Molecular Orbital Coefficients Research Articles

Direct Unconstrained Optimization of Molecular Orbital Coefficients in Density Functional Theory.

One-electron orbitals in Kohn-Sham density functional theory (DFT) are typically constrained to be orthogonal during their variational optimization, leading to elaborate parameterization of the orbitals and complicated optimization algorithms. This work shows that orbital optimization can be performed with nonorthogonal orbitals if the DFT energy functional is augmented with a term that penalizes linearly dependent states. This approach, called variable-metric self-consistent field (VM SCF) optimization, allows us to use molecular orbital coefficients, natural descriptors of one-electron orbitals, as independent variables in a direct, unconstrained minimization, leading to very simple closed-form expressions for the electronic gradient and Hessian. It is demonstrated that efficient convergence of the VM SCF procedure can be achieved with a basic preconditioned conjugate gradient algorithm for a variety of systems, including challenging narrow-gap systems and spin-pure two-determinant states of singlet diradicals. This simple reformulation of the variational procedure can be readily extended to electron correlation methods with multiconfiguration states and to the optimization of excited-state orbitals.

Investigations on the EPR parameters and local structures for the substitutional Ti3+ and W5+ centers in stishovite

Abstract Local structures and electron paramagnetic resonance (EPR) parameters (g factors g x , g y , and g z ) for the substitutional Ti3+ and W5+ centers in stishovite are theoretically investigated by using the high-order perturbation formulas of these parameters for a d1 ion in rhombically compressed octahedra. In the calculation formulas, the related molecular orbital coefficients are obtained from the cluster approach, and the relevant crystal-field (CF) parameters are determined from the superposition model, which enables to connect these CF parameters and, hence, the studied g factors with the local structures of the Ti3+ and W5+ centers in stishovite. Based on the calculations, the impurity–ligand bond lengths parallel and perpendicular to the C 2-axis are found to be R′|| (≈1.751 and 1.717 Å) and R′⊥ (≈1.788 and 1.806 Å) with the planar bond angles θ′ (≈89.0° and 88.2°) for the studied [TiO6]9− and [WO6]7− clusters, respectively. The calculated results are in good agreement with the experimental data, and the validity of the results is discussed.

Variational Lang-Firsov Approach Plus Møller-Plesset Perturbation Theory with Applications to Ab Initio Polariton Chemistry.

We apply the Lang-Firsov (LF) transformation to electron-boson coupled Hamiltonians and variationally optimize the transformation parameters and molecular orbital coefficients to determine the ground state. Møller-Plesset (MP-n, with n = 2 and 4) perturbation theory is then applied on top of the optimized LF mean-field state to improve the description of electron-electron and electron-boson correlations. The method (LF-MP) is applied to several electron-boson coupled systems, including the Hubbard-Holstein model, diatomic molecule dissociation (H2, HF), and the modification of proton transfer reactions (malonaldehyde and aminopropenal) via the formation of polaritons in an optical cavity. We show that with a correction for the electron-electron correlation, the method gives quantitatively accurate energies comparable to that by exact diagonalization or coupled-cluster theory. The effects of multiple photon modes, spin polarization, and the comparison to the coherent state MP theory are also discussed.

Revisiting Kassman’s path deletion procedure for the eigenvector coefficients of molecular graphs

Kassman’s path deletion procedure for the determination of eigenvector polynomials (EPs) and hence the eigenvector or molecular orbital (MO) coefficients of a molecular graph is revisited with required proofs and illustrations. As EPs vanish for n-fold degenerate eigenvalues, the calculation of eigenvector (MO) coefficients for such an eigenvalue requires (n-1)-th derivative of each EP. The eigenvector coefficients for other degenerate eigenvalues are then obtained by exploiting the inherent symmetry of the molecular graph. The method of symmetry-factorisation followed by the path deletion procedure makes such calculations straightforward and simple as symmetry-factorisation distributes the degenerate eigenvalues (if there are any) in the fragmented graphs and the problem of degeneracy is thus avoided in calculating the MO coefficients for the individual fragments. The procedure is illustrated with the molecular graphs having non-degenerate and degenerate eigenvalues.

CoeffNet: predicting activation barriers through a chemically-interpretable, equivariant and physically constrained graph neural network.

