1s Ground State Research Articles

Photochromic properties calculation of diaryl maleic anhydride

Abstract In the calculation of the photochromic mechanism of (2,3-di(3-furyl)maleic anhydride, DFMA) ( as reported in Acta Phys. Sinica. 2021, 70(16): 163101), it was discovered that between the open-ring and closed-ring stable configurations, the potential energy curves of the electronic ground state (S0) and the first excited state (S1) exhibited an ‘X’ shape distribution along the reaction path. The conversion between open-ring and closed-ring occurs at the intersection of the potential energy curves, and a photoinduced ring-closing reaction accompanied by fluorescence was predicted, while a photoinduced ring-opening reaction was not. In this work, we apply the same method to investigate the mechanism of the photoinduced molecular switching process in the compounds of 2,3-di(3-thienyl)maleic anhydride(DTMA) and 2,3-di(3-pyrrolyl)maleic anhydride(DPMA). The transition state (TS) and minimum energy path (MEP) between the open-ring and closed-ring were determined by using the nudged elastic band (NEB) method. The potential energy curves of the lowest eight single excited states of DxMA(x = F, T, P) were computed based on the molecular configurations corresponding to the MEP curve (ground state S0). Interestingly, only the first excited state (S1 state) has a minimum value in the TS configuration among all eight excited states. That is, between the open-ring and closed-ring, the potential curves of S0 and S1 display an ‘X’ shape with a cross occurred at the TS configuration. The calculation of the S1←S0 resonance vibronic absorption spectrum of the open-ring/closed-ring state via molecular dynamics reveals that the transition intensity of the closed-ring state is 3 ∼ 5 times that of the open-ring state, which demonstrates that the efficiency of the closed-ring to the open-ring is higher.

Tuning the photophysical and NLO properties of β-diketonates derived from coumarin-triphenylamine-chalcones: Effect of the BF2 group

Herein the synthesis of three difluoroboron β-diketonate complexes (7a-c) and one chalcone (7d) with coumarin and triphenylamine fragments is described. The effect of the inclusion of the difluoroboron (BF2) group and a phenyl linker on the photophysical properties, intramolecular charge transfer (ICT) and nonlinear optical (NLO) properties was studied. These dyes exhibited excellent ICT properties due to their A-π-D and D-π-A-π-D type push-pull configuration. Thus, all compounds presented a strong solvatochromism, given the absorption and emission maxima shifted to red because of the increase in the polarity of the medium. In addition to this, 7a-d showed the formation of a twisted intramolecular charge transfer (TICT) state, which quenched fluorescence in polar solvents. Compounds 7a, 7b and 7d exhibited aggregation-induced emission (AIE) in MeCN/H2O mixtures, while 7c did not have this behavior. In addition, all compounds showed emission in the solid state. Using DFT and TD-DFT calculations, the molecular geometries of the ground state S0 and the first excited state S1 were elucidated, which confirmed the formation of a TICT state. Furthermore, the theoretical and experimental absorption electronic transitions were correlated by testing different functionals: B3LYP, CAM-B3LYP, PBE0, wB97XD, HSEH1PBE and M062X. Frontier molecular orbitals (FOMs) and molecular electrostatic potentials (MEPs) supported the ICT from the donor to the acceptor group. The global reactivity descriptors were studied and the NLO properties were predicted by calculating first (βtot) and second-order (γave) hyperpolarizabilities, revealing that 7a-d would present promising NLO behavior.

