Excited State Wave Functions Research Articles

Systematic Improvement of Quantum Monte Carlo Calculations in Transition Metal Oxides: sCI-Driven Wavefunction Optimization for Reliable Band Gap Prediction.

Accurate determination of the electronic properties of correlated oxides remains a significant challenge for computational theory. Traditional Hubbard-corrected density functional theory (DFT+U) frequently encounters limitations in precisely capturing electron correlation, particularly in predicting band gaps. We introduce a systematic methodology to enhance the accuracy of diffusion Monte Carlo (DMC) simulations for both ground and excited states, focusing on LiCoO2 as a case study. By employing a selected configuration interaction (sCI) approach, we demonstrate the capability to optimize wavefunctions beyond the constraints of single-reference DFT+U trial wavefunctions. We show that the sCI framework enables accurate prediction of band gaps in LiCoO2, closely aligning with experimental values and substantially improving traditional computational methods. The study uncovers a nuanced mixed state of t2g and eg orbitals at the band edges that is not captured by conventional single-reference methods, further elucidating the limitations of PBE+U in describing d-d excitations. Our findings advocate for the adoption of beyond-DFT methodologies, such as sCI, to capture the essential physics of excited-state wavefunctions in strongly correlated materials. The improved accuracy in band gap predictions and the ability to generate more reliable trial wavefunctions for DMC calculations underscore the potential of this approach for broader applications in the study of correlated oxides. This work not only provides a pathway for more accurate simulations of electronic structures in complex materials but also suggests a framework for future investigations of the excited states of other challenging systems.

Natural perturbation orbital analyses of polarizability and Raman intensity of p-Benzoquinodimethane

The polarizability and Raman intensity of the smallest quinoid hydrocarbon p-benzoquinodimethane were analyzed as electronic deformations in the electric field. The perturbed canonical MOs (CMOs) were transformed to NPOs using the singular value decomposition. The NPOs can represent the intrinsic characters of the electronic deformations that CMOs cannot describe properly. The electronic deformations of HOMO-LUMO type dominate the long-axis polarizability and the strongest Raman intensities. TDDFT calculations demonstrated the relevance of the NPOs to the singly-excited wavefunctions of excited states. The mode-specific predictivity of Raman intensity was discussed based on the polarizability components obtained by B3LYP and CCSD(T) calculations.

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Ensemble variational Monte Carlo for optimization of correlated excited state wave functions

Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a penalty to minimize overlap with lower eigenstates, which has the drawback that states must be computed one at a time. We derive a general framework for constructing objective functions with minima at the the lowest N eigenstates of a many-body Hamiltonian. The objective function uses a weighted average of the energies and an overlap penalty, which must satisfy several conditions. We show this objective function has a minimum at the exact eigenstates for a finite penalty, and provide a few strategies to minimize the objective function. The method is demonstrated using ab initio variational Monte Carlo to calculate the degenerate first excited state of a CO molecule.

The approximate coupled-cluster methods CC2 and CC3 in a finite magnetic field.

In this paper, we report on the implementation of CC2 and CC3 in the context of molecules in finite magnetic fields. The methods are applied to the investigation of atoms and molecules through spectroscopic predictions and geometry optimizations for the study of the atmosphere of highly magnetized White Dwarf stars. We show that ground-state finite-field (ff) CC2 is a reasonable alternative to CCSD for energies and, in particular, for geometrical properties. For excited states, ff-CC2 is shown to perform well for states with predominant single-excitation character. Yet, for cases in which the excited state wavefunction has double-excitation character with respect to the reference, ff-CC2 can easily lead to completely unphysical results. Ff-CC3, however, is shown to reproduce the CCSDT behavior very well and enables the treatment of larger systems at a high accuracy.

A Method of Constructing Superpotentials by Combining Two Functions Based on Shape Invariance

Supersymmetric quantum mechanics (SUSYQM) plays an important role in solving the Schrödinger equation, and it is also important to find more superpotentials that can be solved accurately. On the basis of studying the characteristics of existing superpotentials, the authors find a missing superpotential and put forward a method by combining two functions to construct all existing solvable superpotentials and prove the existence of the missing superpotential. First, based on the idea of SUSYQM, this paper studies the shape invariance of the partner potentials with the form of two functions and obtains the energy spectrum in many different cases. Second, according to the results of solving differential equations satisfied by two functions, the authors not only construct most existing solvable superpotentials successfully but also generate a missing solvable superpotential. Third, for the missing solvable superpotential, some discussions are made, such as the corresponding partner potentials, energy spectrum, ground state wave function, and excited state wave functions. Lastly, the summary is made, and the prospects are projected.

