Excitation Energies Of Low-lying States Research Articles

Electronic Structure Methods for Simulating Flavin's Spectroscopy and Photophysics: Comparison of Multi-reference, TD-DFT, and Single-Reference Wave Function Methods.

The use of flavins and flavoproteins in photocatalytic, sensing, and biotechnological applications has led to a growing interest in computationally modeling the excited-state electronic structure and photophysics of flavin. However, there is limited consensus regarding which computational methods are appropriate for modeling flavin's photophysics. We compare the energies of low-lying excited states of flavin computed with time-dependent density functional theory (TD-DFT), equation-of-motion coupled cluster (EOM-EE-CCSD), scaled opposite-spin configuration interaction [SOS-CIS(D)], multiconfiguration pair-density functional theory (MC-PDFT), and several multireference perturbation theory (MR-PT2) methods. In the first part, we focus on excitation energies of the first singlet excited state (S1) of five different redox and protonation states of flavin, with the goal of finding a suitable active space for MR-PT2 calculations. In the second part, we construct two sets of one-dimensional potential energy surfaces connecting the S0 and S1 equilibrium geometries (S0-S1 path) and the S1 (π,π*) and S2 (n,π*) equilibrium geometries (S1-S2 path). The first path therefore follows a Franck-Condon active mode of flavin while the second path maps crossings points between low-lying singlet and triplet states in flavin. We discuss the similarities and differences in the TD-DFT, EOM-EE-CCSD, SOS-CIS(D), MC-PDFT and MR-PT2 energy profiles along these paths. We find that (TD-)DFT methods are suitable for applications such as simulating the spectra of flavins but are inconsistent with several other methods when used for some geometry optimizations and when describing the energetics of dark (n,π*) states. MR-PT2 methods show promise for the simulation of flavin's low-lying excited states, but the selection of orbitals for the active space and the number of roots used for state averaging must be done carefully to avoid artifacts. Some properties, such as the intersystem crossing geometry and energy between the S1 (π,π*) and T2 (n,π*) states, may require additional benchmarking before they can be determined quantitatively.

Ab initio calculations for well deformed nuclei: 40Mg and 42Si

We performed ab initio valence-space in-medium similarity renormalization group calculations based on chiral nucleon-nucleon and three-nucleon interactions to study the neutron-rich nuclei around N=28, where the experimental and theoretical evidence point to a rapid transition from spherical to rotational regimes. First, the rotational spectra of 40Mg, 42Si, and 44S are established theoretically, anchored by the calculated E2 transition strength. The results suggest that 40Mg and 42Si exhibit large deformations. After that, the erosion of the N=28 shell closure, especially the evolutions of shape deformation and the emergence of shape coexistence, are discussed in N=28 even-even isotones ranging from 40Mg to 48Ca. Finally, the shell evolution of N=28 in Mg and Si chains is discussed based on the experimental and predicted excitation energies of low-lying states. The results from our ab initio calculations align well with available experimental data, furnishing essential insights into the structure of neutron-rich nuclei, particularly deformations in the vicinity of 40Mg and 42Si.

The impact of nuclear shape on the emergence of the neutron dripline.

Atomic nuclei are composed of a certain number of protons Z and neutrons N. A natural question is how large Z and N can be. The study of superheavy elements explores the large Z limit1,2, and we are still looking for a comprehensive theoretical explanation of the largest possible N for a given Z-the existence limit for the neutron-rich isotopes of a given atomic species, known as the neutron dripline3. The neutron dripline of oxygen (Z=8) can be understood theoretically as the result of single nucleons filling single-particle orbits confined by a mean potential, and experiments confirm this interpretation. However, recent experiments on heavier elements are at odds with this description. Here we show that the neutron dripline from fluorine (Z=9) to magnesium (Z=12) can be predicted using a mechanism that goes beyond the single-particle picture: as the number of neutrons increases, the nuclear shape assumes an increasingly ellipsoidal deformation, leading to a higher binding energy. The saturation of this effect (when the nucleus cannot be further deformed) yields the neutron dripline: beyond this maximum N, the isotope is unbound and further neutrons 'drip' out when added. Our calculations are based on a recently developed effective nucleon-nucleon interaction4, for which large-scale eigenvalue problems are solved using configuration-interaction simulations. The results obtained show good agreement with experiments, even for excitation energies of low-lying states, up to the nucleus of magnesium-40 (which has 28 neutrons). The proposed mechanism for the formation of the neutron dripline has the potential to stimulate further thinking in the field towards explaining nucleosynthesis with neutron-rich nuclei.