Activation barriers of elementary reactions are essential to predict molecular reaction mechanisms and kinetics. However, computing these energy barriers by identifying transition states with electronic structure methods (e.g., density functional theory) can be time-consuming and computationally expensive. In this work, we introduce CoeffNet, an equivariant graph neural network that predicts activation barriers using coefficients of any frontier molecular orbital (such as the highest occupied molecular orbital) of reactant and product complexes as graph node features. We show that using coefficients as features offer several advantages, such as chemical interpretability and physical constraints on the network's behaviour and numerical range. Model outputs are either activation barriers or coefficients of the chosen molecular orbital of the transition state; the latter quantity allows us to interpret the results of the neural network through chemical intuition. We test CoeffNet on a dataset of SN2 reactions as a proof-of-concept and show that the activation barriers are predicted with a mean absolute error of less than 0.025 eV. The highest occupied molecular orbital of the transition state is visualized and the distribution of the orbital densities of the transition states is described for a few prototype SN2 reactions.

Investigation of the structural, mechanical, radiation and neutron shielding properties of the TeO2-B2O3-Li2O-MoO3-CuO glass system

In this study, the structural, mechanical, radiation and neutron shielding properties of (78-x)(0.4TeO2-0.6B2O3)− 20Li2O-xMoO3-2CuO glass system, were investigated. A variety of characterisation methods, including optical absorption spectroscopy, FTIR, EPR, and X-ray diffraction, were used to examine the structural characteristics. Molecular orbital coefficients were calculated from EPR and optical absorption measurements. EPR lines of both Cu2+ and Mo5+ ions were observed in the EPR spectra. The mechanical properties were assessed through experimental measurements, while the elastic properties were evaluated using the semi-empirical approaches of the Makishima and Mackenzie model, along with the bond compression model. The inclusion of 4% MoO3 led to noteworthy enhancements in both hardness and fracture toughness. Hardness increased from 4.364 to 4.664 GPa, and fracture toughness improved from 0.980 to 1.226 MPa.m1/2. The mass attenuation coefficients (MAC), mean free paths (MFP), half-value layers (HVL), and effective atomic numbers (Zeff) were measured in the energy range of 59.54–661.62 keV. The measurement of equivalent dose rates resulting from the absorption of fast neutrons was conducted utilizing a 241Am-Be fast neutron source with an activity of 10 mCi. The exposure buildup factor (EBF) and the fast neutron removal cross section (ΣR) were therotically calculated. The potential suitability of glasses for nuclear security applications was assessed by evaluating their proton and alpha shielding properties. The study found that glasses containing higher amounts of TeO2 and MoO3, within the TeO2-B2O3-Li2O-MoO3-CuO composition, demonstrated enhanced capabilities for shielding against radiation and neutrons.

DFT study on the polymerization mechanism of aleuritic acid and jalaric acid in shellac molecule

Shellac is a natural resin composed of a complex mixture of hydroxy aliphatic acids, primarily aleuritic acid (AA), and sesquiterpenoid acids such as jalaric acid (JA). The paper puts forth valuable information on the polymerization mechanism considering AA and JA using Gaussian 16.0 software. Computations of energy, thermochemical values, and molecular orbital coefficients have been done using both Hartree-Fock (HF) and Density Functional Theory (DFT) to establish the mechanism. Global reactivity parameter study revealed that monomers of the shellac are hard whereas the polymer units are soft. HOMO-LUMO, ESP and theoretical FTIR results are coherent with the previously reported works for the prediction of possible polymeric species present in the shellac along with their thermodynamic stability. This is the first attempt to predict the linkages in shellac resin. This study helps understand the mechanism of formation of lac polymer and also highlights the associated properties of shellac.

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects.

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

Studies on the EPR parameters and local angular distortion for the tetragonal Cu2+ center in CaWO4 crystal.

