Tamm Dancoff Research Articles

Q-Deformed quantum mechanics related to the Tamm-Dancoff oscillator algebra and some physical applications

In this paper, we consider a system of the q-deformed bosonic Tamm-Dancoff oscillators, whose spectrum has some exponential cutoff factors at high energies. We first investigate the q-calculus in the Tamm-Dancoff (TD) boson algebra, and within this framework, the q-derivative, q-integral and q-exponential function are introduced. Using these properties, we construct a new formalism for the q-deformed quantum mechanics, which accordingly involve the q-adjoint operator and the q-Hermitian operator properties. We then derive the q-deformed Heisenberg relation, and develop the q-Hermitian momentum operator. The q-deformed Schrödinger equation is introduced, and as applications, we study the momentum eigenfunction and one-dimensional box problem. Another application of the TD type deformation onto lattice oscillations is also discussed through a model of the q-deformed Debye solid. Finally, other potential applications of the TD-oscillators gas model are concisely pointed out.

Adsorption of cadmium selenide clusters: A novel approach to enhance solar energy conversion using armchair graphene nanoribbons

Tailoring the electronic, optical, and transport properties of low-dimensional semiconductor materials is essential to improve the light-conversion efficiency of thin-film solar cell materials. Here, using first-principles calculations and non-equilibrium Green functions, we investigate the enhancement of optoelectronic and transport properties of armchair graphene nanoribbons (AGNRs) upon adsorption of cadmium selenide clusters. Upon adsorption of a CdSe diatomic molecule on an AGNR, the most energetically favorable configuration is the cadmium end sitting on top of a carbon atom. The corresponding electronic bandgap reduces ∼5 times with respect to that of the pristine system, thanks to the formation of a polaron state formed by the p-orbital of the selenide atom. Upon adsorption of CdSe cyclohexane molecules, the bandgap of this system slightly shrinks by 0.121 eV with respect to the pristine system. The charge accumulation induced by these clusters significantly enhances the absorption coefficient of the adsorbed systems, resulting in a red shift of the optical spectra toward the infrared region. More interestingly, by solving the Bethe–Salpeter equations with the Tamm–Dancoff approximation, we provide a direct link between the first-principles optical prediction and experimental observations. In addition, the electron transfer from these molecules to the hosted systems increases the transmission spectra in the vicinity of the Fermi level, leading to a remarkable electronic current passing through these scattering regions. These results highlight the role of cadmium selenide clusters in enhancing the light-to-energy conversion efficiency of next-generation solar cell devices.

Kohn–Sham time-dependent density functional theory with Tamm–Dancoff approximation on massively parallel GPUs

We report a high-performance multi graphics processing unit (GPU) implementation of the Kohn–Sham time-dependent density functional theory (TDDFT) within the Tamm–Dancoff approximation. Our algorithm on massively parallel computing systems using multiple parallel models in tandem scales optimally with material size, considerably reducing the computational wall time. A benchmark TDDFT study was performed on a green fluorescent protein complex composed of 4353 atoms with 40,518 atomic orbitals represented by Gaussian-type functions, demonstrating the effect of distant protein residues on the excitation. As the largest molecule attempted to date to the best of our knowledge, the proposed strategy demonstrated reasonably high efficiencies up to 256 GPUs on a custom-built state-of-the-art GPU computing system with Nvidia A100 GPUs. We believe that our GPU-oriented algorithms, which empower first-principles simulation for very large-scale applications, may render deeper understanding of the molecular basis of material behaviors, eventually revealing new possibilities for breakthrough designs on new material systems.

Libkrylov: A modular open-source software library for extremely large on-the-fly matrix computations.

We present the design and implementation of libkrylov, an open-source library for solving matrix-free eigenvalue, linear, and shifted linear equations using Krylov subspace methods. The primary objectives of libkrylov are flexible API design and modular structure, which enables integration with specialized matrix-vector evaluation "engines." Libkrylov features pluggable preconditioning, orthonormalization, and tunable convergence control. Diagonal (conjugate gradient, CG), Davidson, and Jacobi-Davidson preconditioners are available, along with orthonormal and nonorthonormal (nKs) schemes. All functionality of libkrylov is exposed via Fortran and C application programming interfaces (APIs). We illustrate the performance of libkrylov for eigenvalue calculations arising in time-dependent density functional theory (TDDFT) in the Tamm-Dancoff approximation (TDA) and discuss the convergence behavior as a function of preconditioning and orthonormalization methods.