Multifunctional cyanoaryl porphyrazine pigments with push-pull structure of macrocycle framing: Photophysics and possible applications

We report the experimental study of fluorescence properties of three porphyrazine derivatives, distinct in the number of fused aromatic rings in aryl groups contained in the macrocycle frame and/or presence of Pd in the macrocycle, in solutions with biological molecules and in methanol-glycerol mixtures. Spectral and lifetime fluorescence analysis has revealed that all three pigments demonstrated two fluorescence transition bands from the first S1 and the second S2 electronic excited states to the ground state S0, and thus followed the anti-Kasha’s rule. Strong dependence of the quantum yield and lifetimes in the S1 → S0 fluorescence band on solution viscosity was observed. A significant increase of the fluorescence decay times and fluorescence intensity with albumin concentration and with presence of other biological molecules in solution was observed as well. A model of the low-laying energy states of porphyrazine derivatives has been developed for elucidation of the fluorescence properties observed, that took into account several radiative and non-radiative relaxation channels in molecular excited states. In particular, the model suggests that the first electronic excited state consists of planar and bent conformations separated by a potential energy barrier and shows a typical molecular-rotor behavior as a function of solution viscosity. Potential applications of the porphyrazine pigments as viscosity sensors and fluorescence probes were considered.

Conical Intersections at Interfaces Revealed by Phase-Cycling Interface-Specific Two-Dimensional Electronic Spectroscopy (i2D-ES).

Conical intersections (CIs) hold significant stake in manipulating and controlling photochemical reaction pathways of molecules at interfaces and surfaces by affecting molecular dynamics therein. Currently, there is no tool for characterizing CIs at interfaces and surfaces. To this end, we have developed phase-cycling interface-specific two-dimensional electronic spectroscopy (i2D-ES) and combined it with advanced computational modeling to explore nonadiabatic CI dynamics of molecules at the air/water interface. Specifically, we integrated the phase locked pump pulse pair with an interface-specific electronic probe to obtain the two-dimensional interface-specific responses. We demonstrate that the nonadiabatic transitions of an interface-active azo dye molecule that occur through the CIs at the interface have different kinetic pathways from those in the bulk water. Upon photoexcitation, two CIs are present: one from an intersection of an optically active S2 state with a dark S1 state and the other from the intersection of the progressed S1 with the ground state S0. We find that the molecular conformations in the ground state are different for interfacial molecules. The interfacial molecules are intimately correlated with the locally populated excited state S2 being farther away from the CI region. This leads to slower nonadiabatic dynamics at the interface than in bulk water. Moreover, we show that the nonadiabatic transition from the S1 dark state to the ground state is significantly longer at the interface than that in the bulk, which is likely due to the orientationally restricted configuration of the excited state at the interface. Our findings suggest that orientational configurations of molecules manipulate reaction pathways at interfaces and surfaces.

Kinetic Study and Reaction Mechanism of the Gas-Phase Thermolysis Reaction of Methyl Derivatives of 1,2,4,5-Tetroxane.

Tetroxane derivatives are interesting drugs for antileishmaniasis and antimalaric treatments. The gas-phase thermal decomposition of 3,6,-dimethyl-1,2,4,5-tetroxane (DMT) and 3,3,6,6,-tetramethyl-1,2,4,5-tetroxane (acetone diperoxide (ACDP)) was studied at 493-543 K by direct gas chromatography by means of a flow reactor. The reaction is produced in the injector chamber at different temperatures. The resulting kinetics Arrhenius equations were calculated for both tetroxanes. Including the parent compound of the series 1,2,4,5-tetroxane (formaldehyde diperoxide (FDP)), the activation energy and frequency factors decrease linearly with the number of methyl groups. The reaction mechanisms of ACDP and 3,6,6-trimethyl-1,2,4,5-tetroxane (TMT) decomposition have been studied by means of the DFT method with the BHANDHLYP functional. Our calculations confirm that the concerted mechanism should be discarded and that only the stepwise mechanism occurs. The critical points of the singlet and triplet state potential energy surfaces (S- and T-PES) of the thermolysis reaction of both compounds have been determined. The calculated activation energies of the different steps vary linearly with the number of methyl groups of the methyl-tetroxanes series. The mechanism for the S-PES leads to a diradical O···O open structure, which leads to a C···O dissociation in the second step and the production of the first acetaldehyde/acetone molecule. This last one yields a second C···O dissociation, producing O2 and another acetone/acetaldehyde molecule. The O2 molecule is in the singlet state. A quasi-parallel mechanism for the T-PES from the open diradical to products is also found. Most of the critical points of both PES are linear with the number of methyl groups. Reaction in the triplet state is much more exothermic than the singlet state mechanism. Transitions from the singlet ground state, S0 and low-lying singlet states S1-3, to the low-lying triplet excited states, T1-4, (chemical excitation) in the family of methyl tetroxanes are also studied at the CASSCF/CASPT2 level. Two possible mechanisms are possible here: (i) from S0 to T3 by strong spin orbit coupling (SOC) and subsequent fast internal conversion to the excited T1 state and (ii) from S0 to S2 from internal conversion and subsequent S2 to T1 by SOC. From these experimental and theoretical results, the additivity effect of the methyl groups in the thermolysis reaction of the methyl tetroxane derivatives is clearly highlighted. This information will have a great impact for controlling these processes in the laboratory and chemical industries.

