Excited-state Calculations Research Articles

Efficient Calculation of Magnetic Circular Dichroism Spectra Using Spin-Noncollinear Linear-Response Time-Dependent Density Functional Theory in Finite Magnetic Fields.

Excited-state calculations in finite magnetic fields are presented in the framework of spin-noncollinear linear-response time-dependent density functional theory. To ensure gauge-origin invariance, London atomic orbitals are employed throughout. An efficient implementation into the Turbomole package, which also includes the resolution of the identity approximation, allows for the investigation of excited states of large molecular systems. The implementation is used to investigate the magnetic circular dichroism spectra of sizable organometallic molecules such as a zinc tetraazaporphyrin with two fused naphthalene units, which is a molecule with 57 atoms.

A DFT investigation on theranostic potential of alkaline earth metal doped phosphorenes for ifosfamide anti-cancer drug

Cancer is one of the leading causes of human mortality and a theranostics strategy is essential for its effective treatment. Density function theory (DFT) simulations were executed to examine the drug delivery, photothermal potential, and photoimaging guided cancer diagnostic potential of pristine and alkaline earth metal (M=Be, Mg, and Ca) doped phosphorenes (M-PH). The topological, electronic, and thermodynamic descriptors of M@PH and Ifosfamide (IFO) loaded systems (IFO@M-PH) were calculated. The oxygen atoms of IFO coordinated with the doped M-PH carrier. The adsorption process was exothermic and hence spontaneous. A higher adsorption energy was found for IFO@M-PH systems compared to undoped system. The polarity of the drug-carrying system is increased after doping which is favorable for effective in vivo drug flow. The HOMO-LUMO and natural bond orbital (NBO) analyses revealed that doping facilitated the charge transfer from drug to phosphorene. The quantum theory of atoms in molecules (QTAIM) and non-covalent interaction (NCI) studies show the presence of weak non-covalent interactions among the drug and substrate, supporting the effective drug release. The excited-state calculations for drug loaded complexes show the shifting of λmax from 434 nm to Near-Infrared (NIR) region. This supported IFO@M-PH as a potential candidate for photothermal therapy and photoimaging guided cancer diagnostic.

Simplified GW/BSE Approach for Charged and Neutral Excitation Energies of Large Molecules and Nanomaterials.

Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [Grimme, S. J. Chem. Phys. 2013, 138, 244104], we describe a simplified approach to excited-state calculations within the GW approximation to the self-energy and the Bethe-Salpeter equation (BSE), which we call sGW/sBSE. The primary simplification to the electron repulsion integrals yields the same structure as with tensor hypercontraction, such that our method has a storage requirement that grows quadratically with system size and computational timing that grows cubically with system size. The performance of sGW is tested on the ionization potential of the molecules in the GW100 test set, for which it differs from ab initio GW calculations by only 0.2 eV. The performance of sBSE (based on the sGW input) is tested on the excitation energies of molecules in Thiel's set, for which it differs from ab initio GW/BSE calculations by about 0.5 eV. As examples of the systems that can be routinely studied with sGW/sBSE, we calculate the band gap and excitation energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in 4678 spatial orbitals and the absorption spectra of two large organic dye molecules with hundreds of atoms.

Real-Time Evolution for Ultracompact Hamiltonian Eigenstates on Quantum Hardware

In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground- and excited-state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians, when starting from an appropriate reference state. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time-evolved expansion states, and connects the method to the classical filter-diagonalization algorithm. Furthermore, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise that substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground- and excited-state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Furthermore, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the def2-SVP basis set), and show that it is possible to reach chemical accuracy with as few as approximately 50 time steps.4 MoreReceived 5 April 2021Revised 17 February 2022Accepted 1 March 2022DOI:https://doi.org/10.1103/PRXQuantum.3.020323Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum computationQuantum simulationCondensed Matter, Materials & Applied PhysicsQuantum Information

A DFT approach towards therapeutic potential of phosphorene as a novel carrier for the delivery of felodipine (cardiovascular drug)