The electron paramagnetic resonance (EPR) parameters-g factors gi (i = || and ⊥) and hyperfine structure constants Ai (M) and Ai (N), with M and N belonging to isotopes 63 Cu2+ and 65 Cu2+ -and local structure of Cu2+ ion occupying W6+ site in CaWO4 crystal are theoretically studied based on the perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated tetrahedra. In these formulas, the ligand orbital (LO) and spin-orbit coupling (SOC) contributions are included due to the shorter impurity-ligand distance R (≈1.83 Å) and hence the strong covalency of the studied [CuO4 ]6- cluster, and the related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way; meanwhile, the required crystal field (CF) parameters for the tetragonally distorted tetrahedron (TDT) are estimated from the superposition model and the local structure of the impurity Cu2+ center. According to the calculation, the bond angle θ between the four equivalent Cu2+ -O2- bonds and the C4 axis in the CaWO4 :Cu2+ is found to be about 2.1° smaller than that (θ0 ≈ 54.74°) for an ideal tetrahedron due to the Jahn-Teller (JT) effect and the size mismatch. The fitted results agree well with the observed values, and the validity of the present assignment for the local structure of the Cu2+ center is also discussed.

Ferrocenoyl-adenines: substituent effects on regioselective acylation.

A series of N6-substituted adenine–ferrocene conjugates was prepared and the reaction mechanism underlying the synthesis was explored. The SN2-like reaction between ferrocenoyl chloride and adenine anions is a regioselective process in which the product ratio (N7/N9-ferrocenoyl isomers) is governed by the steric property of the substituent at the N6-position. Steric effects were evaluated by using Charton (empirical) and Sterimol (computational) parameters. The bulky substituents may shield the proximal N7 region of space, which prevents the approach of an electrophile towards the N7 atom. As a consequence, the formation of N7-isomer is a kinetically less feasible process, i.e., the corresponding transition state structure increases in relative energy (compared to the formation of the N9-isomer). In cases where the steric hindrance is negligible, the electronic effect of the N6-substituent is prevailing. That was supported by calculations of Fukui functions and molecular orbital coefficients. Both descriptors indicated that the N7 atom was more nucleophilic than its N9-counterpart in all adenine anion derivatives. We demonstrated that selected substituents may shift the acylation of purines from a regioselective to a regiospecific mode.

Orbital Mixer: Using Atomic Orbital Features for Basis-Dependent Prediction of Molecular Wavefunctions.

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous studies focuses on generating predictions for only a fixed set of properties. Recent lines of research instead aim to explicitly learn the electronic structure via molecular wavefunctions, from which other quantum chemical properties can be directly derived. While previous methods generate predictions as a function of only the atomic configuration, in this work we present an alternate approach that directly purposes basis-dependent information to predict molecular electronic structure. Our model, Orbital Mixer, is composed entirely of multi-layer perceptrons (MLPs) using MLP-Mixer layers within a simple, intuitive, and scalable architecture that achieves competitive Hamiltonian and molecular orbital energy and coefficient prediction accuracies compared to the state-of-the-art.

Structural characterization (XRD, FTIR) and magnetic studies of Cd(II)-Sulfamethoxazole-2,2′-bipyridine: DFT and Hirshfeld Surface Analysis

New cadmium(II) complex have been synthesized by the reaction of nitrogen donor ligand sulfamethoxazole (smtxH: 4-amino-N-(5-methylisoxazol-3-yl)benzenesulfonamide) and nötr ligand 2,2′-bipyridine (bipy). The resulting compound is a neutral [The Cd(smtx)2(bipy)2•H2O] complex. The structure of the metal complex have been elucidated by single-crystal X-ray diffraction. The central Cd(II) ion is coordinated by two monodentate sulfamethoxazole anions together with two bidentate bipy ligand forming the octahedral geometry. The theoretical optimized geometrical parameters is calculated by using the Density Functional Theory (DFT) with the B3LYP method at 6–311G(d,p) bases set. Observed and calculated IR frequencies were found to be agreement. Hirshfeld surface analysis has been performed to study the nature of intermolecular interactions within the crystal structure and the finger- print plots, molecular surface contours. Molecular orbital coefficients were obtained using EPR and UV data. The thermal behavior of compound has been investigated.Cd(II)-smtx-2,2′-bipyridine molecule was synthesized. The complex was characterized by FT-IR, XRD. Molecular orbital coefficients were calculated using data from EPR and UV. With the help of Hirshfeld surface analysis, the intermolecular interactions in the crystal structure were interpreted by reducing them to fingerprint graphics. The TGA curves of compound have been examined. Structural and optical properties of the complex were further analyzed by quantum chemical calculations performed using DFT-TDDFT/B3LYP method in combination with LANL2DZ basis set.

