Calculation Of Electronic States Research Articles

Minimum Energy Conical Intersection Optimization Using DFT/MRCI(2).

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a semiempirical electronic structure approach that is both computationally efficient and has predictive accuracy for the calculation of electronic excited states and for the simulation of electronic spectroscopies. However, given that the reference space is generated via a selected-CI procedure, a challenge arises in the construction of smooth potential energy surfaces. To address this issue, we treat the local discontinuities that arise as noise within the Gaussian progress regression framework and learn the surfaces by explicitly incorporating and optimizing a white-noise kernel. The characteristic polynomial coefficient surfaces of the potential matrix, which are smooth functions of nuclear coordinates even at conical intersections, are learned in place of the adiabatic energies and are used to optimize the DFT/MRCI(2) minimum energy conical intersection geometries for representative intersection motifs in the molecules ethylene, butadiene, and fulvene. One consequence of explicitly treating the noise in the surfaces is that the energy difference cannot be made arbitrarily small at points of nominal intersection. Despite the limitations, however, we find the structures as well as the branching spaces to compare well with ab initio MRCI and conclude that this approach is a viable method to learn a smooth representation of DFT/MRCI(2) surfaces.

Reduced Radial Electric Quadrupole Moment Function for Diatomic Molecules.

The prospect of constructing global electric quadrupole moment functions (EQMFs) of diatomic molecules by morphing their theoretical approximants within the framework of the reduced radial curve (RRC) approach is explored by performing model calculations for the ground electronic states of H2 and HF. The reduced quadrupole moment curves probed, constructed for a set of differently accurate theoretical EQMFs, coincide with their best many-parameter analytic counterparts so closely that they can be used as their accurate few-parameter representations. No other such functional representation is available in the literature.

Enhancement of the Spin-Orbit Forbidden Transition Intensity in Nitric Oxide.

The magnetic field-induced modification of the electric-dipole forbidden transitions between the lowest rotational states of the 2Π1/2 and the 2Π3/2 substates of a 2Π diatomic radical is probed by model calculations for the ground electronic states of NO, OH and CH. Magnetic fields in the range of 0-12 T and more were considered and the intensities of the respective allowed rotational transitions for the given systems were calculated for comparison. In particular, NO shows enhanced field dependence of calculated intensities.

Strategies for the alignment of electronic states in quantum-dot tunnel-injection lasers

In quantum-dot tunnel-injection lasers, the excited charge carriers are efficiently captured from the bulk states via an injector quantum well and then transferred into the quantum dots via a tunnel barrier. The alignment of the electronic levels is crucial for the high efficiency of these processes and especially for the fast modulation dynamics of these lasers. In particular, the quantum mechanical nature of the tunneling process must be taken into account in the transition from two-dimensional quantum well states to zero-dimensional quantum-dot states. This results in hybrid states, from which the scattering into the quantum-dot ground states takes place. We combine electronic state calculations of the tunnel-injection structures with many-body calculations of the scattering processes and insert this into a complete laser simulator. This allows us to study the influence of the structural design and the resulting electronic states as well as limitations due to inhomogeneous quantum-dot distributions. We find that the optimal electronic state alignment deviates from a simple picture in which the quantum-dot ground state energies are one LO-phonon energy below the injector quantum well ground state.

Construction of Antisymmetric Variational Quantum States with Real Space Representation.

Electronic state calculations using quantum computers are mostly based on the second quantized formulation, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is based on the first quantized formulation, which is expected to achieve smaller scaling with respect to the number of basis functions than the second quantized formulation. Among basis functions, a real space basis is an attractive option for quantum dynamics simulations in the fault-tolerant quantum computation (FTQC) era. A major difficulty in the first quantized algorithm with a real space basis is state preparation for many-body electronic systems. This difficulty stems from the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit. In this study, we provide a design principle for constructing variational quantum circuits to prepare an antisymmetric quantum state. The proposed circuit generates the superposition of exponentially many Slater determinants, that is, multiconfiguration state, which provides a systematic approach to approximating the exact ground state. We performed the variational quantum eigensolver (VQE) to obtain the ground state of a one-dimensional hydrogen molecular system. As a result, the proposed circuit well reproduced the exact antisymmetric ground state and its energy, whereas the conventional variational circuit yielded neither the antisymmetric nor the symmetric state. Furthermore, we analyzed the many-body wave functions based on the quantum information theory, which illustrated the relation between the electron correlation and the quantum entanglement.