In this study, Density Functional Theory (DFT) calculations were performed to evaluate the efficiency of phosphorene as a carrier for delivery of felodipine. The felodipine drug, phosphorene carrier, and felodipine-phosphorene complex properties at the ground and excited state were measured to determine the efficacy of phosphorene as a carrier of the cardiovascular drug. The felodipine drug interacts with phosphorene carrier by non-covalent weak interactions. The weak interactions between two components (i.e., phosphorene and felodipine) play a significant role in drug release at a specific targeted site. The excitation from HOMO to LUMO involves the transfer of charge from felodipine to phosphorene which is demonstrated by frontier molecular orbital analysis and further confirmed by Photo-physical results. The excited-state calculation of felodipine-phosphorene complex at CAM-B3LYP/6-31G (d, p) demonstrated that λmax was red-shifted in the gas phase and the solvent phase showed a blue shift. For 1–2 excited states of the felodipine-phosphorene complex, the photoinduced electron-transfer process (PET) was studied. Furthermore, the phosphorene carrier with positive (+1) and negative (–1) charges indicates surface charge analysis and form stable complex systems with felodipine. It is concluded that phosphorene can be used as a carrier for efficient drug-delivery of felodipine drugs.

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting.

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

Machine learned calibrations to high-throughput molecular excited state calculations.

Understanding the excited state properties of molecules provides insight into how they interact with light. These interactions can be exploited to design compounds for photochemical applications, including enhanced spectral conversion of light to increase the efficiency of photovoltaic cells. While chemical discovery is time- and resource-intensive experimentally, computational chemistry can be used to screen large-scale databases for molecules of interest in a procedure known as high-throughput virtual screening. The first step usually involves a high-speed but low-accuracy method to screen large numbers of molecules (potentially millions), so only the best candidates are evaluated with expensive methods. However, use of a coarse first-pass screening method can potentially result in high false positive or false negative rates. Therefore, this study uses machine learning to calibrate a high-throughput technique [eXtended Tight Binding based simplified Tamm-Dancoff approximation (xTB-sTDA)] against a higher accuracy one (time-dependent density functional theory). Testing the calibration model shows an approximately sixfold decrease in the error in-domain and an approximately threefold decrease in the out-of-domain. The resulting mean absolute error of ∼0.14eV is in line with previous work in machine learning calibrations and out-performs previous work in linear calibration of xTB-sTDA. We then apply the calibration model to screen a 250k molecule database and map inaccuracies of xTB-sTDA in chemical space. We also show generalizability of the workflow by calibrating against a higher-level technique (CC2), yielding a similarly low error. Overall, this work demonstrates that machine learning can be used to develop a cost-effective and accurate method for large-scale excited state screening, enabling accelerated molecular discovery across a variety of disciplines.

Calculation of Core-Excited and Core-Ionized States Using Variational Quantum Deflation Method and Applications to Photocatalyst Modeling.

The possibility of performing quantum-chemical calculations using quantum computers has attracted much interest. Variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum devices. Although the validity of this method has been demonstrated, there have been few practical applications, primarily because of the uncertain effect of calculation conditions on the results. In the present study, calculations of the core-excited and core-ionized states for common molecules based on the VQD method were examined using a classical computer, focusing on the effects of the weighting coefficients applied in the penalty terms of the cost function. Adopting a simplified procedure for estimating the weighting coefficients based on molecular orbital levels allowed these core-level states to be successfully calculated. The O 1s core-ionized state for a water molecule was calculated with various weighting coefficients, and the resulting ansatz states were systematically examined. The application of this technique to functional materials was demonstrated by calculating the core-level states for titanium dioxide (TiO2) and nitrogen-doped TiO2 models. The results demonstrate that VQD calculations employing an appropriate cost function can be applied to the analysis of functional materials in conjunction with an experimental approach.

End-capped group modification on cyclopentadithiophene based non-fullerene small molecule acceptors for efficient organic solar cells; a DFT approach

Four acceptor-donor-acceptor (A-D-A) type cyclopentadithiophene core-based non-fullerene small acceptor molecules were designed with the objective to improve the proficiency of photovoltaic cells. A comprehensive density functional theory (DFT) analysis was done by employing B3LYP functional with 6–31G(d,p) basis set to study optoelectronic properties of R as well as M1-M4 molecules, while the time-dependent self-consistent field (TDSCF) was utilized to analyze their excited state calculations. Several essential characteristics must be refined in order to enhance the efficiency of small molecular acceptors, i.e., the density of states (DOS), HOMO-LUMO band gap, transition density matrix (TDM), dipole moment, reorganization energy, light-harvesting efficiency, and open-circuit voltage, etc. In comparison to the R molecule, all the derived molecules show better maximum absorption (in chloroform solvent) with a range of 886–951 nm and a smaller band gap with a range of 1.65–1.55 eV M2 retains the least exciton binding energy of 0.24 eV, and amongst all the investigated molecules M3 molecule has the least interaction coefficient values so, it possesses better charge transport probability. The reorganization energy values in eV for both electron (0.00579) and hole (0.00737) are the least for M3 molecule, so this molecule exhibits better charge mobility for electron and hole. VOC of R and M1-M4 molecule was calculated by theoretically computing the values of their complexes with PTB7-Th donor molecule.