The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation

The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavourable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm–Dancoff approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately sized basis sets. In this work, some of the benefits and limitations of TDDFT/TDA are discussed and analysed with regard to its applicability as a ‘back-end’ electronic structure method for the symmetric quasi-classical Meyer–Miller model (SQC/MM). In order to investigate the benefits and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyse a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated, which highlight some of the deficiencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.

Redox-Triggered Switching of Conformational State in Triple-Decker Lanthanide Phthalocyaninates.

Double- and triple-decker lanthanide phthalocyaninates exhibit unique physical-chemical properties, particularly single-molecule magnetism. Among other factors, the magnetic properties of these sandwiches depend on their conformational state, which is determined via the skew angle of the phthalocyanine ligands. Thus, in the present work we report the comprehensive conformational study of substituted terbium(III) and yttrium(III) trisphthalocyaninates in solution depending on the substituents at the periphery of molecules, redox-states and nature of solvents. Conjunction of UV-vis-NIR spectroscopy and quantum-chemical calculations within simplified time-dependent DFT in Tamm–Dancoff approximation provided the spectroscopic signatures of staggered and gauche conformations of trisphthalocyaninates. Altogether, it allowed us to demonstrate that the butoxy-substituted complex behaves as a molecular switcher with controllable conformational state, while the crown-substituted triple-decker complex maintains a staggered conformation regardless of external factors. The analysis of noncovalent interactions within the reduced density gradient approach allowed to shed light on the nature of factors stabilizing certain conformers.

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe-Salpeter equation calculations of molecules.

The ab initio GW plus Bethe-Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn-Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm-Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn-Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel's set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

Multichannel single center method

A multichannel single center (MCSC) method for the theoretical description of the electron continuum spectrum in molecules is reported. The method includes coupling between different continuum channels via electron correlations and describes, thereby, photoelectron continuum in the Tamm–Dancoff (configuration interaction singles) approximation. Basic equations of the non-iterative one-channel single center (SC) method and their extension to the MCSC method are presented, and an efficient scheme for their numerical solution is outlined. The method is tested on known illustrative examples of the Ar 3s-, HCl 4σ- and N2 1σ-photoionization processes, where inter-channel coupling plays a very important role. Unlike our previous SC studies, the present MCSC method can be reliably applied to photoionization of outer and valence molecular orbitals, where inter-channel correlations in the continuum might be relevant.

Fast and Accurate Determination of the Singlet–Triplet Gap in Donor–Acceptor and Multiresonance TADF Molecules by Using Hole–Hole Tamm–Dancoff Approximated Density Functional Theory

AbstractOne of the requirements to design efficient emitters based on the multiresonance (MR)‐ or donor–acceptor (D‐A) thermally activated delayed fluorescence (TADF) materials is a relatively small energy gap between the lowest singlet and triplet excited states (ΔEST). High‐level ab initio calculations of their ΔEST provide benchmark results, but they are very time consuming and little practical for large‐size systems. Here, the performances of hole–hole Tamm–Dancoff approximated density functional theory (hh‐TDA‐DFT) and the functional dependent accuracy of hh‐TDA are examined on ΔEST of a large number of MR‐ and D‐A TADF molecules. The results indicate that hh‐TDA combined with the hybrid functional B3LYP can predict ΔEST values for a wide number of MR‐TADF molecules with mean absolute error (MAE) within 0.04 eV with correlation as high as 0.75. For D‐A TADF molecules, ΔEST is less sensitive to the nature of the functionals, with MAE as low as 0.07 eV. The larger discrepancy between ΔEST obtained from hh‐TDA‐DFT and experimental data in several oxygen‐containing MR‐TADF molecules is assumed to stem from the aggregation tendency of these compounds in solution. These findings provide important insights on the role of aggregation in reducing the ΔEST of MR‐TADF compounds.

