Incorporating Nuclear Quantum Effects in Molecular Dynamics with a Constrained Minimized Energy Surface

The accurate incorporation of nuclear quantum effects in large-scale molecular dynamics (MD) simulations remains a significant challenge. Recently, we combined constrained nuclear-electronic orbital (CNEO) theory with classical MD and obtained a new approach (CNEO-MD) that can accurately and efficiently incorporate nuclear quantum effects into classical simulations. In this Letter, we provide the theoretical foundation for CNEO-MD by developing an alternative formulation of the equations of motion for MD. In this new formulation, the expectation values of quantum nuclear positions evolve classically on an effective energy surface that is obtained from a constrained energy minimization procedure when solving for the quantum nuclear wave function, thus enabling the incorporation of nuclear quantum effects in classical MD simulations. For comparison with other existing approaches, we examined a series of model systems and found that this new MD approach is significantly more accurate than the conventional way of performing classical MD and generally outperforms centroid MD and ring-polymer MD in describing vibrations in these model systems

Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space

In this article, we propose a method called sequential Lasso (SLasso) for feature selection in sparse high-dimensional linear models. The SLasso selects features by sequentially solving partially penalized least squares problems where the features selected in earlier steps are not penalized. The SLasso uses extended BIC (EBIC) as the stopping rule. The procedure stops when EBIC reaches a minimum. The asymptotic properties of SLasso are considered when the dimension of the feature space is ultra high and the number of relevant feature diverges. We show that, with probability converging to 1, the SLasso first selects all the relevant features before any irrelevant features can be selected, and that the EBIC decreases until it attains the minimum at the model consisting of exactly all the relevant features and then begins to increase. These results establish the selection consistency of SLasso. The SLasso estimators of the final model are ordinary least squares estimators. The selection consistency implies the oracle property of SLasso. The asymptotic distribution of the SLasso estimators with diverging number of relevant features is provided. The SLasso is compared with other methods by simulation studies, which demonstrates that SLasso is a desirable approach having an edge over the other methods. The SLasso together with the other methods are applied to a microarray data for mapping disease genes. Supplementary materials for this article are available online.</p

Incorporating Nuclear Quantum Effects in Molecular Dynamics with a Constrained Minimized Energy Surface

The accurate incorporation of nuclear quantum effects in large-scale molecular dynamics (MD) simulations remains a significant challenge. Recently, we combined constrained nuclear-electronic orbital (CNEO) theory with classical MD and obtained a new approach (CNEO-MD) that can accurately and efficiently incorporate nuclear quantum effects into classical simulations. In this Letter, we provide the theoretical foundation for CNEO-MD by developing an alternative formulation of the equations of motion for MD. In this new formulation, the expectation values of quantum nuclear positions evolve classically on an effective energy surface that is obtained from a constrained energy minimization procedure when solving for the quantum nuclear wave function, thus enabling the incorporation of nuclear quantum effects in classical MD simulations. For comparison with other existing approaches, we examined a series of model systems and found that this new MD approach is significantly more accurate than the conventional way of performing classical MD and generally outperforms centroid MD and ring-polymer MD in describing vibrations in these model systems

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the N-electron system as the sum of the (N – 2)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle–particle Tamm–Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation

Origin of the Nonmonotonic Pressure Dependence of the Band Gap in the Orthorhombic Perovskite CsPbBr₃

The perovskite CsPbBr3 exhibits an unusual nonmonotonic dependence of the band gap on increasing pressure to about 2.0 GPa as compared to conventional semiconductors. Using the first-principles calculation method, we show that under pressure, isotropic volume deformation induces considerable compression of the Pb–Br bond length and thus an enhanced interaction between atomic orbitals of the antibonding valence band maximum states and the mostly nonbonding conduction band minimum states, resulting in a monotonic decrease in the band gap. On the other hand, structural relaxation tends to reduce the strain energy by decompressing the Pb–Br bond length and simultaneously compressing the Pb–Br–Pb bond angle, which increases the band gap energy. We find that the competition between the volume deformation effect and structural relaxation effect is the origin of the nonmonotonic behavior of the dependence of the band gap on pressure

Molecular Dynamics with Constrained Nuclear Electronic Orbital Density Functional Theory: Accurate Vibrational Spectra from Efficient Incorporation of Nuclear Quantum Effects