Triple proton transfer after water rearrangement in (2,6-aza)Ind·(H2O)2

We have studied the electronic equilibrium structures and the tautomerization process in (2,6-aza)Ind·(H2O)2-3 cluster in the gas phase and in solvent water by DFT and TDDFT methods. In (2,6-aza)Ind·(H2O)2 cluster, we found three novel stable clusters (NCHB-I1, NCHB-I2 and NCHB-O) with water line hydrogen boned in the molecular plane and under the molecular plane, respectively. Especially, the water line in NCHB-O is connected with the proton donor and proton acceptor, which provides a route for proton transfer. Atoms in molecules (AIM) and non-covalent interactions (NCI) analysis were used to analyze the interaction strength and interaction type in them. We also found that NCHB-I1 and NCHB-I2 could isomerize to NCHB-O via water rearrangement, from where triple proton transfer takes place. Further analysis shows that excited-state triple proton transfer follows an asynchronous concerted mechanism but with considerably high energy barrier in both gas phase and in water which makes it difficult to occur. In (2,6-aza)Ind·(H2O)3, the ADMP simulations show that water rearrangement could occur from the bridged normal cluster to the 2 + 1 type cluster (2,6-aza)Ind·(H2O)2+1 with two water molecules in the first shell and a single water in the second shell. The excited-state IRC calculation shows that energy barrier for the excited-state triple proton transfer in (2,6-aza)Ind·(H2O)2+1 is slightly lowered after a single water in the second shell compared with the one in (2,6-aza)Ind·(H2O)2. On the other hand, the energy barrier for the excited-state quadruple proton transfer in (2,6-aza)Ind·(H2O)3 is considerably lower than the ones for triple proton transfer in (2,6-aza)Ind·(H2O)2 and (2,6-aza)Ind·(H2O)2+1, suggesting that the quadruple proton transfer mechanism is more preferred instead of triple proton transfer. This study provides significant insight into the proton transfer behavior in similar cluster systems, also shows the significance of water rearrangement in the proton transfer processes.

Theoretical insights into the effects of RE doping on the structural, electronic, and optical properties of magnesium clusters

Doping of magnesium-based materials with the rare earth (RE) elements allows one to adjust or modify the structures and properties of the materials. In the present work, the structural, electronic, and optical properties of the global minima Mgn (n = 2–10) and MgnX (X = Sc, Y, La, Nd, Gd, n = 1–9) clusters have been examined using the density functional theory (DFT) and the time-dependent DFT. The identified structures show that the RE atoms tend to occupy the center of the surface of the geometries, which enhances their structural stability. Further analyses on average bonding energies, the second-order differences in energy, and HOMO–LUMO gaps indicate that the Mg3Nd cluster is more stable than others. The excellent stability of this cluster is caused by the strong Nd 4f and Mg 2p interactions through the analyses of molecular orbitals. The natural population analyses imply that the electron transfers mainly occur among the s-p-d orbitals in MgnX (X = Sc, Y, La) clusters and the s-d-f orbitals in MgnX (X = Nd, Gd). In addition, the results of the excited-state calculations reveal that the absorption spectra of all MgnX clusters emerge red-shift phenomena compared with that of Mgn, and the absorbance strongest resonances of Mg4X clusters concentrate at visible light region (about 600 nm).

A DFT approach for finding therapeutic potential of two dimensional (2D) graphitic carbon nitride (GCN) as a drug delivery carrier for curcumin to treat cardiovascular diseases