Multi-body wave function of ground and low-lying excited states using unornamented deep neural networks

Multi-body wave function of ground and low-lying excited states using unornamented deep neural networks

Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory.

State-specific electronic structure theory provides a route toward balanced excited-state wave functions by exploiting higher-energy stationary points of the electronic energy. Multiconfigurational wave function approximations can describe both closed- and open-shell excited states and avoid the issues associated with state-averaged approaches. We investigate the existence of higher-energy solutions in complete active space self-consistent field (CASSCF) theory and characterize their topological properties. We demonstrate that state-specific approximations can provide accurate higher-energy excited states in H2 (6-31G) with more compact active spaces than would be required in a state-averaged formalism. We then elucidate the unphysical stationary points, demonstrating that they arise from redundant orbitals when the active space is too large or symmetry breaking when the active space is too small. Furthermore, we investigate the singlet-triplet crossing in CH2 (6-31G) and the avoided crossing in LiF (6-31G), revealing the severity of root flipping and demonstrating that state-specific solutions can behave quasi-diabatically or adiabatically. These results elucidate the complexity of the CASSCF energy landscape, highlighting the advantages and challenges of practical state-specific calculations.

Kajian Literatur Fase Adiabatik untuk mempercepat Dinamika Kuantum Adiabatik pada Osilator Harmonik

<p>This research is a theoretical research by reviewing the literature that discusses the method of accelerating quantum dynamics adiabatically. This method for accelerating quantum dynamics is so- called the fast-forward method. This method was proposed by Masuda and Nakamura in 2010. In this method, the ground state and first excited state wave function is modified by adding an additional term to the wave function which is called the adiabatic phase. This is done so that the time-dependent Schrodinger equation remains fulfilled. The accelerating process is carried out using an adiabatic parameter that goes to zero. Fast-forward method is applied first to get the adiabatic phase. Furthermore, by reviewing the wave function at the ground state and first excited state we get the adiabatic phase which ensures that the harmonic oscillator can move from the initial state to the final state in a shorter time.</p>

Energy Component Analysis for Electronically Excited States of Molecules: Why the Lowest Excited State Is Not Always the HOMO/LUMO Transition

The ability to tune excited-state energies is crucial to many areas of molecular design. In many cases, this is done based on the energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). However, this viewpoint is incomplete neglecting the many-body nature of the underlying excited-state wave functions. Within this work, we highlight the importance of two crucial terms, other than orbital energies, that contribute to the excitation energies and show how to quantify them from quantum chemistry computations: a Coulomb attraction and a repulsive exchange interaction. Using this framework, we explain under which circumstances the lowest excited state of a molecule, of either singlet or triplet multiplicity, is not accessed via the HOMO/LUMO transition and show two paradigmatic examples. In the case of the push-pull molecule ACRFLCN, we highlight how the lowest triplet excited state is a locally excited state lying below the HOMO/LUMO charge transfer state due to enhanced Coulomb binding. In the case of the naphthalene molecule, we highlight how the HOMO/LUMO transition (the 1La state) becomes the second excited singlet state due to its enhanced exchange repulsion term. More generally, we explain why excitation energies do not always behave like orbital energy gaps, providing insight into photophysical processes as well as methodogical challenges in describing them.

An ab initio method on large sized molecular aggregate system: Predicting absorption spectra of crystalline organic semiconducting films.

Theoretical description of electronically excited states of molecular aggregates at an ab initio level is computationally demanding. To reduce the computational cost, we propose a model Hamiltonian approach that approximates the electronically excited state wavefunction of the molecular aggregate. We benchmark our approach on a thiophene hexamer, as well as calculate the absorption spectra of several crystalline non-fullerene acceptors, including Y6 and ITIC, which are known for their high power conversion efficiency in organic solar cells. The method qualitatively predicts the experimentally measured spectral shape, which can be further linked to the molecular arrangement in the unit cell.