Multireference Ab Initio Calculations on Excited Electronic States of Carbazole-Based Organic Compounds for Thermally Activated Delayed Fluorescence.

The emerging technology of organic light-emitting diodes takes advantage of the thermally activated delayed fluorescence (TADF) mechanism for improved efficiency. Carbazole-based organic molecules are suitable for TADF emission because of charge transfer excitations between the electron-donor carbazole and an electron-acceptor unit. Computational design of new TADF molecules with the desired properties is challenging because charge-transfer excitations cannot be predicted accurately by time-dependent density functional theory. Four groups of carbazole-based donor-acceptor molecules have been studied using multireference ab initio methods to understand the nature of excited electronic states. The state-averaged complete active space self-consistent field (SA-CASSCF) and the N-electron valence state perturbation theory (NEVPT2) were used to calculate energies and oscillator strengths for multiple excited electronic states. The number of active electrons and orbitals and the number of excited states included in state-averaged CASSCF were selected such that the accuracy of ab initio predictions could be improved systematically. The procedure introduced here for the calculation of multiple excited electronic states of TADF candidates can be used to accelerate the computational search for efficient TADF materials.

Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation.

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following.

Calculations of excited electronic states are carried out by finding saddle points on the surface describing the variation of the energy of the system as a function of the electronic degrees of freedom. This approach has several advantages over commonly used methods especially in the context of density functional calculations, as collapse to the ground state is avoided, and yet, the orbitals are variationally optimized for the excited state. Such a state-specific optimization makes it possible to describe excitations with large charge transfer, where calculations based on ground state orbitals, such as linear response time-dependent density functional theory, can be problematic. A generalized mode following method is presented where an nth-order saddle point is found by inverting the components of the gradient in the direction of the eigenvectors of the n lowest eigenvalues of the electronic Hessian matrix. This approach has the distinct advantage of following a chosen excited state by its saddle point order through molecular configurations where the symmetry of the single determinant wave function is broken, thereby making it possible to calculate potential energy curves even at avoided crossings, as demonstrated here in calculations of the ethylene and dihydrogen molecules. Results of calculations are, furthermore, presented for charge transfer excitations in nitrobenzene and N-phenylpyrrole, corresponding to fourth- and sixth-order saddle points, respectively, where an approximate initial estimate of the saddle point order could be found by energy minimization with excited electron and hole orbitals frozen. Finally, calculations of a diplatinum-silver complex are presented, illustrating the applicability of the method to larger molecules.

A Multiconfigurational Wave Function Implementation of the Frenkel Exciton Model for Molecular Aggregates.

We present an implementation of the Frenkel exciton model into the OpenMolcas program package enabling calculations of collective electronic excited states of molecular aggregates based on a multiconfigurational wave function description of the individual monomers. The computational protocol avoids using diabatization schemes and, thus, supermolecule calculations. Additionally, the use of the Cholesky decomposition of the two-electron integrals entering pair interactions enhances the efficiency of the computational scheme. The application of the method is exemplified for two test systems, that is, a formaldehyde oxime and a bacteriochlorophyll-like dimer. For the sake of comparison with the dipole approximation, we restrict our considerations to situations where intermonomer exchange can be neglected. The protocol is expected to be beneficial for aggregates composed of molecules with extended π systems, unpaired electrons such as radicals or transition metal centers, where it should outperform widely used methods based on time-dependent density functional theory.

Synthesis and Characterization of New Mononuclear Ru (II) PolypyridylComplexes with Catalytic Activity

AbstractIn this work, we report the synthesis and physicochemical characterization of new chloro and aqua mononuclear Ru (II) complexes of formula [Ru(LLL)(dpp)Cl]PF6and [Ru(LLL)(dpp)OH2](PF6)2(LLL=tpy =2,2’ : 6’,2’’‐terpyridine; tptz=2,4,6‐tris(2‐pyridyl)‐1,3,5‐triazine and dpp=2,3‐bis(2‐pyridil)pyrazine). For the complex [Ru(tptz)(dpp)Cl]PF6, the complete structure was determined by X‐ray diffraction. Catalytic studies of aqua‐complexes revealed that they are active for the water oxidation reaction at pH 1 using cerium ammonium nitrate (CAN) as a sacrificial oxidant. Also, we were able to establish the reaction mechanism and rate constants of each stage of the catalytic cycle, turnover frequencies (TOFs), and turnover numberes (TONs). The experimental TON values for the aqua complexes were very close to the theoretical value of 7.5, indicating a high degree of recovery. DFT and TD‐DFT calculations of electronic states for all complexes were consistent with experimental results and allowed the complete assignment of their UV‐Visible bands and redox states.