The density functional theory (DFT) analysis is used to predict the therapeutic potential of Graphitic carbon nitride (GCN) as a medicinal carrier for curcumin for the treatment of cardiovascular diseases. To evaluate the drug transport capacity of GCN, the electronic, ground, and excited-state properties of curcumin, GCN, and the GCN-curcumin-complex were investigated. The adsorption energy of the GCN-curcumin-complex is higher in the gas phase (−0.25 eV) than in the aqueous phase (−0.09 eV), implying that the GCN-curcumin-complex is more stable in the gas phase. Weak NH bonds anchored the curcumin at GCN surface. The GCN-curcumin-complex has a higher dipole moment in the aqueous medium (2.37 D) than in the gas phase (1.36 D) which aids in the efficient transport of the drug through biological systems. Molecular electrostatic potential and frontier molecular orbitals revealed that during excitation, curcumin behaves as a HOMO, transferring charge to the LUMO (GCN). The charge decomposition analysis, which determines the highest overlap between the curcumin and GCN orbitals, was also employed to investigate the charge transfer process. For several transitions from the donor to the acceptor, Natural bond orbital (NBO) analysis revealed that charge was transferred between the curcumin and GCN molecules. For the GCN-curcumin-complex, excited-state calculations show that λmax is redshifted by 131 nm. The redshift for the GCN-curcumin-complex in the solvent phase is 149 nm. The theoretically generated spectra match experimentally observed spectra quite well. Moreover, the in silico infrared spectra of GCN and Curcumin is also close to the experimental spectra. For the graphical explanation of various excited states, electron-hole and photoinduced electron-transfer analysis are performed. The Photoinduced electron transfer (PET) mechanism perceives quenching of fluorescence because of an interaction. Moreover, GCN +1/−1 showed little structural change and produces stable curcumin complexes. All findings indicated that GCN has substantial therapeutic potential as a carrier for curcumin in cardiovascular disease cure. Researchers will be motivated to investigate alternative 2D nanomaterials for drug delivery applications due to this theoretical study.

Half‐Projected Hartree–Fock method: History and application to excited states of the same symmetry as the ground state

AbstractSpin projected wave functions are generalizations of the Hartree–Fock wave function. Among them, the Half‐Projected Hartree–Fock (HPHF) wave function is a nearly pure wave function of spin and recovers a small part of the spin correlation energy. This paper reviews the history of the HPHF theory, not only from the conceptual point of view but also providing a compilation of the publications of this method over the years until now. In addition, the extension of the HPHF method to the calculation of excited states with the same symmetry as the ground state will be discussed. The possible variational collapse during the calculation of a singlet excited state of the same symmetry as the ground state is avoided by orthogonalizing a pair of corresponding orbitals, one occupied and one virtual orbital, at every step of the variational process. As an example, the potential energy surfaces of the S0 ground and 1S1(n, π*) first excited state of the formic acid HCOOH are calculated.

X-ray absorption spectra of aqueous cellobiose: Experiment and theory

The hydration structure of cellulose is very important for understanding the hydrolysis of cellulose at the molecular level. In this paper, we report a joint experimental and theoretical study on x-ray absorption spectroscopy (XAS) of aqueous cellobiose, a disaccharide unit of cellulose. In the experimental part, high resolution measurements of the carbon K-edge XAS spectra were taken. In the theoretical part, ab initio molecular dynamics simulations and ensemble calculations of electronic excited states were performed to obtain the continuous XAS spectra. The XAS spectra were found to have three characteristic peaks at 289.3, 290.7, and 293.6eV, each representing the absorption by carbon atoms of the alcohol group, the hemiacetal group, and both of these functional groups. It was found that the peak heights in the spectrum change considerably over the temperature range of 25-60 °C, which is a reflection of the number of hydrogen bonds between cellobiose and water. We suggest that this spectral change could be useful information for identifying the hydration of cellulose in various environments.

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of S1 and T1 excited states giving rise to a negative energy difference (ΔEST) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems.

Low-Scaling Excited State Calculation Using the Block Interaction Product State.

We develop an automatic and efficient scheme for the accurate construction of the bases for excitonic models, which can enable "black-box" excited state structure calculations for large molecular systems. These new and optimized bases, which are named the block interaction product state (BIPS), can be expressed as the direct products of the local states for each chromophore. Each chromophore's local states are selected by diagonalization of its reduced density matrix, which is obtained by quantum chemical calculation of the small subsystem composed of the chromophore and its nearest neighbors. We implemented the BIPS framework with fragment-based calculations considering two- and three-body interactions. Test calculations for eight different molecular aggregates demonstrate that this framework provides an accurate description of not only the excitation energies but also the first-order wave function properties (dipole moment and transition dipole moment) of the low-lying excited states at a low-scaling computational cost.

