Potential-Energy Curves for the Ground and Several Electronic States of NdO and NdS.

Potential energy curves (PECs) were calculated for 21 and 18 electronic states of NdO and NdS molecules, respectively. In each case, static electron correlation effects were described by incomplete model space multiconfiguration self-consistent field wave functions based on an active space that included the most important valence orbitals. Dynamic electron correlation was included by the multireference second-order generalized Van Vleck perturbation theory method. Scalar-relativistic contributions were included by the effective core potential approach, using def2-TZVPP basis sets. Spin-dependent relativistic corrections were determined to be small and negligible for the Nd atom and so were not included in the calculations. The 21 and 18 electronic states of NdO and NdS were predicted to be in the excitation energy range of ∼3.2 and ∼2.7 eV, respectively. The ground electronic states of NdO and NdS were determined as 15H (6s4fσ4fϕ4fδ) and 15H (4fϕ4fπ4fπ6s), with spectroscopic constants: bond length Re = 1.780 and 2.325 Å, and harmonic frequency ωe = 891 and 538 cm-1, respectively.

Exploring the biointerfaces: ab initio investigation of nano-montmorillonite clay, and its interaction with unnatural amino acids.

We investigated the interaction between biomimetic Fe and Mg co-doped montmorillonite nanoclay and eleven unnatural amino acids. Employing three different functionals (PBE-GGA, PBE-GGA + U, and HSE06), we examined the clay's structural, electronic, and magnetic properties. Our results revealed the necessity of using PBE-GGA + U with U ≥ 4 eV to accurately describe key clay properties. We identified amino acids that strongly interacted with the clay surface, with steric orientation playing a crucial role in facilitating binding. Our DFT calculations highlighted significant electrostatic interactions between the amino acids and the clay slab, with the amino group's predominant role in this interaction. These findings hold promise for designing amino acids for clay-amino acid systems, leading to innovative bio-material composites for various applications. Additionally, our ab-initio molecular dynamics simulations confirmed the stability of clay-amino acid systems under ambient conditions, and the introduction of an implicit water solvent enhanced the binding energy of amino acids on the clay surface.

Riemannian Trust Region Method for Minimization of the Fourth Central Moment for Localized Molecular Orbitals.

The importance of localized molecular orbitals (MOs) in correlation treatments beyond mean-field calculation and in the illustration of chemical bonding (and antibonding) can hardly be overstated. However, the generation of orthonormal localized occupied MOs is significantly more straightforward than obtaining orthonormal localized virtual MOs. Orthonormal MOs allow facile use of highly efficient group theoretical methods (e.g., graphical unitary group approach) for calculation of Hamiltonian matrix elements in multireference configuration interaction calculations (such as MRCISD) and in quasi-degenerate perturbation treatments, such as the Generalized Van Vleck Perturbation Theory. Moreover, localized MOs can elucidate qualitative understanding of bonding in molecules, in addition to high-accuracy quantitative descriptions. We adopt the powers of the fourth moment cost function introduced by Jørgensen and coworkers. Because the fourth moment cost functions are prone to having multiple negative Hessian eigenvalues when starting from easily available canonical (or near-canonical) MOs, standard optimization algorithms can fail to obtain the orbitals of the virtual or partially occupied spaces. To overcome this drawback, we applied a trust region algorithm on an orthonormal Riemannian manifold with an approximate retraction from the tangent space built into the first and second derivatives of the cost function. Moreover, the Riemannian trust region outer iterations were coupled to truncated Conjugate Gradient inner loops, which avoided any costly solutions of simultaneous linear equations or eigenvector/eigenvalue solutions. Numerical examples are provided on model systems, including the high-connectivity H10 set in 1-, 2-, and 3-dimensional arrangements, and on a chemically realistic description of cyclobutadiene (c-C4H4) and the propargyl radical (C3H3). In addition to demonstrating the algorithm on occupied and virtual blocks of orbitals, the method is also shown to work on the active space at the MCSCF level of theory.

Theoretical Calculations of the 242 nm Absorption of Propargyl Radical.