Molecular Structures and Redox Properties of Homoleptic Aluminum(III) Complexes with Azobisphenolate (azp) Ligands

To elucidate the oxidation behavior of the 2,2′-azobisphenolate (azp) ligand, a series of homoleptic 1:2 AlIII complexes of four azp derivatives (L1) with 5,5′-dichloro-, 5,5′-dimethyl-, 5,5′-di-t-butyl-, 3,3′,5,5′-tetramethyl-substituents and of one imino derivative (L2) were synthesized and obtained as TPP[Al(L)2]·solvent (TPP = tetraphenylphosphonium ion). The X-ray crystal structure analyses showed that the two ONO-tridentate ligands were meridionally coordinated to a central AlIII ion in an almost perpendicular manner to give a homoleptic octahedral coordination structure in all the AlIII complexes. The proton nuclear magnetic resonance spectra suggested that all the AlIII complexes retained the homoleptic coordination structure in solution. From the cyclic voltammetry measurements in dichloromethane solutions, all the AlIII complexes with the azp ligands showed two partially reversible oxidation waves, and an additional reversible or partially reversible reduction wave. The substitution effects on the first oxidation and reduction peak potentials were revealed in the AlIII complexes with the azp ligands. On the other hand, the imino complex showed a partially reversible oxidation wave accompanying a film deposition. The density functional theory (DFT) calculations indicated that the molecular orbital (MO) coefficients of the frontier MOs in the AlIII complexes were present on the ligands and were absent on the AlIII ion. These results confirmed that the azp ligands are susceptible to oxidation and can give a relatively stable oxidation species depending upon substituent effects.

Synthesis, spectroscopic and evaluation of anticancer activity of new hydrazone-containing dipyrromethane using experimental and theoretical approaches

The purpose of this work is to study in-vitro anticancer activity, chemical reactivity and non-linear optical properties of newly synthesized and characterized hydrazide-hydrazone linkage containing dipyrromethane derivatives. The appearance of singlet at 5.9, 6.9, 5.0, 5.8 and 3.7 ppm of meso–proton designates formation of products (3a-3e). All synthesized compounds have been well characterized by modern spectroscopic (1H and 13C NMR, UV–Visible, FT–IR) techniques. TD–DFT has been used to calculate oscillatory strength (f) and wavelength absorption maxima (λmax), electronic excitations and their molecular orbital coefficients and molecular plots analysis assigns nature of both electronic excitations as π →π* and n →π*. The computed first hyperpolarizability (β0 =14.38, 17.34, 15.47. 19.21, 22.21 × 10–30esu) evaluate the molecules (3a-3e) to be suitable for non–linear optical (NLO) response. The p–Nitroaniline(p–NA), is used a reference molecule having β0 = 11.54 × 10–30 esu). Compounds 3a, 3b, 3c, 3d and 3e exhibited moderate to very high anti-cancer activity against HL-60 and HCT-116, with percentage inhibition of 65.02%, 76.54%, 80.47%, 68.76%, 53.04% and 66.87%, 79.31%, 79.58%, 63.66%, 53.66, respectively; the reference 5-fluorouracil had aninhibitory percentage of 86.53% and 70.54%.

Theoretical studies on the EPR parameters and local structure of Cu2+ center in [Co(nicotinamide)2(H2O)4](saccharinate)2 crystal

Local structure and electron paramagnetic resonance (EPR) parameters for Cu2+ center in [Co(nicotinamide)2(H2O)4](saccharinate)2 (CoNAS) crystal are theoretically investigated using high-order perturbation formulas for 3d9 ions in rhombically elongated octahedra. In the calculated formulas, the related molecular orbital coefficients are acquired from the superposition model which enables to correlate the crystal field parameters and hence the EPR parameters with the studied Cu2+ center, the admixtures of d-orbitals in the ground state wave function as well as the ligand orbital and spin–orbit coupling contributions are taken into account. Based on the studies, the [CuO4N2]12− cluster of the studied Cu2+ center are found to suffer the axial and perpendicular bond length variations Δz (≈ 0.0612 Å) along z-axis and δr (≈ 0.0360 Å) along x- and y-axes, respectively, due to the Jahn–Teller effect.

