Enhancing carrier transfer properties of Na-rich anti-perovskites, Na4OM2 with tetrahedral anion groups: an evaluation through first-principles computational analysis.

The practical application of Na-based solid-state electrolytes (SSEs) is limited by their low level of conduction. To evaluate the impact of tetrahedral anion groups on carrier migration, we designed a set of anti-perovskite SSEs theoretically based on the previously reported Na4OBr2, including Na4O(BH4)2, Na4O(BF4)2, and Na4O(AlH4)2. It is essential to note that the excessive radius of anionic groups inevitably leads to lattice distortion, resulting in asymmetric migration paths and a limited improvement in carrier migration rate. Na4O(AlH4)2 provides a clear example of where Na+ migrates in two distinct environments. In addition, due to different spatial charge distributions, the interaction strength between anionic groups and Na+ is different. Strong interactions can cause carriers to appear on a swing, leading to a decrease in conductivity. The low conductivity of Na4O(BF4)2 is a typical example. This study demonstrates that Na4O(BH4)2 exhibits remarkable mechanical and dynamic stability and shows ionic conductivity of 1.09 × 10-4 S cm-1, two orders of magnitude higher than that of Na4OBr2. This is attributed to the expansion of the carrier migration channels by the anion groups, the moderate interaction between carriers and anionic groups, and the "paddle-wheel" effect generated by the anion groups, indicating that the "paddle-wheel" effect is still effective in low-dimensional anti-perovskite structures, in which atoms are arranged asymmetrically.

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules.

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations.

As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747-4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper(II) compound as well as Ln(III) and An(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets.

Machine-learning assisted scheduling optimization and its application in quantum chemical calculations.

Easy and effective usage of computational resources is crucial for scientific calculations, both from the perspectives of timeliness and economic efficiency. This work proposes a bi-level optimization framework to optimize the computational sequences. Machine-learning (ML) assisted static load-balancing, and different dynamic load-balancing algorithms can be integrated. Consequently, the computational and scheduling engine of the ParaEngine is developed to invoke optimized quantum chemical (QC) calculations. Illustrated benchmark calculations include high-throughput drug suit, solvent model, P38 protein, and SARS-CoV-2 systems. The results show that the usage rate of given computational resources for high throughput and large-scale fragmentation QC calculations can primarily profit, and faster accomplishing computational tasks can be expected when employing high-performance computing (HPC) clusters.

New Light on an Old Story: Breaking Kasha's Rule in Phosphorescence Mechanism of Organic Boron Compounds and Molecule Design.

In this work, the phosphorescence mechanism of (E)-3-(((4-nitrophenyl)imino)methyl)-2H-thiochroman-4-olate-BF2 compound (S-BF2) is investigated theoretically. The phosphorescence of S-BF2 has been reassigned to the second triplet state (T2) by the density matrix renormalization group (DMRG) method combined with the multi-configurational pair density functional theory (MCPDFT) to approach the limit of theoretical accuracy. The calculated radiative and non-radiative rate constants support the breakdown of Kasha's rule further. Our conclusion contradicts previous reports that phosphorescence comes from the first triplet state (T1). Based on the revised phosphorescence mechanism, we have purposefully designed some novel compounds in theory to enhance the phosphorescence efficiency from T2 by replacing substitute groups in S-BF2. Overall, both S-BF2 and newly designed high-efficiency molecules exhibit anti-Kasha T2 phosphorescence instead of the conventional T1 emission. This work provides a useful guidance for future design of high-efficiency green-emitting phosphors.

A theoretical study of the electrochemical reduction of CO2 on cerium dioxide supported palladium single atoms and nanoparticles.