The propargyl radical, the most stable isomer of neutral C3H3, is important in combustion reactions, and a number of spectroscopic and reaction dynamics studies have been performed over the years. However, theoretical calculations have never been able to find a state that can generate strong absorption around 242 nm as seen in experiments. In this study, we calculated the low-lying electronic energy levels of the propargyl radical using the highly accurate multireference configuration interaction singles and doubles method with triples and quadruples treated perturbatively [denoted as MRCISD(TQ)]. Calculations indicate that this absorption can be attributed to a Franck-Condon-allowed electronic transition from the ground 2B1 state to the Rydberg-like excited state 12A1. Further insight into the behavior of the multireference perturbative theory methods, GVVPT2 and GVVPT3, on a very challenging system are also obtained.

Low-Lying Electronic States of the Nickel Dimer.

The generalized Van Vleck second order multireference perturbation theory (GVVPT2) method was used to investigate the low-lying electronic states of Ni2. Because the nickel atom has an excitation energy of only 0.025 eV to its first excited state (the least in the first row of transition elements), Ni2 has a particularly large number of low-lying states. Full potential energy curves (PECs) of more than a dozen low-lying electronic states of Ni2, resulting from the atomic combinations 3F4 + 3F4 and 3D3 + 3D3, were computed. In agreement with previous theoretical studies, we found the lowest lying states of Ni2 to correlate with the 3D3 + 3D3 dissociation limit, and the holes in the d-subshells were in the subspace of delta orbitals (i.e., the so-dubbed δδ-states). In particular, the ground state was determined as X 1Γg and had spectroscopic constants: bond length (R e) = 2.26 Å, harmonic frequency (ωe) = 276.0 cm-1, and binding energy (D e) = 1.75 eV; whereas the 1 1Σg + excited state (with spectroscopic constants: R e = 2.26 Å, ωe = 276.8 cm-1, and D e = 1.75) of the 3D3 + 3D3 dissociation channel lay at only 16.4 cm-1 (0.002 eV) above the ground state at the equilibrium geometry. Inclusion of scalar relativistic effects through the spin-free exact two component (sf-X2C) method reduced the bond lengths of both of these two states to 2.20 Å, and increased their binding energies to 1.95 eV and harmonic frequencies to 296.0 cm-1 for X 1Γg and 297.0 cm-1 for 1 1Σg +. These values are in good agreement with experimental values of R e = 2.1545 ± 0.0004 Å, ωe = 280 ± 20 cm-1, and D 0 = 2.042 ± 0.002 eV for the ground state. All states considered within the 3F4 + 3F4 dissociation channel proved to be energetically high-lying and van der Waals-like in nature. In contrast to most previous theoretical studies of Ni2, full PECs of all considered electronic states of the molecule were produced.

Further Development of iCIPT2 for Strongly Correlated Electrons.

The efficiency of the recently proposed iCIPT2 [iterative configuration interaction (iCI) with selection and second-order perturbation theory (PT2); J. Chem. Theory Comput. 2020, 16, 2296] for strongly correlated electrons is further enhanced (by up to 20×) by using (1) a new ranking criterion for configuration selection, (2) a new particle-hole algorithm for Hamiltonian construction over randomly selected configuration state functions (CSF), and (3) a new data structure for the quick sorting of the variational and first-order interaction spaces. Meanwhile, the memory requirement is also significantly reduced. As a result, this improved implementation of iCIPT2 can handle 1 order of magnitude more CSFs than the previous version, as revealed by taking the chromium dimer and an iron-sulfur cluster, [Fe2S2(SCH3)]42-, as examples.

The Ground State Electronic Energy of Benzene.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

Iterative Configuration Interaction with Selection.

Even when starting with very poor initial guess, the iterative configuration interaction (iCI) approach [J. Chem. Theory Comput. 12, 1169 (2016)] for strongly correlated electrons can converge from above to full CI (FCI) very quickly by constructing and diagonalizing a very small Hamiltonian matrix at each macro/micro-iteration. However, as a direct solver of the FCI problem, iCI is computationally very expensive. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and hence do not contribute discernibly to the correlation energy. The real questions are as follows: (a) how to identify those important configurations as early as possible in the calculation and (b) how to account for the residual contributions of those unimportant configurations. It is generally true that if a high-quality yet compact variational space can be determined for describing static correlation, a low-order treatment of the residual dynamic correlation would then be sufficient. While this is common to all selected CI schemes, the "iCI with selection" scheme presented here has the following distinctive features: (1) the full spin symmetry is always maintained by taking configuration state functions (CSF) as the many-electron basis. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFGs) that are used as the organizing units. (3) Given a coefficient pruning-threshold Cmin (which determines the size of the variational space for static correlation), the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration, for the growth of the wave function, the first-order interacting space is decomposed into disjoint subspaces so as to reduce memory requirement on the one hand and facilitate parallelization on the other hand. (5) Upper bounds (which involve only two-electron integrals) for the interactions between doubly connected oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon convergence of the static correlation for a given Cmin, dynamic correlation is estimated using the state-specific Epstein-Nesbet second-order perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated numerically using benchmark examples, including C2, O2, Cr2, and C6H6.

iVI: An iterative vector interaction method for large eigenvalue problems.

