of salicylideneaniline and the TICT photochemistry reactions.

The study of salicylideneaniline (SA) and its derivatives is critical due to their special photophysical properties and environmental sensitivity. In this work, the density time-dependent functional theory (TDDFT) and complete-active-space self-consistent-field (CASSCF) methods were carried out to calculate the substituent effect on excited-state properties and dynamics of SA derivatives. We found the para-substitution triggers the excited-state intramolecular proton transfer (ESIPT) reaction, exhibiting the dual-fluorescent phenomena. However, the meta- and ortho-substitutions impel the non-radiative transition process along the minimum energy conical intersection (MECI), forming the twisted intramolecular charge transfer (TICT) state to prevent ESIPT. This investigation of substituent effects on the photochemical processes and photophysical properties will provide the benchmarks for the design of fluorescent materials.

Tunable optical properties of isoreticular UiO-67 MOFs for photocatalysis: a theoretical study.

A theoretical study of the reported photocatalytic systems based on Zr-based MOF (UiO-67) with biphenyl-4,4'-dicarboxylic acid (bpdc) and 2,2'-bipyridine-5,5'-dicarboxylic acid (bpydc) as linkers was performed. Quantum chemical calculations were carried out to understand the optical properties of the materials and to facilitate the rational design of new UiO-67 derivatives with potentially improved features as photocatalysts under ambient conditions. Hence, the effect of the structural modifications on the optical properties was studied considering different designs based on the nature of the linkers: in 1 only the bpdc linker was considered, or the mixture 1 : 1 between bpdc and bpydc linkers (labeled as 1A). Also, substituents R, -NH2, and -SH, were included in the 1A MOF only over the bpdc linker (labeled as 1A-bpdc-R) and on both bpdc and bpydc linkers (labeled as 1A-R). Thus a family of six isoreticular UiO-67 derivatives was theoretically characterized using Density Functional Theory (DFT) calculations on the ground singlet (S0) and first excited states (singlet and triplet) using Time-Dependent Density Functional Theory (TD-DFT), multiconfigurational post-Hartree-Fock method via Complete Active Space Self-Consistent Field (CASSCF). In addition, the use of periodic DFT calculations suggest that the energy transfer (ET) channel between bpdc and bpydc linkers might generate more luminescence quenching of 1A when compare to 1. Besides, the results suggest that the 1A-R (R: -SH and NH2) can be used under ambient conditions; however, the ET exhibited by 1A, cannot take place in the same magnitude in these systems. These ET can favor the photocatalytic reduction of a potential metal ion, that can coordinate with the bpydc ligand, via LMCT transition. Consequently, the MOF might be photocatalytically active against molecules of interest (such as H2, N2, CO2, among others) with photo-reduced metal ions. These theoretical results serve as a useful tool to guide experimental efforts in the design of new photocatalytic MOF-based systems.

Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor.

Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.

Tris-Silanide f-Block Complexes: Insights into Paramagnetic Influence on NMR Chemical Shifts.

The paramagnetism of f-block ions has been exploited in chiral shift reagents and magnetic resonance imaging, but these applications tend to focus on 1H NMR shifts as paramagnetic broadening makes less sensitive nuclei more difficult to study. Here we report a solution and solid-state (ss) 29Si NMR study of an isostructural series of locally D 3h -symmetric early f-block metal(III) tris-hypersilanide complexes, [M{Si(SiMe3)3}3(THF)2] (1-M; M = La, Ce, Pr, Nd, U); 1-M were also characterized by single crystal and powder X-ray diffraction, EPR, ATR-IR, and UV-vis-NIR spectroscopies, SQUID magnetometry, and elemental analysis. Only one SiMe3 signal was observed in the 29Si ssNMR spectra of 1-M, while two SiMe3 signals were seen in solution 29Si NMR spectra of 1-La and 1-Ce. This is attributed to dynamic averaging of the SiMe3 groups in 1-M in the solid state due to free rotation of the M-Si bonds and dissociation of THF from 1-M in solution to give the locally C 3v -symmetric complexes [M{Si(SiMe3)3}3(THF) n ] (n = 0 or 1), which show restricted rotation of M-Si bonds on the NMR time scale. Density functional theory and complete active space self-consistent field spin-orbit calculations were performed on 1-M and desolvated solution species to model paramagnetic NMR shifts. We find excellent agreement of experimental 29Si NMR data for diamagnetic 1-La, suggesting n = 1 in solution and reasonable agreement of calculated paramagnetic shifts of SiMe3 groups for 1-M (M = Pr and Nd); the NMR shifts for metal-bound 29Si nuclei could only be reproduced for diamagnetic 1-La, showing the current limitations of pNMR calculations for larger nuclei.

XMS-CASPT2//XMS-CASPT2 and XMS-CASPT2//CASSCF at comparison: The impact of dynamic correlation in the excited state optimization of nitronaphthalene.

Here, analytical extended multi-state complete active space second-order perturbation method (XMS-CASPT2) gradients are used to rationalize the decreasing triplet quantum yield trend in 2-nitronaphthalene, 1-nitronaphthalene, and 2-methyl-1-nitronaphthalene, a series of nitro-substituted aromatic compounds. Comparison with the XMS-CASPT2//CASSCF (where CASSCF stands for complete active space self-consistent field method) results highlights the importance of dynamic correlation in geometry optimization and challenges the validity of an XMS-CASPT2//CASSCF approach: XMS-CASPT2 S1 minima leads to planar structures, while CASSCF optimizations trigger a pyramidalization of the nitro group. The XMS-CASPT2 results correlate the reported decreasing triplet quantum yield trend in these species to a decrease in S1 to T2 population transfer and an increase in S1-S0 decay, while no such correlation is observed when using XMS-CASPT2//CASSCF data.

Distinguishing homolytic vs heterolytic bond dissociation of phenylsulfonium cations with localized active space methods

Modeling chemical reactions with quantum chemical methods is challenging when the electronic structure varies significantly throughout the reaction and when electronic excited states are involved. Multireference methods, such as complete active space self-consistent field (CASSCF), can handle these multiconfigurational situations. However, even if the size of the needed active space is affordable, in many cases, the active space does not change consistently from reactant to product, causing discontinuities in the potential energy surface. The localized active space SCF (LASSCF) is a cheaper alternative to CASSCF for strongly correlated systems with weakly correlated fragments. The method is used for the first time to study a chemical reaction, namely the bond dissociation of a mono-, di-, and triphenylsulfonium cation. LASSCF calculations generate smooth potential energy scans more easily than the corresponding, more computationally expensive CASSCF calculations while predicting similar bond dissociation energies. Our calculations suggest a homolytic bond cleavage for di- and triphenylsulfonium and a heterolytic pathway for monophenylsulfonium.