Assessing Recent Time-Dependent Double-Hybrid Density Functionals on Doublet-Doublet Excitations.

This work is the first thorough investigation of time-dependent double-hybrid density functionals (DHDFs) for the calculation of doublet-doublet excitation energies. It sheds light on the current state-of-the-art techniques in the field and clarifies if there is still room for future improvements. Overall, 29 hybrid functionals and DHDFs are investigated. We separately analyze the individual impacts of the Tamm-Dancoff approximation (TDA), range separation, and spin-component/opposite scaling (SCS/SOS) on 45 doublet-doublet excitations in 23 radicals before concluding with an overarching analysis that includes and excludes challenging excitations with double-excitation or multireference character. Our results show again that so-called "nonempirical" DHDFs are outperformed by semiempirical ones. While the best assessed functionals are DHDFs, some of the worst are also DHDFs and outperformed by all assessed hybrids. SCS/SOS is particularly beneficial for range-separated DHDFs. Spin-scaled, range-separated DHDFs paired with the TDA belong to the best tested methods here, and we particularly highlight SCS-ωB2GP-PLYP, SOS-ωB2PLYP, SOS-ωB2GP-PLYP, SOS-ωB88PP86, SOS-RSX-QIDH, and SOS-ωPBEPP86. When comparing our functional rankings with previous studies on singlet-singlet and singlet-triplet excitations, we recommend TDA-SOS-ωB88PP86 and TDA-SOS-ωPBEPP86 as robust methods for excitation energies in general until further improvements have been achieved that surpass the chemical accuracy threshold for challenging open-shell excitations without increasing the computational effort.

Impact of Adsorption of Straight Chain Alcohol Molecules on the Optical Properties of Calcite (10.4) Surface.

Calcium carbonate plays a central role in controlling the chemistry of the oceans, biomineralization and oil production, to name a few. In this work, using density functional theory with semiempirical dispersion corrections and simplified TD-DFT using Tamm–Dancoff approximation, we investigated the impact of the adsorption of straight chain alcohol (ethanol and pentanol) molecules on the optical properties of a calcite (10.4) surface. Our results show that ethanol and/or pentanol molecules form a well-ordered monolayer (through their hydroxyl group with carbon chains sticking away in a standing-up position) on the calcite (10.4) surface. Additionally, we found intriguing modulations in the photoabsorption spectra and circular dichroism spectra. In particular, the latter was a unique optical fingerprint for a molecule-adsorbed calcite (10.4) surface. Our findings provide useful insights into the structural and optical features of calcite-based systems at the atomic level.

Inelastic Electron Scattering Form Factor of Isoscalar (T = 0) and Isovector (T = 1) Particle-hole States in 12C and 16O

Inelastic longitudinal and transverse electron scattering form factors of low-lying T = 0, T = 1 particle-hole states of 12C and 16O are studied in the framework of the Tamm–Dancoff approximation (TDA). The Hamiltonian with the Michigan-three-Yukawa (M3Y) potential is diagonalized. To obtain a good agreement with the experimental data, the ground state is corrected by including the admixture from higher orbits with regard for the core polarization effects.

The ground and ionized states of azulene: A combined study of the vibrational energy levels by photoionization, configuration interaction, and density functional calculations.

A synchrotron-based photoionization spectrum of azulene shows a significant additional vibrational fine structure when compared to previous studies. This spectrum was successfully analyzed by using Franck-Condon (FC) methods. Previously reported zero-kinetic-energy electron spectra for azulene have been reinterpreted in FC terms, leading to some alternative assignments to the earlier work. The sequence of ionic states has been determined by using ab initio configuration interaction (CI) methods, leading to reliable theoretical values for both the calculated adiabatic ionization energy (AIE) and vertical ionization energy (VIE). VIEs were calculated by both symmetry-adapted cluster (SAC-CI), together with Green's function (GF) and Tamm-Dancoff approximation (TDA), and single excitation CI methods; AIEs for highest states of each symmetry were determined by open-shell self-consistent field (SCF) methods at the restricted Hartree-Fock level. Complete active space SCF was used for the pairs of 12A2 + 22A2 and 12B1 + 22B1 states, each of which occurs as antisymmetric and symmetric (higher energy) combinations. The combined ionic state sequences (AIE and VIE) from these methods are 12A2 < 12B1 < 22A2 < 22B1. The photoelectron spectrum (PES) shows a series of broadbands above 11eV, each of which is attributed to more than one ionization. The calculated PES sequence of states of up to 19eV shows that the SAC-CI and GF results are in almost exact agreement. The internal spacing of the bands is best reproduced by the simpler GF and TDA methods. States involving simultaneous ionization and electronic excitation are considered by both SAC-CI and TDA methods.