Characterizing Superradiant Phase of the Quantum Rabi Model

Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model (QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two successive diagonalizations to accurately obtain the ground-state and excited states wavefunctions of the QRM in full parameter regime ranging from weak to deep-strong couplings. Thus, one is able to see how the phase transition occurs and how the photons populate in Fock space of the superradiant phase. We characterize the photon populations by borrowing the distribution concept in random matrix theory and find that the photon population follows a Poissonian-like distribution once the phase transition takes place and further exhibits the statistics of Gaussian unitary ensemble with increasing coupling strength. More interestingly, the photons in the excited states behave even like the statistics of Gaussian orthogonal ensemble. Our results not only deepen understanding on the superradiant phase transition but also provide an insight on the nature of the superradiant phase of the QRM and related models.

Confinement of the Triplet States in π-Conjugated BODIPY Dimers Linked with Ethynylene or Butadiynylene Bridges: A Different View on the Effect of Symmetry.

Understanding the impact of the excited state wavefunction confinement is crucial for the engineering of the photophysical properties and applications of organic chromophores. In the present contribution, the localization of the triplet state wavefunctions of some symmetric ethyne/butadiyne bridged BODIPY dimers and asymmetric BODIPY derivatives presenting extended π-conjugation frameworks is studied with time-resolved electron paramagnetic resonance spectroscopy and time-dependent density functional theory computations. Based on the Zero Field Splitting D parameters, we conclude that the triplet state wavefunctions are highly localized on one BODIPY unit in the symmetric dimers, which is consistent with the ab initio modelling that finds delocalized triplet state destabilized by 12-14 kcal mol-1 as compared to its localized counterpart. The result provides a new insight into the study of triplet excited state confinement and the design of molecular wires or photosensitizers for photovoltaics and photocatalysis.

Confinement of the Triplet States in π‐Conjugated BODIPY Dimers Linked with Ethynylene or Butadiynylene Bridges: A Different View on the Effect of Symmetry

AbstractUnderstanding the impact of the excited state wavefunction confinement is crucial for the engineering of the photophysical properties and applications of organic chromophores. In the present contribution, the localization of the triplet state wavefunctions of some symmetric ethyne/butadiyne bridged BODIPY dimers and asymmetric BODIPY derivatives presenting extended π‐conjugation frameworks is studied with time‐resolved electron paramagnetic resonance spectroscopy and time‐dependent density functional theory computations. Based on the Zero Field Splitting D parameters, we conclude that the triplet state wavefunctions are highly localized on one BODIPY unit in the symmetric dimers, which is consistent with the ab initio modelling that finds delocalized triplet state destabilized by 12–14 kcal mol−1 as compared to its localized counterpart. The result provides a new insight into the study of triplet excited state confinement and the design of molecular wires or photosensitizers for photovoltaics and photocatalysis.

Synthesis, characterization, computational, excited state properties, wave function and molecular docking studies of (E)-1-(perfluorophenyl)-N-(p-tolyl) methanimine

The compound (E)-1-(perfluorophenyl)-N-(p-tolyl)methanimine (PFPT) was synthesized and characterized by the Infrared, UV–Visible, and NMR analysis. Using density functional theory, the current work is a set of theoretical studies on PFPT. The compound molecular structure and geometry were defined using DFT. Topological studies, like electron localized function, localized orbital locator, average localized ionization energy, and reduced density gradient studies, were done with the Multiwfn-3.8 to find the main binding areas and weak interactions in the molecule. Using the IEFPCM solvation model used to study the calculated UV–Visible spectrum, we used two different solvents. The HOMO-LUMO, MEP, and NLO properties were carried out by DFT/B3LYP/cc-pVDZ in the gas phase. The NBO calculations are used to study how charges move between and within the molecule and the stability of this molecule. A pharmacological analysis is done using an online tool like Swiss-ADME, to see if the molecule could be a potential drug candidate; this evaluation looks at the drug-likeness, ADME, and eco-friendly toxicity properties of the PFPT molecule. Auto-dock suite and Discovery studio Visualizer are used to do molecular docking against 2QFA protein.

Anisotropic photoelectric properties in GaN/AlN quantum dots under terahertz laser polarization

The linear and nonlinear anisotropic optical absorption coefficients(OACs) and refractive index changes(RICs) of GaN/AlN cubical quantum dots(CQDs) subjected to terahertz laser field(TLF) are investigated. The results show that under the polarization of TLF, with the increase of laser dressing parameters, the peak of OACs and RICs increases nonlinearly and have a redshift. More importantly, our work indicated that with the enhancement of TLF polarization, the redistribution of electron excited state wave function will lead to the “loss” of optical properties in the specific frequency band. The redistribution of electron ground state wave function has a significant modulation effect on the magnitude of OACs(RICs) peak. • The enhancement of the refractive index changes was observed at low frequencies. • The phenomenon of wave function exchange in laser field modulation is found. • The modulation of laser field on optical coefficient cannot cover the whole frequency band.