Implementation of Relativistic Coupled Cluster Theory for Massively Parallel GPU-Accelerated Computing Architectures.

In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on the electronic structure are included from the outset. In the current work, we thereby focus on exact two-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as the starting point, but it is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program.

Theoretical studies of the EPR parameters and local structures for Ni3+ and Cu2+ centers in MgNH4PO4·6H2O

ABSTRACT The electron paramagnetic resonance (EPR) parameters of the impurity Ni3+ (and Cu2+) in MgNH4PO4·6H2O (MAPH) are theoretically studied from the perturbation formulas for 3d7 (and 3d9) ions under orthorhombically compressed (and elongated) octahedra, respectively. In the above formulas, the related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way. In the calculation model, the impurity Ni3+ and Cu2+ ions were ascribed to occupy the host octahedral Zn2+ site, the required crystal-field parameters are correlated with the local structures of the impurity Ni3+ and Cu2+ in MAPH. Based on calculation, the compressed [NiO6]9- cluster (and elongated [CuO6]10- cluster) are found to suffering the axial compression of 0.051 Å (and elongation of 0.125 Å) along z-axis, meanwhile, the planar bonds are found to experience the relative variations of 0.028 Å (and 0.05 Å), respectively, due to the Jahn–Teller effect. The theoretical EPR parameters based on the above lattice distortions agree well with the experimental data, and the local structures of the Ni3+ and Cu2+ in MAPH are discussed.

The aug-cc-pVTZ-J basis set for the p-block fourth-row elements Ga, Ge, As, Se, and Br.

The aug-cc-pVTZ-J basis set family is extended to include the fourth-row p-block elements Ga, Ge, As, Se, and Br. We use the established approach outlined by Sauer and coworkers (J. Chem. Phys. 115, 1324 [2001], J. Chem. Phys. 133, 054308 [2010], J. Chem. Theory Comput. 7, 4070 [2011], and J. Chem. Theory Comput. 7, 4077 [2011]) where the completely uncontracted aug-cc-pVTZ basis set is saturated with tight s-, p-, d-, and f-functions to form the aug-cc-pVTZ-Juc basis set for the tested elements. The saturation is carried out on the simplest hydrides possible for the tested elements GaH, GeH4 , AsH3 , H2 Se, and HBr until an improvement is less than 0.01% for all s-, p-, and d-functions added. f-Functions are added to an improvement less than or equal to 1.0% due to the computational expense these functions add. The saturated aug-cc-pVTZ-Juc (26s16p12d5f) is then recontracted using the molecular orbital coefficients from self-consistent field calculations on the simple hydrides to improve computational efficiency. During contraction of the basis set, we observe that the linear hydrogen bromide molecule has a slower convergence than the other tested molecules which sets a limit on the accuracy obtained. All calculations with the contracted aug-cc-pVTZ-J [17s10p7d5f] gives results that are within 1.0% of the uncontracted results at considerable computational savings.

Smeared Coulomb potential orbitals: I—asymptotic expansion

We consider an 1-electron model Hamiltonian, whose potential energy corresponds to the Coulomb potential of an infinite wire with charge Z distributed according to a Gaussian function. The time independent Schrödinger equation for this Hamiltonian is solved perturbationally in the asymptotic limit of small amplitude vibration (Gaussian function width close to zero). We propose to use the naturally polarized functions so-obtained, as orbital basis sets for quantum chemical calculations. In particular, they should be well suited to perform electron-nucleus mean field configuration interaction calculations. Since the free-parameters of the model have the remarkable property to factorize the perturbative corrections to the eigenfunctions, these corrective part in factor can be simply added as additional functions to standard basis sets, leaving it to the molecular orbital calculation to optimize the free parameters within molecular orbital coefficients.

Double-Stranded DNA Matrix for Photosensitization Switching

Photosensitization, originated from the activation of triplet states, is the basis of many photodynamic applications, but often competes with a series of nonradiative processes. Herein, we communic...