Mean field and beyond mean field calculations of hypernuclei for study of electroproduction

We present two methods, the Nucleon-Lambda Tamm Dancoff Approximation (NΛ TDA) and the Equation of Motion Phonon Method (EMPM) suitable for calculating hypernuclear energy spectra and structure. These methods are applicable for hypernuclei of wide range of masses with one Λ particle replacing one nucleon in an even-even nuclear cores. Using an effective Lambda-nucleon (ΛN) potential both methods were applied to calculate the energy spectrum of 12ΛB and also one body density matrix elements (OBDME). The OBDME were applied to calculate the electroproduction cross section of 12ΛB. We obtained better agreement with the experimental data by using EMPM than NΛ TDA. We plan to provide theoretical prediction (by applying the same methods and ΛN potentials) of the cross section in electroproduction of 40ΛK and 48ΛK.

Porous Pyrene Organic Cage with Unusual Absorption Bathochromic-Shift Enables Visible Light Photocatalysis

Porous Pyrene Organic Cage with Unusual Absorption Bathochromic-Shift Enables Visible Light Photocatalysis

Computing molecular excited states on a D-Wave quantum annealer

The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree–Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm–Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example hbox {H}_2 molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for hbox {NH}_3 as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.

ν − ν interactions in supernovae environments as a function of density and temperature

Neutrinos in astrophysical environments, such as Supernovae (SNe), may interact through pair interactions. These interactions are density and temperature-dependent. Under certain conditions, a neutrino-condensate may form. In this work, we have adapted the separable nonlocal pairing interactions to the SN conditions and studied the temperature and density dependence of the pairing gap as well as the collective response with respect to these variables. We have applied the Bogoliubov transformations and solved the Bardeen, Cooper and Schrieffer (BCS) equations to construct the free quasi-particle sector of the Hamiltonian. The residual two-quasi-particle terms have been treated by applying the Tamm–Dancoff approximation (TDA) and random-phase approximation (RPA), suited to the extended neutrino media. With this, we have constructed neutrino energy distributions both in the superfluid and normal regimes and extracted critical values of the density and temperature.

Excited-State Geometry Optimization of Small Molecules with Many-Body Green’s Functions Theory

We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green’s functions theory within the GW approximation and the Bethe–Salpeter equation (BSE) employing numerical gradients. We scrutinize the influence of several typical approximations in the GW-BSE framework; we used one-shot G0W0 or eigenvalue self-consistent evGW, employing a fully analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm–Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC) method, second-order approximate coupled cluster (CC2) method, and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G0W0 and 1.5% for the evGW variants based on a PBE0 ground state, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the GW-BSE method does not only yield excitation energies but also geometries in good agreement with established higher-order wave function methods.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States.

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm–Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Photoionization of Xe 5s: angular distribution and Wigner time delay in the vicinity of the second Cooper minimum

The angular distribution and photoionization Wigner time delay of Xe 5s photoelectrons are studied in the region of the second Cooper minimum (SCM) using (i) the relativistic multiconfiguration Tamm–Dancoff approximation, (ii) the relativistic-random-phase approximation (RRPA) and (iii) the RRPA-with-relaxation to demonstrate how differing treatments of correlation, and the relativistic interactions, affect the results. The results of the three methods are compared with each other and with available experimental data. The comparison reveals the importance of electron correlations for which a multiconfiguration description of the initial state is essential. The spin-resolved and spin-averaged photoionization time delay results show important signatures in the region of the SCM in the Xe 5s photoionization cross-section.