Nuclear quantum effects play a crucial role in many chemical and biological systems involving hydrogen atoms yet are difficult to include in practical molecular simulations. In this paper, we combine our recently developed methods of constrained nuclear–electronic orbital density functional theory (cNEO-DFT) and constrained minimized energy surface molecular dynamics (CMES-MD) to create a new method for accurately and efficiently describing nuclear quantum effects in molecular simulations. By use of this new method, dubbed cNEO-MD, the vibrational spectra of a set of small molecules are calculated and compared with those from conventional ab initio molecular dynamics (AIMD) as well as from experiments. With the same formal scaling, cNEO-MD greatly outperforms AIMD in describing the vibrational modes with significant hydrogen motion characters, demonstrating the promise of cNEO-MD for simulating chemical and biological systems with significant nuclear quantum effects

Calculating Vibrational Excited State Absorptions with Excited State Constrained Minimized Energy Surfaces

The modeling and interpretation of vibrational spectra are crucial for studying reaction dynamics using vibrational spectroscopy. Most prior theoretical developments focused on describing fundamental vibrational transitions while fewer developments focused on vibrational excited state absorptions. In this study, we present a new method that uses excited state constrained minimized energy surfaces (CMESs) to describe vibrational excited state absorptions. The excited state CMESs are obtained similarly to the previous ground state CMES development in our group but with additional wave function orthogonality constraints. Using a series of model systems, including the harmonic oscillator, Morse potential, double-well potential, quartic potential, and two-dimensional anharmonic potential, we demonstrate that this new procedure provides good estimations of the transition frequencies for vibrational excited state absorptions. These results are significantly better than those obtained from harmonic approximations using conventional potential energy surfaces, demonstrating the promise of excited state CMES-based methods for calculating vibrational excited state absorptions in real systems

Defects in Halide Perovskites: Does It Help to Switch from 3D to 2D?

Two-dimensional (2D) organic–inorganic hybrid iodide perovskites have been put forward in recent years as stable alternatives to their three-dimensional (3D) counterparts. Using first-principles calculations, we demonstrate that equilibrium concentrations of point defects in the 2D perovskites PEA2PbI4, BA2PbI4, and PEA2SnI4 (PEA, phenethylammonium; BA, butylammonium) are much lower than in comparable 3D perovskites. Bonding disruptions by defects are more destructive in 2D than in 3D networks, making defect formation energetically more costly. The stability of 2D Sn iodide perovskites can be further enhanced by alloying with Pb. Should, however, point defects emerge in sizable concentrations as a result of nonequilibrium growth conditions, for instance, then those defects likely hamper the optoelectronic performance of the 2D perovskites, as they introduce deep traps. We suggest that trap levels are responsible for the broad sub-bandgap emission in 2D perovskites observed in experiments

Linear Scaling Calculations of Excitation Energies with Active-Space Particle–Particle Random-Phase Approximation

We developed an efficient active-space particle–particle random-phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle–particle and the hole–hole spaces. The resulting matrix, whose eigenvalues are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N – 2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts the excitation energies of valence, charge-transfer, Rydberg, double, and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space GRSTRS@PBE approach predicts accurate absolute and relative core-level binding energies with the MAEs around 1.58 and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems

Strategy for Fluorescence/Photoacoustic Signal Maximization Using Dual-Wavelength-Independent Excitation

Dual-mode imaging of fluorescence-photoacoustics has emerged as a promising technique for biomedical applications. However, conventional dual-mode imaging is based on single-wavelength excitation, which often results in opposing fluorescence and photoacoustic signals due to competing photophysical processes in one agent, rendering the maximization of both signals infeasible. To meet this challenge, we herein propose a new strategy by using the dual-excitation approach, where one excitation wavelength generates a fluorescence signal and the other produces a photoacoustic signal, thus achieving simultaneous maximization of both signals in one fluorescence-photoacoustic molecule. Based on this strategy, three dye molecules were employed for comparison, and it was surprising to find that QHD dye with two types of excitation wavelengths could generate fluorescence and photoacoustic signals, respectively. Furthermore, this strategy was successfully implemented in dual-mode imaging of rheumatoid arthritis mice. Importantly, this study emphasizes a new design guideline for the maximization of fluorescence-photoacoustic signals by using dual-wavelength-independent excitation