Reversible Optical Switching of Polyoxovanadates and Their Communication via Photoexcited States.

The 2-bit Lindqvist-type polyoxometalate (POM) [V6O13((OCH2)3CCH2N3)2]2- with a diamagnetic {V6O19} core and azide termini shows six fully oxidized VV centers in solution as well as the solid state, according to 51V NMR spectroscopy. Under UV irradiation, it exhibits reversible switching between its ground S0 state and the energetically higher lying states in acetonitrile and water solutions. TD-DFT calculations demonstrate that this process is mainly initialized by excitation from the S0 to S9 state. Pulse radiolysis transient absorption spectroscopy experiments with a solvated electron point out photochemically induced charge disproportionation of VV into VIV and electron communication between the POM molecules via their excited states. The existence of this unique POM-to-POM electron communication is also indicated by X-ray photoelectron spectroscopy (XPS) studies on gold-metalized silicon wafers (Au//SiO2//Si) under ambient conditions. The amount of reduced vanadium centers in the "confined" environment increases substantially after beam irradiation with soft X-rays compared to non-irradiated samples. The excited state of one POM anion seems to give rise to subsequent electron transfer from another POM anion. However, this reaction is prohibited as soon as the relaxed T1 state of the POM is reached.

BeM(CO)3- (M = Co, Rh, Ir) and BeM(CO)3 (M = Ni, Pd, Pt): Triply bonded terminal beryllium in zero oxidation state.

We perform detailed potential energy surface explorations of BeM(CO)3- (M = Co, Rh, Ir) and BeM(CO)3 (M = Ni, Pd, Pt) using both single-reference and multireference-based methods. The present results at the CASPT2(12,12)/def2-QZVPD//M06-D3/def2-TZVPPD level reveal that the global minimum of BeM(CO)3- (M = Co, Rh, Ir) and BePt(CO)3 is a C3v symmetric structure with an 1A1 electronic state, where Be is located in a terminal position bonded to M along the center axis. For other cases, the C3v symmetric structure is a low-lying local minimum. Although the present complexes are isoelectronic with the recently reported BFe(CO)3- complex having a B-Fe quadruple bond, radial orbital-energy slope (ROS) analysis reveals that the highest occupied molecular orbital (HOMO) in the title complexes is slightly antibonding in nature, which bars a quadruple bonding assignment. Similar weak antibonding nature of HOMO in the previously reported BeM(CO)4 (M = Ru, Os) complexes is also noted in ROS analysis. The bonding analysis through energy decomposition analysis in combination with the natural orbital for chemical valence shows that the bonding between Be and M(CO)3q (q = -1 for M = Co, Rh, Ir and q = 0 for M = Ni, Pd, Pt) can be best described as Be in the ground state (1S) interacting with M(CO)30/- via dative bonds. The Be(spσ) → M(CO)3q σ-donation and the complementary Be(spσ) ← M(CO)3q σ-back donation make the overall σ bond, which is accompanied by two weak Be(pπ) ← M(CO)3q π-bonds. These complexes represent triply bonded terminal beryllium in an unusual zero oxidation state.