Pd/CeO2 catalysts show superior catalytic performance owing to their optimal cycling activity and stability. In this study, single-atom Pd and eight-atom Pd nanoparticle clusters were supported on the surface of CeO2(110) to investigate the effect of loaded-metal size on the catalytic performance of the Pd-CeO2 system for CO2 reduction. We investigated the CO2 reduction reaction (CRR) that produces C1 products (CO, HCOOH, CH3OH, and CH4) on Pd8/CeO2 and Pd/CeO2 by density functional theory. The structures, CO2 adsorption configurations, and CO2 reduction mechanisms of these two electrocatalysts were systematically studied. Subsequently, different reduction pathways on Pd8/CeO2 and Pd/CeO2 were investigated to identify the optimal reaction pathway for further assessment. The results showed that both of these catalysts are more selective towards the production of CH3OH than CH4. Moreover, compared to Pd/CeO2 and Pd4/CeO2 (from a previously reported study) the production of CH3OH via the CRR on Pd8/CeO2 exhibited the lowest limiting potential. These results demonstrate the superiority of Pd8/CeO2 as an electrocatalyst for the electrochemical reduction of CO2 to CH3OH.

Optimizing two-electron repulsion integral calculations with McMurchie-Davidson method on graphic processing unit.

In this article, several optimization methods of two-electron repulsion integral calculations on a graphic processing unit (GPU) are presented. These methods are based on the investigations of the method presented by McMurchie and Davidson (MD). A new Boys function evaluation method for the GPU calculation is introduced. The series summation, the error function, and the finite sum formula method are combined; thus, good performance on the GPU can be achieved. By taking some theoretical study of the McMurchie-Davidson recurrence relations, three major optimization approaches are derived from the deduction of the general term formula for the Hermite expansion coefficient. The three approaches contain a new form of the Hermite expansion coefficients with corresponding recurrence relations, which is more efficient for one-electron integrals and [ss|∗∗] or [∗∗|ss] type two-electron integrals. In addition, a simple yet efficient new recurrence formula for the coefficient evaluation is derived, which is more efficient both in float operations and memory operations than its original one. In average, the new recurrence relation can save 26% float operations and 37% memory operations. Finally, a common sub-expression elimination (CSE) method is implemented. This CSE method is directly generated from some equalities we discovered from the general term formula other than by computer algebra system software. This optimized method achieved up to 3.09 speedups compared to the original MD method on the GPU and up to 92.75 speedups compared to the GAMESS calculation on the central processing unit.

iCAS: Imposed Automatic Selection and Localization of Complete Active Spaces.

It is shown that in the spirit of "from fragments to molecule" for localizing molecular orbitals [J. Chem. Theory Comput. 2011, 7, 3643], a prechosen set of occupied/virtual valence/core atomic/fragmental orbitals can be transformed to an equivalent set of localized occupied/virtual pre-localized molecular orbitals (pre-LMO), which can then be taken as probes to select the same number of maximally matching localized occupied/virtual Hartree-Fock (HF) or restricted open-shell HF (ROHF) molecular orbitals as the initial local orbitals spanning the desired complete active space (CAS). In each cycle of the self-consistent field (SCF) calculation, the CASSCF orbitals can be localized by means of the noniterative "top-down least-change" algorithm for localizing ROHF orbitals [J. Chem. Phys. 2017, 146, 104104] such that the maximum matching between the orbitals of two adjacent iterations can readily be monitored, leading finally to converged localized CASSCF orbitals that overlap most the guess orbitals. Such an approach is to be dubbed as "imposed CASSCF" (iCASSCF or simply iCAS in short) for good reasons: (1) it has been assumed that only those electronic states that have largest projections onto the active space defined by the prechosen atomic/fragmental orbitals are to be targeted. This is certainly an imposed constraint but has wide applications in organic and transition metal chemistry where valence (or core) atomic/fragmental orbitals can readily be identified. (2) The selection of both initial and optimized local active orbitals is imposed from the very beginning by the pre-LMOs (which span the same space as the prechosen atomic/fragmental orbitals). Apart from the (imposed) automation and localization, iCAS has two additional merits: (a) the guess orbitals are guaranteed to be the same for all geometries, for the pre-LMOs do not change in character with geometry and (b) the use of localized orbitals facilitates the SCF convergence, particularly for large active spaces. Both organic molecules and transition-metal complexes are taken as showcases to reveal the efficacy of iCAS.

Quantum Chemical Simulation of the Qy Absorption Spectrum of Zn Chlorin Aggregates for Artificial Photosynthesis.