Based on the generic "static-dynamic-static" framework for strongly coupled basis vectors (Liu and Hoffman, Theor. Chem. Acc. 2014, 133, 1481), an iterative Vector Interaction (iVI) method is proposed for computing multiple exterior or interior eigenpairs of large symmetric/Hermitian matrices. Although it works with a fixed-dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The efficacy of iVI is demonstrated by taking both mathematical and physical matrices as examples. © 2017 Wiley Periodicals, Inc.

Simultaneous quantitation of the BACE1 inhibitor AZD3293 and its metabolite AZ13569724 in human matrices by LC-MS/MS.

AIM: AZD3293 is a novel BACE1 inhibitor in Phase III development for Alzheimer's disease. Sensitive and robust bioanalytical methods were required to quantitate AZD3293 and its metabolite AZ13569724 in human biological matrices. METHODOLOGY/RESULTS: Human plasma was prepared by protein precipitation. Linearity for both analytes was in the range of 0.5-500 ng/ml with up to 100-fold dilution. Plasma ultrafiltrate samples were prepared using Centrifree® ultrafiltration device. Urine and CSF samples were analyzed directly after dilution. A 27% decrease in AZD3293 concentrations in the CSF collection apparati was found due to nonspecific binding. Incurred sample reanalysis was acceptable. CONCLUSION: Methods for simultaneous quantitation of AZD3293 and its metabolite AZ13569724 in human biological matrices have been validated and successfully applied to clinical studies.

Accurate Dissociation of Chemical Bonds Using DFT-in-DFT Embedding Theory with External Orbital Orthogonality.

Our recent density functional theory (DFT)-in-DFT embedding protocol, which enforces intersubsystem (or external orbital) orthogonality, is used for the first time to investigate covalent bond dissociation and is shown to do so accurately. Full potential energy curves for the dissociation of a H-O bond in H2O and the C-C bond in H3C-CH3 have been constructed using the new embedding method, as have the challenging ionic bonds in LiH and LiF, and were found to match the reference Kohn-Sham (KS)-DFT curves to at least one part in 106. The added constraint of external orbital orthogonality allows for the formulation of an embedding protocol that does not rely on approximate kinetic energy functionals for the evaluation of the so-called nonadditive kinetic potential, does not introduce compensatory potentials, and does not require a total system calculation at any stage. The present work extends the demonstrated applicability of the external orthogonality variant of embedding theory by more than a factor of 2 to the interaction strength range of strong single bonds. In particular, it is demonstrated that homolytic cleavage of both covalent and ionic bonds into radicals can be accomplished.

iCI: Iterative CI toward full CI.

It is shown both theoretically and numerically that the minimal multireference configuration interaction (CI) approach [Liu, W.; Hoffmann, M. R. Theor. Chem. Acc. 2014, 133, 1481] converges quickly and monotonically from above to full CI by updating the primary, external, and secondary states that describe the respective static, dynamic, and again static components of correlation iteratively, even when starting with a rather poor description of a strongly correlated system. In short, the iterative CI (iCI) is a very effective means toward highly correlated wave functions and, ultimately, full CI.

Competitive excited-state single or double proton transfer mechanisms for bis-2,5-(2-benzoxazolyl)-hydroquinone and its derivatives.