Cavity Ring-Down Spectroscopy of Anthracene, 9-Methylanthracene, and 2-Methylanthracene in Supersonic Expansion.

The S0-S1 absorption spectra of anthracene (C14H10), 9-methylanthracene (C15H12), and 2-methylanthracene (C15H12) are measured in the ultraviolet region between 330 and 375 nm (26,666 to 30,303 cm-1) with cavity ring-down spectroscopy in supersonic free-jet expansions of argon. The associated vibronic band systems and their spectroscopic assignments are discussed and compared to previous studies performed using fluorescence excitation and dispersed fluorescence techniques. Density functional theory (DFT) calculations were carried out to study the structures and evaluate the vibrational transitions of the ground and excited states. Time-dependent DFT calculations of the first electronic excited states and Franck-Condon factor calculations were carried out to assist in the assignment of the experimentally measured vibronic bands. The vibronic spectra obtained in absorption agree well with fluorescence excitation spectra in terms of peak positions but exhibit different relative band intensities. We find a very good match between experimentally obtained vibronic line positions and the peak positions of the quantum chemically calculated Franck-Condon excitation lines.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics.

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

Environmental considerations in ab initio calculations of electronic states of PtCl4 -2 complexes.

Many quantum chemical methods used for large complexes are based on a limited treatment of electrons due to the computational demand dictated by the number of electrons that must be explicitly considered, especially when considering the chemical environment. Such treatments can fail to correlate accurately with electronic spectra. Ab initio electronic structure theory using the spin-orbit configuration interaction method is applied in a study of spectral transitions in PtCl4 2- including counter-ion environmental effects. In this method, electronic wave functions are eigenfunctions of the total angular momentum operator belonging to one of the symmetry types of the molecular double group. PtCl4 2- is investigated as a charged gas phase complex, a point-charge-neutralized complex, and a pseudopotential-neutralized complex. Results indicate that the use of a whole-atom relativistic effective core potential for the potassium cation provides a more accurate representation of the environment than a point charge and accurately represents electronic states without increasing the complexity of the calculation and, therefore, its computational demand.

Automatic purpose-driven basis set truncation for time-dependent Hartree–Fock and density-functional theory

Real-time time-dependent density-functional theory (RT-TDDFT) and linear response time-dependent density-functional theory (LR-TDDFT) are two important approaches to simulate electronic spectra. However, the basis sets used in such calculations are usually the ones designed mainly for electronic ground state calculations. In this work, we propose a systematic and robust scheme to truncate the atomic orbital (AO) basis set employed in TDDFT and TD Hartree–Fock (TDHF) calculations. The truncated bases are tested for both LR- and RT-TDDFT as well as RT-TDHF approaches, and provide an acceleration up to an order of magnitude while the shifts of excitation energies of interest are generally within 0.2 eV. The procedure only requires one extra RT calculation with 1% of the total propagation time and a simple modification on basis set file, which allows an instant application in any quantum chemistry package supporting RT-/LR-TDDFT calculations. Aside from the reduced computational effort, this approach also offers valuable insight into the effect of different basis functions on computed electronic excitations and further ideas on the design of basis sets for special purposes.

Double Hybrid Density Functionals for the Electronic Excitation Energies of Linear Cyanines.