Zn chlorin (Znchl) is easy to synthesize and has similar optical properties to those of bacteriochlorophyll c in the nature, which is expected to be used as a light-harvesting antenna system in artificial photosynthesis. In order to further explore the optical characteristics of Znchl, various sizes of a parallel layered Znchl-aggregate model and the THF-Znchl explicit solvent monomer model were constructed in this study, and their Qy excited state properties were simulated by using time-dependent density functional theory (TDDFT) and exciton theory. For the Znchl monomer, with a combination of the explicit solvent model and the implicit solvation model based on density (SMD), the calculated Qy excitation energy agreed very well with the experimental one. The Znchl aggregates may be simplified to a Zn36 model to reproduce the experimental Qy absorption spectrum by the Förster coupling theory. The proposed Znchl aggregate model provides a good foundation for the future exploration of other properties of Znchl and simulations of artificial light-harvesting antennas. The results also indicate that J-aggregrates along z-direction, due to intermolecular coordination bonds, are the dominant factor in extending the Qy band of Znchl into the near infrared region.

Theoretical Study of the Anisotropy Spectra of the Valine Zwitterion and Glyceraldehyde.

The electronic absorption (EA), circular dichroism (ECD), and anisotropy spectra of the l-valine zwitterion and d-glyceraldehyde are calculated by time-dependent density functional theory (TDDFT) with the M06-2X and B3LYP functionals. It is found that the absorption and ECD spectra from TDDFT/M06-2X agree well with experimental results measured from the amorphous film of l-valine. Moreover, the calculations reproduce all three major peaks observed in the experimental anisotropy spectra. For d-glyceraldehyde, the TDDFT/M06-2X calculations indicate that the excitation wavelengths of the first excited state of 32 stable conformers distribute from 288 to 322 nm, giving rise to two ECD peaks with opposite signs centered at 288 and 322 nm. The very weak absorption of the first excited state (S1) induces two high peaks in the anisotropy spectra of d-glyceraldehyde, which should be seen in future experimental studies.

A self-consistent coulomb bath model using density fitting.

A self-consistent Coulomb bath model is presented to provide an accurate and efficient way of performing calculations for interfragment electrostatic and polarization interactions. In this method, a condensed-phase system is partitioned into molecular fragment blocks. Each fragment is embedded in the Coulomb bath due to other fragments. Importantly, the present Coulomb bath is represented using a density fitting method in which the electron densities of molecular fragments are fitted using an atom-centered auxiliary basis set of Gaussian type. The Coulomb bath is incorporated into an effective Hamiltonian for each fragment, with which the electron density is optimized through an iterative double self-consistent field (DSCF) procedure to realize the mutual many-body polarization effects. In this work, the accuracy of interfragment interaction energies enumerated using the Coulomb bath is tested, showing a good agreement with the exact results from an energy decomposition analysis. The qualitative features of many-body polarization effects are visualized by electron density difference plots. It is also shown that the present DSCF method can yield fast and robust convergence with near-linear scaling in performance with increase in system size.

BDF: A relativistic electronic structure program package.

The BDF (Beijing Density Functional) program package is in the first place a platform for theoretical and methodological developments, standing out particularly in relativistic quantum chemical methods for chemistry and physics of atoms, molecules, and periodic solids containing heavy elements. These include the whole spectrum of relativistic Hamiltonians and their combinations with density functional theory for the electronic structure of ground states as well as time-dependent and static density functional linear response theories for electronically excited states and electric/magnetic properties. However, not to be confused by its name, BDF nowadays comprises also of standard and novel wave function-based correlation methods for the ground and excited states of strongly correlated systems of electrons [e.g., multireference configuration interaction, static-dynamic-static configuration interaction, static-dynamic-static second-order perturbation theory, n-electron valence second-order perturbation theory, iterative configuration interaction (iCI), iCI with selection plus PT2, and equation-of-motion coupled-cluster]. Additional features of BDF include a maximum occupation method for finding excited states of Hartree-Fock/Kohn-Sham (HF/KS) equations, a very efficient localization of HF/KS and complete active space self-consistent field orbitals, and a unique solver for exterior and interior roots of large matrix eigenvalue problems.

Analytic Energy Gradients and Hessians of Exact Two-Component Relativistic Methods: Efficient Implementation and Extensive Applications.

