Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding

Projection-based embedding provides a simple, robust, and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction method while the remainder of the system is described at the level of density functional theory. Here, we present the derivation, implementation, and numerical demonstration of analytical nuclear gradients for projection-based wavefunction-in-density functional theory (WF-in-DFT) embedding. The gradients are formulated in the Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. An important aspect of the gradient theory is that WF contributions to the total WF-in-DFT gradient can be simply evaluated using existing WF gradient implementations without modification. Another simplifying aspect is that Kohn-Sham (KS) DFT contributions to the projection-based embedding gradient do not require knowledge of the WF calculation beyond the relaxed WF density. Projection-based WF-in-DFT embedding gradients are thus easily generalized to any combination of WF and KS-DFT methods. We provide numerical demonstration of the method for several applications, including calculation of a minimum energy pathway for a hydride transfer in a cobalt-based molecular catalyst using the nudged-elastic-band method at the CCSD-in-DFT level of theory, which reveals large differences from the transition state geometry predicted using DFT.Comment: 15 pages, 4 figure

Quantum coherent plasmon in silver nanowires: a real-time TDDFT study

A plasmon-like phenomenon, arising from coinciding resonant excitations of different electronic characteristics in 1D silver nanowires, has been proposed based on theoretical linear absorption spectra. Such a molecular plasmon holds the potential for anisotropic nanoplasmonic applications. However, its dynamical nature remains unexplored. In this work, quantum dynamics of longitudinal and transverse excitations in 1D silver nanowires are carried out within the real-time time-dependent density functional theory framework. The anisotropic electron dynamics confirm that the transverse transitions of different electronic characteristics are collective in nature and oscillate in-phase with respect to each other. Analysis of the time evolutions of participating one-electron wave functions suggests that the transverse transitions form a coherent wave packet that gives rise to a strong plasmon resonance at the molecular level

Linear-response time-dependent embedded mean-field theory

We present a time-dependent (TD) linear-response description of excited electronic states within the framework of embedded mean-field theory (EMFT). TD-EMFT allows for subsystems to be described at different mean-field levels of theory, enabling straightforward treatment of excited states and transition properties. We provide benchmark demonstrations of TD-EMFT for both local and nonlocal excitations in organic molecules, as well as applications to chlorophyll a, solvatochromic shifts of a dye in solution, and sulfur K-edge X-ray absorption spectroscopy (XAS). It is found that mixed-basis implementations of TD-EMFT lead to substantial errors in terms of transition properties; however, as previously found for ground-state EMFT, these errors are largely eliminated with the use of Fock-matrix corrections. These results indicate that TD-EMFT is a promising method for the efficient, multilevel description of excited-state electronic structure and dynamics in complex systems

Analytical Gradients for Molecular-Orbital-Based Machine Learning

Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 data set while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures, at a computational cost for the gradient evaluation that is comparable to Hartree-Fock theory or hybrid DFT

Modulate Molecular Interaction between Hole Extraction Polymers and Lead Ions toward Hysteresis-Free and Efficient Perovskite Solar Cells

Herein three polymeric hole extraction materials (HEMs), poly(benzene‐dithiophene) (PB2T)‐O, PB2T‐S, and PB2T‐SO are presented for p–i–n perovskite solar cells (PVSCs). This study reveals that the perovskite device hysteresis and performance heavily rely on the perovskite grain boundary conditions. More specifically, they are predetermined through the molecular interaction between Lewis base atoms of HEMs and perovskites. It is revealed that only changing the side chain terminals (-OCH_3, -SCH_3, and –SOCH_3) of HEMs results in effective modulating PVSC performance and hysteresis, due to the effective tune of interaction strength between HEM and perovskite. With an in situ grown perovskite‐HEM bulk heterojunction structure, PB2T‐O with weak binding group (-OCH_3, −78.9 kcal mol^(−1) bonding energy) to lead ions allows delivering hysteresis‐free and efficient devices, which is sharp contrast to the strong binding PB2T‐SO (−119.3 kcal mol^(−1) bonding energy). Overall, this work provides new insights on PVSC hysteresis and the related curing methods via multifunctional HEM design in PVSCs

Embedded mean-field theory with block-orthogonalized partitioning

Embedded mean-field theory (EMFT) provides a simple, flexible framework for describing subsystems at different levels of mean-field theory. Subsystems are defined by partitioning a one-particle basis set, with a natural choice being the atomic orbital (AO) basis. Although generally well behaved, EMFT with AO partitioning can exhibit unphysical collapse of the self-consistent solution. To avoid this issue, we introduce subsystem partitioning of a block-orthogonalized (BO) basis set; this eliminates the unphysical collapse without significantly increasing computational cost. We also investigate a non-self-consistent implementation of EMFT, in which the density matrix is obtained using BO partitioning and the final energy evaluated using AO partitioning; this density-corrected EMFT approach is found to yield more accurate energies than BO partitioning while also avoiding issues of the unphysical collapse. Using these refined implementations of EMFT, previously proposed descriptions of the exact-exchange coupling between subsystems are compared: although the EX1 coupling scheme is slightly more accurate than EX0, the small improvement does not merit its substantially greater computational cost

Linear-Response Time-Dependent Embedded Mean-Field Theory

We present a time-dependent (TD) linear-response description of excited electronic states within the framework of embedded mean-field theory (EMFT). TD-EMFT allows for subsystems to be described at different mean-field levels of theory, enabling straightforward treatment of excited states and transition properties. We provide benchmark demonstrations of TD-EMFT for both local and nonlocal excitations in organic molecules, as well as applications to chlorophyll a, solvatochromic shifts of a dye in solution, and sulfur K-edge X-ray absorption spectroscopy (XAS). It is found that mixed-basis implementations of TD-EMFT lead to substantial errors in terms of transition properties; however, as previously found for ground-state EMFT, these errors are largely eliminated with the use of Fock-matrix corrections. These results indicate that TD-EMFT is a promising method for the efficient, multilevel description of excited-state electronic structure and dynamics in complex systems