The excited state intramolecular proton transfer (ESIPT) mechanisms of 2-(2-hydroxyphenyl)benzoxazole (HBO), bis-2,5-(2-benzoxazolyl)-hydroquinone (BBHQ) and 2,5-bis(5'-tert-butyl-benzoxazol-2'-yl)hydroquinone (DHBO) have been investigated using time-dependent density functional theory (TDDFT). The calculated vertical excitation energies based on the TDDFT method reproduced the experimental absorption and emission spectra well. Three kinds of stable structures were found on the S1 state potential energy surface (PES). A new ESIPT mechanism that differs from the one proposed previously (Mordzinski et al., Chem. Phys. Lett., 1983, 101, 291. and Lim et al., J. Am. Chem. Soc., 2006, 128, 14542.) is proposed. The new mechanism includes the possibility of simultaneous double proton transfer, or successive single transfers, in addition to the accepted single proton transfer mechanism. Hydrogen bond strengthening in the excited state was based on primary bond lengths, angles, IR vibrational spectra and hydrogen bond energy. Intramolecular charge transfer based on the frontier molecular orbitals (MOs) also supports the proposed mechanism of the ESIPT reaction. To further elucidate the proposed mechanism, reduced dimensionality PESs of the S0 and S1 states were constructed by keeping the O-H distance fixed at a series of values. The potential barrier heights among the local minima on the S1 surface imply competitive single and double proton transfer branches in the mechanism. Based on the new ESIPT mechanism, the observed fluorescence quenching can be satisfactorily explained.

New excited-state proton transfer mechanisms for 1,8-dihydroxydibenzo[a,h]phenazine.

The excited state intramolecular proton transfer (ESIPT) mechanisms of 1,8-dihydroxydibenzo[a,h]phenazine (DHBP) in toluene solvent have been investigated based on time-dependent density functional theory (TD-DFT). The results suggest that both a single and double proton transfer mechanisms are relevant, in constrast to the prediction of a single one proposed previously (Piechowska et al. J. Phys. Chem. A 2014, 118, 144-151). The calculated results show that the intramolecular hydrogen bonds were formed in the S0 state, and upon excitation, the intramolecular hydrogen bonds between -OH group and pyridine-type nitrogen atom would be strengthened in the S1 state, which can facilitate the proton transfer process effectively. The calculated vertical excitation energies in the S0 and S1 states reproduce the experimental UV-vis absorption and fluorescence spectra well. The constructed potential energy surfaces of the S0 and S1 states have been used to explain the proton transfer process. Four minima have been found on the S1 state surface, with potential barriers between these excited-state minima of less than 10 kcal/mol, which supports concomitant single and double proton transfer mechanisms. In addition, the fluorescence quenching can be explained reasonably based on the proton transfer process.

Use of density functional theory orbitals in the GVVPT2 variant of second-order multistate multireference perturbation theory.

A new variation of the second-order generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structure is suggested. In contrast to the established procedure, in which CASSCF or MCSCF orbitals are first obtained and subsequently used to define a many-electron model (or reference) space, the use of an orbital space obtained from the local density approximation (LDA) variant of density functional theory is considered. Through a final, noniterative diagonalization of an average Fock matrix within orbital subspaces, quasicanonical orbitals that are otherwise indistinguishable from quasicanonical orbitals obtained from a CASSCF or MCSCF calculation are obtained. Consequently, all advantages of the GVVPT2 method are retained, including use of macroconfigurations to define incomplete active spaces and rigorous avoidance of intruder states. The suggested variant is vetted on three well-known model problems: the symmetric stretching of the O-H bonds in water, the dissociation of N2, and the stretching of ground and excited states C2 to more than twice the equilibrium bond length of the ground state. It is observed that the LDA-based GVVPT2 calculations yield good results, of comparable quality to conventional CASSCF-based calculations. This is true even for the C2 model problem, in which the orbital space for each state was defined by the LDA orbitals. These results suggest that GVVPT2 can be applied to much larger problems than previously accessible.

New insights into the dual fluorescence of methyl salicylate: effects of intermolecular hydrogen bonding and solvation.

In this paper, we propose a new and complete mechanism for dual fluorescence of methyl salicylate (MS) under different conditions using a combined experimental (i.e., steady-state absorption and emission spectra and time-resolved fluorescence spectra) and theoretical (i.e., time-dependent density function theory) study. First, our theoretical study indicates that the barrier height for excited state intramolecular proton transfer (ESIPT) reaction of ketoB depends on the solvent polarity. In nonpolar solvents, the ESIPT reaction of ketoB is barrierless; the barrier height will increase with increasing solvent polarity. Second, we found that, in alcoholic solvents, intermolecular hydrogen bonding plays a more important role. The ketoB form of MS can form two hydrogen bonds with alcoholic solvents; one will facilitate ESIPT and produce the emission band in the blue region; the other one precludes ESIPT and produces the emission band in the near-UV region. Our proposed new mechanism can well explain previous results as well as our new experimental results.