The algebraic exact two-component (X2C) relativistic Hamiltonian can be viewed as a matrix functional of the decoupling (X) and renormalization (R) matrices. It is precisely their responses to external perturbations that render X2C-based response theories different in form from the nonrelativistic counterparts. However, the situation is not really bad. Sticking to the energy gradients, it can be shown that the nuclear derivatives of X and R (Xµ and Rµ, respectively) can be transformed away to favor transformed, nucleus-independent density matrices, viz., the X2C energy gradients can be written in a form that does not depend explicitly on Xµ and Rµ. Further combined with the storage of quantities that are already available in the energy calculation, only 35 matrix multiplications are needed to construct the one-electron (relativistic) part of the X2C gradients, thereby rendering the gradient calculations very efficient. More efficiency can be gained by approximating the molecular X as the superposition of the atomic ones (denoted as X2C/AXR) and by further approximating the molecular R also as the superposition of the atomic ones (denoted as X2C/AU): The numbers of matrix multiplications required for constructing the one-electron (relativistic) parts of the X2C/AXR and X2C/AU gradients are reduced to 18 and 4, respectively. Similar approximations can also be applied to the X2C Hessian. It will be shown numerically that the X2C/AXR gradients and Hessians are extremely accurate (almost indistinguishable from the full X2C ones), whereas the X2C/AU ones do have discernible errors but which are tolerable in view of the dramatic gain in efficiency.

Unraveling the Emission Mechanism of Radical-Based Organic Light-Emitting Diodes.

Stable doublet radical molecules have recently emerged as a promising new type of emitters in organic light-emitting diodes (OLEDs), approaching 100% internal quantum efficiency. However, the detailed emission mechanism of these open-shell emitters remains elusive. Through theoretical model analysis and first-principles calculations, we unraveled the emission mechanism of a typical emitter, (4-N-carbazolyl-2,6-dichlorophenyl)bis(2,4,6-trichlorophenyl)methyl (TTM-1Cz). Our study showed that the electroluminescence arises from the first doublet excited state generated by injecting one electron into the singly occupied molecule orbital (SOMO) and one hole into the highest doubly occupied molecule orbital (HDMO). Because of the distinct charge-transfer rates in charge-injection processes, the puzzle of 100% formation ratio of the emissive doublet exciton in experiments is revealed. On the basis of this understanding, we propose simple molecular designs via substitutions that can tune the HDMO-SOMO gap and hence shift the emission wavelength to the region of yellow and green light.

Electronic Structure of OsSi Calculated by MS-NEVPT2 with Inclusion of the Relativistic Effects.

The electronic states of OsSi are calculated by multi-state N-electron valence state second order perturbation theory (MS-NEVPT2) with all-electron basis sets. The relativistic effects are considered comprehensively that allows us to identify the X3Σ0+- ground state. The theoretical equilibrium bond length 2.103 Å is close to the experimental measurement of 2.1207 Å while the vibrational frequency 466 cm-1 is smaller than the experimental value of 516 cm-1. Two excited states, namely 3Π1(I) and 3Π1(II), are located at 15568 and 18316 cm-1 above the ground state, respectively. The 3Π1(I) ← X3Σ0+- transition has been assigned to the experimental spectra at 15729 cm-1 and 3Π1(II) ← X3Σ0+- may produce the bands near 18469 cm-1. Although the latter transition energy is in accord with the experimental spectra, theoretical calculations give too small oscillator strength. Moreover, plenty of excited states with considerable oscillator strengths are located that could serve as reference data in future experiments. The four low-lying states of OsC are also calculated for comparison.

Performance of TD-DFT for Excited States of Open-Shell Transition Metal Compounds.