The lowest bright electronic excitations of seven model linear cyanines (CN3-CN15) using 28 double-hybrid (DH) density functionals are benchmarked against accurate and recent CC3 results. Some of these DH functionals are recently designed specifically for excited electronic state calculations. In addition, CIS, CIS(D), SCS-CIS(D), and SOS-CIS(D) were also tested. Four different basis sets were used for the vertical electronic excitation calculations: cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis. Augmented basis sets (e.g. aug-cc-pVDZ and aug-cc-pVTZ) are found to be required for accurate and consistent results using DH functionals. The DH functionals tested in this work are classified into four main groups: global double-hybrids (GDH), range-separated double-hybrids (RSDH), spin-component and spin-opposite scaling global double-hybrids (SCS/SOS-GDH), and spin-component and spin-opposite scaling range-separated double-hybrids (SCS/SOS-RSDH). Within these groups, the SCS/SOS-RSDH group of functionals is found to provide the lowest mean absolute error (MAE) values (in the range 0.020-0.148 eV) in comparison with the GDH group (0.195-0.441 eV), the RSDH group (0.186-0.511 eV), and the SCS/SOS-GDH group (0.079-0.461 eV). Of all the DH functionals and ab initio methods investigated in the present contribution, the following functionals are found to be the most accurate and consistent: SCS-ωB2GPPLYP (MAE = 0.036 eV), SOS-ωB2GPPLYP (MAE = 0.020 eV), SOS-ωB88PP86 (MAE = 0.035 eV), and SOS-ωPBEPP86 (MAE = 0.037 eV). In general, the ab initio methods tested here show mediocre performance as compared to many DH functionals.

Ultraviolet photodissociation of Mg+-NO complex: Ion imaging of a reaction branching in the excited states.

Ultraviolet photodissociation processes of gas phase Mg+-NO complex were studied by photofragment ion imaging experiments and theoretical calculations for excited electronic states. At 355nm excitation, both Mg+ and NO+ photofragment ions were observed with positive anisotropy parameters, and theoretical calculations revealed that the two dissociation channels originate from an electronic transition from a bonding orbital consisting of Mg+ 3s and NO π* orbitals to an antibonding counterpart. For the NO+ channel, the photofragment image exhibited a high anisotropy (β = 1.53 ± 0.07), and a relatively large fraction (∼40%) of the available energy was partitioned into translational energy. These observations are rationalized by proposing a rapid dissociation process on a repulsive potential energy surface correlated to the Mg(1S) + NO+(1Σ) dissociation limit. In contrast, for the Mg+ channel, the angular distribution was more isotropic (β = 0.48 ± 0.03) and only ∼25% of the available energy was released into translational energy. The differences in the recoil distribution for these competing channels imply a reaction branching on the excited state surface. On the theoretical potential surface of the excited state, we found a deep well facilitating an isomerization from bent geometry in the Franck-Condon region to linear and/or T-shaped isomer. As a result, the Mg+ fragment was formed via the structural change followed by further relaxation to lower electronic states correlated to the Mg+(2S) + NO(2Π) exit channel.

Carrier dynamics in quantum-dot tunnel-injection structures: Microscopic theory and experiment

Tunneling-injection structures are incorporated in semiconductor lasers in order to overcome the fundamental dynamical limitation due to hot carrier injection by providing a carrier transport path from a cold carrier reservoir. The tunneling process itself depends on band alignment between quantum-dot levels and the injector quantum well, especially as in these devices LO-phonon scattering is dominant. Quantum dots with their first excited state near the quantum well bottom profit the most from tunnel coupling. As inhomogeneous broadening is omnipresent in quantum dot structures, this implies that individual members of the ensemble couple differently to the injector quantum well. Quantum dots with higher energy profit less, as the phonon couples to higher, less occupied states. Likewise, if the energy difference between ground state and quantum well exceeds the LO-phonon energy, scattering becomes increasingly inefficient. Therefore, within 20–30 meV, we find quantum dots that benefit substantially different from the tunnel coupling. Furthermore, in quantum dots with increasing confinement depth, excited states become successively confined. Here, scattering gets more efficient again, as subsequent excited states reach the phonon resonance with the quantum well bottom. Our results provide guidelines for the optimization of tunnel-injection lasers. Theoretical results for electronic state calculations in connection with carrier–phonon and carrier–carrier scattering are compared to the experimental results of the temporal gain recovery after a short pulse perturbation.