DFT and TD-DFT Calculations of Orbital Energies and Photovoltaic Properties of Small Molecule Donor and Acceptor Materials Used in Organic Solar Cells

DFT and TD-DFT calculations of HOMO and LUMO energies and photovoltaic properties are carried out on four selected pentathiophene donor and one IDIC-4F acceptor molecules using B3LYP and PBE0 functionals for the ground state energy calculations and CAM-B3LYP functional for the excited state calculations. The discrepancy between the calculated and experimental energies is reduced by correlating them with a linear fit. The fitted energies of HOMO and LUMO are used to calculate the Voc of an OSC based on these donors and acceptor blend and compared with experimental values. Using the Scharber model the calculated PCE of the donor-acceptor molecules agree with the experiment. It has been found that fluorine substitution can be used to improve charge transport by reducing the electron and hole reorganization energies of the molecules. It is also found that the introduction of fluorine onto the donor pentathiophene unit of the donor molecule results in a change of polarity of the distributed charges in the molecule due to the high electronegativity of the fluorine atom. The quantum chemical potential (μ), chemical hardness (η) and electronegativity (χ), and electrostatic potential maps (EPMs) are also calculated to identify different charge distribution regions in all five molecules.

Synthesis, crystal structures and characterization of Nickel(II) complexes with dithiobenzoate derivatives

New nickel(II) complexes with dithiobenzoate ligands, [NiII(Me-dtb)2] and [NiII(Oct-dtb)2]2 (Me-dtb = 4-methyl-dithiobenzoate and Oct-dtb = 4-octyl-dithiobenzoate), were synthesized and structurally characterized using X–ray diffraction analysis. [NiII(Me-dtb)2] has a mononuclear structure, including a nickel(II) ion with a square planar coordination geometry, and [NiII(Oct-dtb)2]2 has a dinuclear structure connected by weak Ni•••S interactions in the apical position of the nickel ion. The solutions of these complexes show strong light absorption at approximately 600 nm with a dark blue color. To reveal the electronic states and mechanism of the light absorption of Ni(II)- dithiobenzoate complexes, optimization of the ground-state molecular structures and excited-state calculations for [NiII(dtb)2] (dtb = dithiobenzoate) and [NiII(Me2dtc)2] (Me2dtc = dimethyl-dithiocarbamate) were performed by DFT/B3LYP method and TD-DFT/CAM-B3LYP method, respectively.

Excited States Calculations of MoS2@ZnO and WS2@ZnO Two-Dimensional Nanocomposites for Water-Splitting Applications

Transition metal dichalcogenide (TMD) MoS2 and WS2 monolayers (MLs) deposited atop of crystalline zinc oxide (ZnO) and graphene-like ZnO (g-ZnO) substrates have been investigated by means of density functional theory (DFT) using PBE and GLLBSC exchange-correlation functionals. In this work, the electronic structure and optical properties of studied hybrid nanomaterials are described in view of the influence of ZnO substrates thickness on the MoS2@ZnO and WS2@ZnO two-dimensional (2D) nanocomposites. The thicker ZnO substrate not only triggers the decrease of the imaginary part of dielectric function relatively to more thinner g-ZnO but also results in the less accumulated charge density in the vicinity of the Mo and W atoms at the conduction band minimum. Based on the results of our calculations, we predict that MoS2 and WS2 monolayers placed at g-ZnO substrate yield essential enhancement of the photoabsorption in the visible region of solar spectra and, thus, can be used as a promising catalyst for photo-driven water splitting applications.

Multicomponent heat-bath configuration interaction with the perturbative correction for the calculation of protonic excited states.

In this study, we extend the multicomponent heat-bath configuration interaction (HCI) method to excited states. Previous multicomponent HCI studies have been performed using only the variational stage of the HCI algorithm as they have largely focused on the calculation of protonic densities. Because this study focuses on energetic quantities, a second-order perturbative correction after the variational stage is essential. Therefore, this study implements the second-order Epstein-Nesbet correction to the variational stage of multicomponent HCI for the first time. Additionally, this study introduces a new procedure for calculating reference excitation energies for multicomponent methods using the Fourier-grid Hamiltonian (FGH) method, which should allow the one-particle electronic basis set errors to be better isolated from errors arising from an incomplete description of electron-proton correlation. The excited-state multicomponent HCI method is benchmarked by computing protonic excitations of the HCN and FHF- molecules and is shown to be of similar accuracy to previous excited-state multicomponent methods such as the multicomponent time-dependent density-functional theory and equation-of-motion coupled-cluster theory relative to the new FGH reference values.