Time-dependent density functional theory (TD-DFT) has been very successful in accessing low-lying excited states of closed-shell systems. However, it is much less so for excited states of open-shell systems: unrestricted Kohn-Sham based TD-DFT (U-TD-DFT) often produces physically meaningless excited states due to heavy spin contaminations, whereas restricted Kohn-Sham based TD-DFT often misses those states of lower energies. A much better variant is the explicitly spin-adapted TD-DFT (X-TD-DFT) [J. Chem. Phys. 2011, 135, 194106] that can capture all the spin-adapted singly excited states yet without computational overhead over U-TD-DFT. While the superiority of X-TD-DFT over U-TD-DFT has been demonstrated for open-shell systems of main group elements, it remains to be seen if this is also the case for open-shell transition metal compounds. Taking as benchmark the results by MS-CASPT2 (multistate complete active space second-order perturbation theory) and ic-MRCISD (internally contracted multireference configuration interaction with singles and doubles), it is shown that X-TD-DFT is indeed superior to U-TD-DFT for the vertical excitation energies of ZnH, CdH, ScH2, YH2, YO, and NbO2. Admittedly, there exist a few cases where U-TD-DFT appears to be better than X-TD-DFT. However, this is due to a wrong reason: the underestimation (due to spin contamination) and the overestimation (due to either the exchange-correlation functional itself or the adiabatic approximation to the exchange-correlation kernel) happen to be compensated in the case of U-TD-DFT. As for [Cu(C6H6)2]2+, which goes beyond the capability of both MS-CASPT2 and ic-MRCISD, X-TD-DFT revises the U-TD-DFT assignment of the experimental spectrum.

Theoretical Study of Low-Lying Ω Electronic States of PtH and PtH.

Potential energy curves of 65 and 147 low-lying Ω states of PtH and PtH+ are respectively constructed using the multireference configuration interaction with singles, doubles, and Davidson's cluster corrections (MRCISD+Q), and the spin-orbit coupling effects are considered through the state-interaction approach with relativistic effective core potential spin-orbit operators. Spectroscopic constants fitted from these curves are reported and are compared with the available experimental or theoretical values. With the aid of the theoretical results including transition dipole moments, some experimentally reported electronic states and spectral bands of PtH are analyzed and reassigned. This work provides useful reference data for future experimental and theoretical studies of PtH and PtH+.

Localization of open-shell molecular orbitals via least change from fragments to molecule.

Both top-down and bottom-up localization schemes are proposed for constructing localized molecular orbitals (LMOs) of open-shell systems, via least change from fragments to molecule. The success of both schemes stems from (1) the primitive fragment LMOs that are local not only in space but also in energy and (2) the "conquer step" that allows arbitrary assignment of the unpaired electrons to fragments. Moreover, integral occupations are retained, so as to facilitate subsequent treatment of electron correlation and excitation.

High-resolution electronic spectra of yttrium oxide (YO): The D2Σ+-X2Σ+ transition.

The D2Σ+-X2Σ+ electronic absorption spectrum of the astrophysically relevant yttrium oxide (YO) molecule has been recorded for the first time in the 400-440 nm region using laser induced fluorescence. YO molecules are produced by corona discharge of oxygen between the tips of two yttrium needles in a supersonic jet expansion. An unambiguous spectroscopic identification of the D2Σ+-X2Σ+ transition becomes possible from a combined analysis of the moderate-resolution laser excitation spectrum and dispersed fluorescence spectrum. We have also performed multi-state complete active space second order perturbation theory calculations on the first six doublets of YO, and the results support our assignment of the D2Σ+ state. Accurate spectroscopic constants for D2Σ+ν' = 0 and 1 levels have been determined from a rotational analysis of the high resolution spectra that are recorded with a resolution of ∼0.018 cm-1. Severe perturbations are observed in the experimental spectra and are considered to originate from interactions with at least one nearby 2/4Π electronic state, e.g., the undetected C2Π state. We have also measured the radiative lifetimes of B2Σ+ν' = 0, and D2Σ+ν' = 0 and 1 states, based on which the B2Σ+-X2Σ+ (0, 0) and D2Σ+-X2Σ+ (0/1, 0) band oscillator strengths have been determined.

Theoretical Study of Low-Lying Electronic States of PtX (X = F, Cl, Br, and I) Including Spin-Orbit Coupling.

The low-lying electronic states of platinum ions (Pt(+)) and platinum monohalides (PtX; X = F, Cl, Br, and I) are calculated using the multireference configuration interaction method with relativistic effective core potentials. The spin-orbit coupling is taken into account through the perturbative state-interaction approach. For the Ω states of PtX below 35000 cm(-1), the potential energy curves and the corresponding spectroscopic constants are reported. It is found that the lowest Ω = 3/2 state is the ground one for the four species of PtX. Overall, the theoretical results are in reasonable agreement with the available experimental data.