Density differences in embedding theory with external orbital orthogonality.

First results on electron densities and energies for a number of molecular complexes with different interaction strengths (ranging from ca. 0.3 to 40 kcal/mol), obtained using our recently introduced DFT-in-DFT embedding equations (i.e., Kohn-Sham equations with constrained electron density (KSCED) and external orbital orthogonality (ext orth), KSCED(x, ext orth), where x denotes the single particle support: monomer (m); supermolecular (s); or extended monomer (e)) are compared with densities from supermolecular Kohn-Sham (KS)-DFT calculations and traditional DFT-in-DFT results. Because our methodology does not rely on error-prone potentials that are not present in supermolecular KS-DFT calculations, it allows DFT-in-DFT calculations to achieve much higher accuracy than previous protocols of DFT-in-DFT that employed such potentials. It is shown that whereas conventional DFT-in-DFT embedding theory leads to errors in the electron density at the boundary between subsystems, the situation is remedied when orbital orthogonality between subsystems (i.e., external orthogonality) is enforced. Our approach reproduces KS-DFT total energies at least to the seventh decimal place (and exactly at most geometries) for the tested systems. Potential energy curves (PECs) of the separation of some of the tested systems into fragments are calculated. PECs, obtained with the new equations, using the usual Kohn-Sham equations with constrained electron density and supermolecular basis expansion [KSCED(s, ext orth, v(T) = 0), where v(T) is the nonadditive kinetic potential] were found to be virtually identical to those from conventional KS-DFT; equilibrium distances and interaction energies were reproduced to all reported digits for both local density approximation (LDA) and generalized gradient approximation (GGA) functionals. As an additional approximation, an alternative one-particle space (to the common monomer or supermolecular spaces) in which KS orbitals of a subsystem are expanded is introduced. This expansion, which we refer to as the extended monomer expansion [e.g., KSCED(e)], includes basis functions centered on atom(s) of the complementary subsystem in the interfacial region. Density differences and PECs obtained with the new equations and new one-particle space [i.e., KSCED(e, ext orth, v(T) = 0)] were closely related to those obtained from KSCED(s, ext orth, v(T) = 0). The new approach does not require any supermolecular calculations.

Relativistic GVVPT2 multireference perturbation theory description of the electronic states of Y2 and Tc2.

The multireference generalized Van Vleck second-order perturbation theory (GVVPT2) method is used to describe full potential energy curves (PECs) of low-lying states of second-row transition metal dimers Y(2) and Tc(2), with scalar relativity included via the spin-free exact two-component (sf-X2C) Hamiltonian. Chemically motivated incomplete model spaces, of the style previously shown to describe complicated first-row transition metal diatoms well, were used and again shown to be effective. The studied states include the previously uncharacterized 2(1)Σ(g)(+) and 3(1)Σ(g)(+) PECs of Y(2). These states, together with 1(1)Σ(g)(+), are relevant to discussion of controversial results in the literature that suggest dissociation asymptotes that violate the noncrossing rule. The ground state of Y(2) was found to be X(5)Σ(u)(­) (similar to Sc(2)) with bond length R(e) = 2.80 Å, binding energy D(e) = 3.12 eV, and harmonic frequency ω(e) = 287.2 cm(­1), whereas the lowest 1(1)(g)(+) state of Y(2) was found to lie 0.67 eV above the quintet ground state and had spectroscopic constants R(e) = 3.21 Å, D(e) = 0.91 eV, and ω(e) = 140.0 cm(­1). Calculations performed on Tc(2) include study of the previously uncharacterized relatively low-lying 1(5)Σ(g)(+) and 1(9)Σ(g)(+) states (i.e., 0.70 and 1.84 eV above 1(1)Σ(g)(+), respectively). The ground state of Tc(2) was found to be X(3)Σ(g)(­) with R(e) = 2.13 Å, D(e) = 3.50 eV, and ω(e) = 336.6 cm(­1) (for the most stable isotope, Tc-98) whereas the lowest (1)Σ(g)(+) state, generally accepted to be the ground state symmetry for isovalent Mn(2) and Re(2), was found to lie 0.47 eV above the X(3)Σ(g)(­) state of Tc(2). The results broaden the range of demonstrated applicability of the GVVPT2 method.