A study of non-iterative triples contributions in relativistic equation-of-motion coupled-cluster calculations using an exact two-component Hamiltonian with atomic mean-field spin-orbit integrals: Application to uranyl and other heavy-element compounds.

The implementation of an equation-of-motion coupled-cluster singles and doubles augmented with a noniterative triples correction [EOM-CCSD(T)(a)*] method [D. A. Matthews and J. F. Stanton, J. Chem. Phys. 145, 124102 (2016)] with an exact two-component Hamiltonian using atomic mean-field spin-orbit integrals (X2CAMF) is reported. Benchmark calculations show that both the correction from triple excitations in the cluster operator to the similarity-transformed Hamiltonian and the contribution from triple excitations in excited-state eigenvalue equations make important contributions to computed excitation energies of molecules containing heavy elements. X2CAMF-EOM-CCSD(T)(a)* excitation energies and excited-state properties for low-lying excited states of As2, Sb2, and Bi2 are in significantly better agreement with corresponding experimental values than EOM-CCSD ones. X2CAMF-EOM-CCSD(T)(a)* calculations have also been demonstrated to provide accurate results for excitation energies of low-lying excited states of bare uranyl ion UO2 2+, hereby resolving a long-standing debate on this topic.

Rank-one basis made from matrix-product states for a low-rank approximation of molecular aggregates.

An efficient low-rank approximation to complete active space (CAS) wavefunctions for molecular aggregates is presented. Molecular aggregates usually involve two different characteristic entanglement structures: strong intramolecular entanglement and weak intermolecular entanglement. In the method, low-lying electronic states of molecular aggregates are efficiently expanded by a small number of rank-one basis states that are direct products of monomolecular wavefunctions, each of which is written as a highly entangled state such as the matrix product state (MPS). The complexities raised by strong intramolecular entanglement are therefore encapsulated by the MPS and eliminated from the degree of freedom of the effective Hamiltonian of molecular aggregates. It is demonstrated that the excitation energies of low-lying excited states of a pair of bacteriochlorophyll units with CAS(52e, 50o) are accurately reproduced by only five rank-one basis states. Because the rank-one basis states naturally have diabatic character and reproduce the low-lying spectrum of the CAS space, off-diagonal elements of the Hamiltonian are expected to give accurate diabatic couplings. It is also demonstrated that the energy splitting and the diabatic couplings in anthracene dimer systems are improved by augmenting with additional rank-one basis states.

Choosing an atomic basis set for TD-DFT, SOPPA, ADC(2), CIS(D), CC2 and EOM-CCSD calculations of low-lying excited states of organic dyes

Aiming to pinpoint an atomic basis set providing accurate transition energies at a minimal computational cost, we investigate the evolution with basis set size of the energy of low-lying excited states in nine representative conjugated dyes with a wide panel of theoretical approaches, namely TD-DFT, SOPPA, ADC(2), CIS(D), CC2, EOM-CCSD, as well as several scaled opposite spin variants, namely SOS-CIS(D), SOS-CIS(D0) and SOS-ADC(2). At the exception of TD-DFT that displays the lowest basis set dependence, it turns out that the changes obtained when increasing the size of the basis set are rather independent of the selected wavefunction model, but strongly change according to the nature of the excited state considered. Reasonable compromises between accuracy and computational burden can be attained with 6-311+G(2d,p) that allows much faster calculations than the typical reference basis set, namely aug-cc-pVTZ, for an average loss of accuracy limited to ca. 0.02 eV.

Energy Properties of rotational bands of 170-174Yb isotopes

Accounting for Coriolis mixing of experimentally known rotational bands non-adiabatic effects in energy of low-lying excited states are investigated, within phenomenological model. The Calculations for isotopes 170,172,174,176yb, are carried out.The energy and wave function structure of excited states are calculated. The finding reveals that the bands mixing has been found to have considerable impact on the wave function of low-lying states 0+ and 2+ bands.

Exact diagonalization study of the spin-1 two-dimensional J1–J3 Heisenberg model on a triangular lattice

The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1=-(1-p)J$ and $J_2=pJ$, $J>0$ $ (0 \leq p \leq 1)$, is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa$_2$S$_4$. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained with Mori's projection operator technique.

Symmetry-adapted formulation of the combined G-particle-hole hypervirial equation and Hermitian operator method

High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole hypervirial (GHV) equation method (Alcoba et al. in Int J Quantum Chem 109:3178, 2009) and the Hermitian operator (HO) one (Bouten et al. in Nucl Phys A 202:127, 1973). This work reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, which leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries. The new formulation is used to study the low-lying excited states torsional potentials in the ethylene molecule.