Properties of doubly heavy spin- 12 baryons: The ground and excited states

We determine the masses and residues of the ground and excited spin-12 baryons consist of two heavy b or c quark utilizing the QCD sum rule formalism. In the calculations, we consider the nonperturbative operators up to ten mass dimensions in order to increase the accuracy compared to the previous calculations. We report the obtained results for both the symmetric and antisymmetric currents defining the doubly heavy baryons of the ground state (1S), first orbitally excited state (1P), and first radially excited state (2S). We compare our results with the predictions of other nonperturbative approaches as well as existing experimental data which is available only for the ground state of Ξcc channel. These predictions can help the experimental groups in their searches for all members of the doubly heavy baryons in their ground and exited states. Published by the American Physical Society 2024

Rayleigh and Raman scattering cross-sections and phase matrices of the ground-state hydrogen atom, and their astrophysical implications

ABSTRACT We present explicit expressions for Rayleigh and Raman scattering cross-sections and phase matrices of the ground 1s state hydrogen atom based on the Kramers–Heisenberg–Waller dispersion formula. The Rayleigh scattering leaves the hydrogen atom in the ground-state while the Raman scattering leaves the hydrogen atom in either ns (n ≥ 2; s-branch) or nd (n ≥ 3; d-branch) excited state, and the Raman scattering converts incident ultraviolet (UV) photons around the Lyman resonance lines into optical-infrared (IR) photons. We show that this Raman wavelength conversion of incident flat UV continuum in dense hydrogen gas with a column density of NH > 1021 cm−2 can produce broad emission features centred at Balmer, Paschen, and higher level lines, which would mimic Doppler-broadened hydrogen lines with the velocity width of ≳1000 km s−1 that could be misinterpreted as signatures of active galactic nuclei, supernovae, or fast stellar winds. We show that the phase matrix of the Rayleigh and Raman s-branch scatterings is identical to that of the Thomson scattering while the Raman d-branch scattering is more isotropic, thus the Paschen and higher level Raman features are depolarized compared to the Balmer features due to the flux contribution from the Raman d-branch. We argue that observations of the line widths, line flux ratios, and linear polarization of multiple optical/IR hydrogen lines are crucial to discriminate between the Raman-scattered broad emission features and Doppler-broadened emission lines.

Dynamics of photoexcited 5-bromouracil and 5-bromo-2'-deoxyuridine studied by extreme ultraviolet time-resolved photoelectron spectroscopy in liquid flat jets.

The UV-induced photo-relaxation dynamics of 5-bromouracil (BrU) and 5-bromo-2'-deoxyuridine (BrUrd) in aqueous solution were investigated using femtosecond time-resolved photoelectron spectroscopy with an extreme ultraviolet (XUV) probe in a flat liquid jet. Upon excitation to the 1ππ* state by 4.66 eV UV photons, both molecules exhibited rapid relaxation into lower-lying electronic states followed by decay to the S0 ground state. By employing a 21.7 eV XUV probe pulse, we were able to differentiate the relaxation of the excited state population from the initially excited 1ππ* state to an intermediate electronic state with 100 fs. Computational results identify this intermediate as the 1πσ* excited state, accessed by a 1ππ*/1πσ* conical intersection, and the signal from this intermediate state disappears within ∼200 fs. In contrast to thymine, formation of neither the 1nπ* state nor a long-lived triplet state was observed. Although the 1πσ* state is largely repulsive, prior studies have reported a low quantum yield for dissociation, and we observe weak signals that are consistent with production of hot S0 ground state (for BrUrd) on a time scale of 1.5-2 ps. It thus appears that solvent caging effects limit the dissociation yield in solution.