TurboMagnon – A code for the simulation of spin-wave spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory

We introduce turboMagnon, an implementation of the Liouville-Lanczos approach to linearized time-dependent density-functional theory, designed to simulate spin-wave spectra in solid-state materials. The code is based on the noncollinear spin-polarized framework and the self-consistent inclusion of spin-orbit coupling that allow to model complex magnetic excitations. The spin susceptibility matrix is computed using the Lanczos recursion algorithm that is implemented in two flavors - the non-Hermitian and the pseudo-Hermitian one. turboMagnon is open-source software distributed under the terms of the GPL as a component of Quantum ESPRESSO. As with other components, turboMagnon is optimized to run on massively parallel architectures using native mathematical libraries (LAPACK and FFTW) and a hierarchy of custom parallelization layers built on top of MPI. The effectiveness of the code is showcased by computing magnon dispersions for the CrI3 monolayer, and the importance of the spin-orbit coupling is discussed. Program summaryProgram title:turboMagnonCPC Library link to program files:https://doi.org/10.17632/6zxwzv5dt4.1Licensing provisions: GNU General Public License V 2.0Programming language: Fortran 95External routines:turboMagnon is a tightly integrated component of the Quantum ESPRESSO distribution and requires the standard libraries linked by it: BLAS, LAPACK, FFTW, MPI.Nature of problem: Calculation of the spin-wave spectra for solid-state materials.Solution method: The spin susceptibility matrix of a periodic system is expressed in terms of the resolvent of its Liouvillian superoperator within time-dependent density-functional perturbation theory. It is calculated using non-Hermitian or pseudo-Hermitian variants of the Lanczos recursion scheme, whose implementation does not require the calculation of empty electronic states. Norm-conserving pseudopotentials are used in conjunction with plane-wave basis sets and periodic boundary conditions. Relativistic effects (spin-orbit coupling) can be included in calculations.Additional comments including restrictions and unusual features: Linear-response regime only. Collinear spin-polarized formalism is not supported, only noncollinear spin-polarized case can be used. Adiabatic LSDA exchange-correlation functionals only (no GGA, no meta-GGA, no hybrid functionals, no Hubbard U, etc.). No ultrasoft and projector-augmented-wave pseudopotentials. No symmetry.Empty states are not used, nor even calculated. Three Lanczos recursions give access to the whole spectrum of magnetic excitations at fixed transferred momentum; one Lanczos recursion is enough for a specific orientation of the magnetic field and the ground-state magnetization of the system.The distribution file of this program can be downloaded from the Quantum ESPRESSO website: http://www.quantum-espresso.org/, and the development version of this program can be downloaded via Git from the GitLab website: https://gitlab.com/QEF/q-e. Interactions with end users of the turboMagnon code happen via a mailing-list forum of Quantum ESPRESSO: https://www.quantum-espresso.org/forum. Documentation of the turboMagnon code is tightly coupled with the code and is done via standard code comments.

Schrödinger representation of quantum mechanics, Berry connection, and superconductivity

The standard quantum mechanical electronic state calculations for molecules and solids use the Schrödinger representation where the momentum conjugate to the coordinate qr is given by −iħ∂∂qr. This formalism contains an extra U(1) phase degree-of-freedom. We show that it can be regarded as a Berry phase arising from many-electron interaction, and when it is non-trivial, it gives rise to a current carrying ground state identified as the superconducting ground state. It is shown that this superconducting state is connected to the BCS one, and captures the experimentally verified results of the BCS theory. There are also gratifying differences that remove the shortcomings of the BCS theory; the ground state is particle-number-conserving, and the mass appearing in the London moment phenomenon is the free electron mass.

Optical nonlinearities in the excited carrier density of atomically thin transition metal dichalcogenides

In atomically thin semiconductors based on transition metal dichalcogenides, photoexcitation can be used to generate high densities of electron-hole pairs. Due to optical nonlinearities, which originate from Pauli blocking and many-body effects of the excited carriers, the generated carrier density will deviate from a linear increase in pump fluence. In this paper, we describe nonlinear absorption properties and excited carrier dynamics using a theoretical approach that combines results from ab initio electronic-state calculations with a many-body treatment of optical excitation. We determine the validity range of a linear approximation for the excited carrier density vs pump power and identify the role and magnitude of optical nonlinearities at elevated excitation carrier densities for ${\mathrm{MoS}}_{2}, {\mathrm{MoSe}}_{2}, {\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$ considering various excitation conditions. For photoexcitation at the bandgap, we find that the use of a linear absorption coefficient of the unexcited system can strongly underestimate the achievable carrier density in ${\mathrm{MoS}}_{2}$ due to many-body renormalizations of the two-particle density of states. The same holds for excitation of the high-energy band continuum in W-based materials.