Variational calculations on the energy levels of graphene quantum antidots

Within the Dirac-Weyl description of the graphene, the ground and low-lying excited state energies of a graphene quantum antidot subjected to a uniform static magnetic field is calculated by employing a variational scheme. The procedure is based on the choice of exact solutions of the Dirac-Weyl equation corresponding to massless fermions under the homogeneous magnetic field as basis sets for the trial wave functions. It is found that, for parabolic graphene antidots, the valley splitting occurs due to the introduction of spatial confinement, and it increases as the confinement strength increases. Furthermore, it is also investigated that, in such dot structures, switching an antidot potential on enhances this splitting. Therefore, we investigated that it is possible to control valley splitting by geometrical parameters of a graphene quantum antidot and/or by the strength of external magnetic field.

Energy density functional description of low-lying states in neutron-deficient Sn isotopes

The investigation of the low-lying states in Sn isotopes with 50 < N < 82 in the collective Hamiltonian based on the PC-PK1 density functional in Li et al (2012 Phys. Lett. B 717 470) is extended to using other popular density functionals DD-PC1 and PC-F1. It is found that the enhanced collectivity in neutron-deficient Sn isotopes can also be reproduced by other density functionals, and the proposed microscopic mechanism does not depend on the choice of functionals. Moreover, the collective Hamiltonian has achieved an overall successful description of the excitation energies of low-lying states in neutron-deficient Sn isotopes.

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

Abstract The ground state energy, some low-lying excited state energies and oscillator strengths for a hydrogen atom confined in both a Debye screening potential and finite impenetrable spherical box have been calculated. These have been calculated using a linear variational method based on B-spline basis functions. The results have been compared with those of other authors. The evaluated energies and oscillator strengths with respect to different plasma screening parameters with a certain confinement radii are discussed.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients.

Benchmarking the Approximate Second-Order Coupled-Cluster Method on Biochromophores

Extensive benchmarking calculations are presented to assess the accuracy of commonly used quantum chemical methods in studying excited state properties of biochromophores. The first few excited states of 12 common model chromophores of photoactive yellow protein, green fluorescent protein, and rhodopsin have been studied using approximate second-order coupled-cluster (CC2) and linear-response time-dependent density functional theory (TDDFT) calculations. The study comprises investigations of basis-set dependences on CC2 excitation energies as well as comparisons of the CC2 results with excitation energies obtained at other computational levels and with experimental data. The basis-set study shows that the accuracy of the two lowest excitation energies is generally sufficient when triple-ζ basis sets augmented with polarization functions are employed, whereas the third and higher excited states were found to require diffuse basis functions in the basis set. Augmenting the basis set with diffuse functions contributes less than 0.15 eV to the excitation energies of low-lying excited states, except for some of the studied anionic states and for Rydberg states. Calculations at the TDDFT level using the B3LYP functional show the necessity of stabilizing anions with point charges or counterions when aiming at reliable electronic excitation spectra. The two lowest excitation energies of the green fluorescent protein and rhodopsin chromophores calculated at the CC2 level agree within 0.15 eV with experimental excitation energies, whereas the B3LYP values are somewhat less accurate, with a maximum deviation of 0.27 eV. The computed excitation energies for the photoactive yellow protein chromophore models deviate from available experimental values by 0.3-0.4 eV and 0.1-0.5 eV, at the CC2 and B3LYP levels of theory, respectively.

Excitation energy calculation of conjugated hydrocarbons: A new Pariser–Parr–Pople model parameterization approaching CASPT2 accuracy

A new parameterization for the Pariser-Parr-Pople (PPP) model for conjugated hydrocarbons is proposed in this work. The distance-dependence of PPP parameters are obtained from CASPT2 ground state and low-lying excited state energies of ethylene and its cation at various C-C single bond lengths and are fitted to a set of carefully chosen mathematical functions. Our new PPP model is applied to the calculation of vertical singlet-triplet energy gaps and the excitation energies for low-lying π→π(*) valence excitations in various π-conjugated molecules. Results with the new PPP model are consistently better than the standard PPP model in use. It often surpasses density functional theory and single-reference excited state methods such as configuration interaction singles or time-dependent density functional theory in terms of its accuracy and agrees reasonably well with high-level theories or experiments.