Self-trapped excitons in diamond: A Δ-SCF approach.

This paper reports the first variationally based predictions of the lowest excited state in diamond (Γ25' → Γ15) in the unrelaxed (optical) and structurally relaxed (thermal) configurations, from direct Δ-self-consistent-field (SCF) calculations based on B3LYP, PBE0, HSE06, and GGA functionals. For the B3LYP functional, which has the best overall performance, the energy of the optical state, 7.27eV, is within the observed range of (7.2-7.4) eV and is predicted to be insulating, with indirect bandgaps of (5.6-5.8) eV. Mulliken analyses of the excited state wavefunction indicate extensive redistributions of charge and spin resulting in a strongly excitonic state with a central charge of -0.8ǀeǀ surrounded by charges of +0.12ǀeǀ at the four nearest neighbor sites. The thermally relaxed state is predicted to be similarly excitonic, with comparable bandgaps and atomic charges. Calculations of the ground and excited state relaxations lead to a Stokes shift of 0.47eV and predicted Γ-point luminescence energy of 6.89eV. Assuming a similar shift at the band edge (X1), an estimate of 5.29eV is predicted for the luminescence energy, which compares with the observed value of 5.27eV. Excited state vibrational spectra show marked differences from the ground state, with the introduction of an infrared peak at 1150cm-1 and a modest shift of 2cm-1 in the TO(X) Raman mode at 1340cm-1. Similar calculations of the lowest energy bi- and triexcitons predict these to be bound states in both optical and thermal configurations and plausible precursors to exciton condensation. Estimates of bi- and triexciton luminescence energies predict red shifts with respect to the single exciton line, which are compared to the recently reported values.

Energy levels, absorption oscillator strengths, transition probabilities, polarizabilities, and g factors of Ar13+ ions

An accurate determination of various parameters of ${\mathrm{Ar}}^{13+}$ is presented in this work. The wave functions and energy levels of the low-lying states within the configurations of $2{s}^{2}2p$ and $2s2{p}^{2}$ are calculated using the fully relativistic multiconfiguration Dirac-Hartree-Fock method, while the wave functions of higher excited states with the configurations $2{s}^{2}nl\phantom{\rule{4pt}{0ex}}(n\ensuremath{\ge}3$, $l=s,p,d)$ are obtained using the relativistic configuration interaction plus core polarization method. Then, the absorption oscillator strengths, transition probabilities, polarizabilities, and $g$ factors are determined. The contributions of electron correlation effects, Breit interaction, and quantum electrodynamics effects are also investigated. The present results agree well with the available theoretical and experimental results. The $g$ factors of the $2{s}^{2}2p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2,3/2}$ states agree with the experimental measurements on a level of ${10}^{\ensuremath{-}6}$.

Angle-resolved one and Two-Photon absorption spectrum in twisted bilayer graphene quantum dots

In this paper, one-photon absorption (OPA) spectrum and two-photon absorption (TPA) spectrum and its electronic excitation, charge transfer, partial density of states (PDOS) and magnetic induction current density of zigzag edge twisted bilayer graphene quantum dots (Z-TwBLG-QDs) with different twisted angles which were divide into two pattern of Moiré superlatrate (MS) are qualitativly and quantitativly analyed by using density functional theory (DFT), excited state wave function, single electron approximation, and gauge-invariant atomic orbital (GIAO) method. The inter-layer local excitation in the electronic transition and intra-layer charge transfer dominated by MS and anti-symmetric electron-hole pair density induced by PDOS are discussed. The twisted angle is decisive to the absorption spectrum, large twisted angle will lead to the red shift of the absorption spectrum. The two-photon transition shows that the twisted angle can regulate the TPA cross section and the boundary effect of Z-TwBLG-QDs in a specific wavelength range. The edge effect of two-step transition can be enhanced by MS with specific twisted angles. The physical mechanism of twisted angle regulating electron transition behavior is revealed by magnetic induction current density analysis.

Universality of excited three-body bound states in one dimension

We study a heavy–heavy–light three-body system confined to one space dimension in the regime where an excited state in the heavy–light subsystems becomes weakly bound. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy–light state and (ii) the presence of deeply-bound heavy–light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find a strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy–light subsystems.