Comparison of some multireference electronic structure methods in illustrative applications

The performances of several multireference electronic structure methods including complete active space self-consistent field (CASSCF)-based second-order perturbation theory (CASPT2), multireference configuration interaction with single and double excitations (MR-CISD), MR-CISD with the Davidson correction (MR-CISD+Q), and the CASSCF-based block-correlated coupled cluster method (CAS-BCCC4) we developed recently are compared by applying them to study several different chemical problems involving computation of ground state potential energy surfaces, the singlet-triplet gaps in diradicals, reaction barriers, and the excitation energies of low-lying excited states. Comparison with the results from other highly accurate theoretical methods or the available experimental data demonstrate that for all the problems studied, the overall performance of CAS-BCCC4 is competitive with that of MR-CISD+Q, and better than that of CASPT2 and MR-CISD methods. Thus the CAS-BCCC4 approach is expected to be a promising theoretical method for quantitative descriptions of the electronic structures of molecules with noticeable multireference character.

Theoretical studies on electronic spectroscopy and dynamics with the real-time time-dependent density functional theory

Time-dependent density functional theory (TDDFT) has evolved into a general routine to extract the energies of low-lying excited states over the last decades. Driven by the remarkable progress of laser technology, the study of the interaction between matter and intense laser fields with ultrashort pulse duration develops rapidly. A great number of new strong field phenomena emerge. The requirement of a theoretical tool to study the intense field phenomena and dynamical processes of polyatomic systems is urgent. To extend the power of the TDDFT beyond the linear responses, an alternative scheme has been developed by numerically solving the time-dependent Kohn-Sham equations directly in real-time domain. In this article, we summarize the algorithms and capabilities of the real-time TDDFTon studying electron spectroscopy and dynamics of polyatomic systems. The failure of TDDFT with the adiabatic localdensity approximation on some dynamical processes and the possible solutions are synopsized as well. The numerical implementation of algorithms and applications of RT-TDDFT on the linear and nonlinear spectroscopies and electronic dynamics of nano-size nonmetal clusters are displayed.

On the photochemistry of impurity molecules in a photonic crystal

The behavior of the quantum yield of the photochemical processes occurring in polyatomic impurity molecules incorporated in a photonic crystal and its dependence on the relative position of the band gaps of the crystal and the energy of low-lying excited states of a molecule are discussed. Provided that the energy of the low-lying singlet photoactive state of a molecule is in the crystal band gap, an increase in the quantum yield of a photochemical reaction over its value in standard solutions must be observed. The processes of isomerization, dissociation, proton transfer, and oxidation are among these reactions. Examples of systems where the manifestation of this effect should be expected are given. The reactions that occur in the low-lying and high-lying triplet states, which are initiated by two-phonon excitation, and those sensitized upon the intermolecular transfer of electronic excitation energy are discussed.

Energies of low-lying excited states of linear polyenes.

Room temperature absorption and emission spectra of the all-trans isomers of decatetraene, dodecapentaene, tetradecahexaene, and hexadecaheptaene have been obtained in a series of nonpolar solvents. The resolved vibronic features in the optical spectra of these model systems allow the accurate determination of S(0) (1(1)A(g)(-)) --> S(2) (1(1)B(u)(+)) and S(1) (2(1)A(g)(-)) --> S(0) (1(1)A(g)(-)) electronic origins as a function of solvent polarizability. These data can be extrapolated to predict the transition energies in the absence of solvent perturbations. The effects of the terminal methyl substituents on the transition energies also can be estimated. Franck-Condon maxima in the absorption and emission spectra were used to estimate differences between S(0) (1(1)A(g)(-)) --> S(1) (2(1)A(g)(-)) and S(0) (1(1)A(g)(-)) --> S(2) (1(1)B(u)(+)) electronic origins and "vertical" transition energies. Experimental estimates of the vertical transition energies of unsubstituted, all-trans polyenes in vacuum as a function of conjugation length are compared with long-standing multireference configuration interaction (MRCI) treatments and with more recent ab initio calculations of the energies of the 2(1)A(g)(-) (S(1)) and 1(1)B(u)(+) (S(2)) states.

Large-scale parallel calculations with combined coupled cluster and molecular mechanics formalism: Excitation energies of zinc–porphyrin in aqueous solution

The need for combined QM/MM approaches with high-level coupled cluster (CC) methods in the QM core is unquestionable. In an effort to make these methods widely applicable, the scalability of CC approaches across hundreds/thousands of CPUs will play a central role. In this Letter we report the performance of our CC codes in calculations of vertical excitation energies of low-lying excited states of the zinc–porphyrin molecule in aqueous solution. Coupled cluster description of excited states is based on equation-of-motion approach with singles and doubles (EOMCCSD) as well as its non-iterative extension for triply excited configurations. These results are compared with those obtained with time-dependent density functional theory (TD-DFT).