Mid-IR narrow bandwidth tuneable laser source for the FAMU experiment

The FAMU (Fisica degli Atomi MUonici) collaboration aims to measure the proton Zemach radius through muonic hydrogen (μp) spectroscopy. The experimental setup relies on a custom-developed pulsed mid-IR laser source that can be tuned over a specific 6780-6790 nm wavelength range needed to ignite the hyperfine transition of the μp ground state 1S (also known as spin-flip transition). The excitation is observed as a distinctive muonic X-rays emission resulting from the oxygen impurity present in the hydrogen target. The mid-IR emission is produced by Difference Frequency Generation (DFG) in a non-linear crystal, pumped with a fixed wavelength 1064 nm Nd-YAG laser and a tuneable Cr:forsterite laser centred on 1262 nm. This setup produces more than 1.2 mJ at 6780 nm with a linewidth smaller than 30 pm. The experiment requires the laser to run continuously 24/7 in a restricted/radiation-controlled area and for this reason a specifically developed control software permits to remotely act on the laser. The characterization of a series of different non-linear crystals was performed during the development of the laser, resulting in the choice of BaGa4Se7.

Time-dependent wave-packet approach to the excited-state intramolecular proton transfer based on relaxed potential energy surfaces of benzimidazole molecule

The wave-packet dynamical approach was used to investigate the excited-state intramolecular proton transfer (PT) of 5′-amino-2-(2′-hydroxyphenyl) benzimidazole (P1) based on the relaxed potential surfaces. For the involved PT process of P1 molecule, the quantum chemical calculation shows that relative to the ground state S0 with a single potential well, the excited state S1 with a double potential well can give much dynamical information. It is also found that because of the existence of a shallow potential barrier on the excited state S1, the PT in it is much easier than that in the ground state S0. When a laser field is used to pump the wave packet and induce the PT process, the external field parameters, such as the frequency and the envelope, also have influences on the PT process because of the impact of both pump time and the energy gap between two states. This kind of external field effect on the PT process gives a specific perspective to examine its dynamical mechanism and provides a reference for exploring the light-induced biophysical processes.

Electrochemical Properties of Derivatives of 1,3-Diphenylisobenzofuran – Chromophores for Singlet Fission

Nowadays, there are efforts to apply alternative sources of renewable energy. One of these sources is solar energy. Solar energy represents a renewable free source of energy that is sustainable and totally inexhaustible. The standard efficiency of solar cells is now below 30 %. Singlet fission has attracted rising attention because it promises to increase the maximum of theoretical efficiency of single-junction solar cells. While solar cells after absorption one photon generates one electron, singlet fission is a photophysical process, whereby a singlet exciton generated by irradiation splits into two triplet excitons [1,2]. In this way, one photon can generate theoretically two electrons which should increase the efficiency of inexpensive single-junction solar cells. Therefore, recently substantial attention has been paid to search for suitable chromophores for singlet fission.When looking for new chromophores for efficient SF, their crystalline form and molecular packing, the relative energies of the S0 (ground state), T1 (lowest triplet), and S1 (first excited singlet) states, where energy of the triplet state should be lower than a half of the first excited singlet energy, and the potentials of one-electron reduction and one-electron oxidation are crucial. Redox properties of molecules for SF are thus critical for their use, therefore electrochemical approach is necessary.Molecules on the base of 1,3-diphenylisobenzofuran (DPIBF) attract an interest because of their possible efficiency for singlet fission. In the last few years we have started to investigate various types of derivatives of DPIBF. One of our first studies [3] was focused on a series of fluorinated derivatives of DPIBF where the influence of number and position of fluorine atoms in the molecule on the redox potentials and mechanism is followed. Next to that we studied series of dimer derivatives of DPIBF [4]. The location and the nature of the bridging unit between two DPIBF redox centres attracted our attention because in this way the shape of the molecule, its extent of electron delocalization and, thus, possible ability of formation of biradicaloid can be changed.The most interesting dimeric molecule appeared to be that one with the elongated π-conjugated system, the “quasi dimer” of DPIBF (2). Because of that, quasi dimer was investigated in more details in comparison with other three molecules by standard electrochemical techniques, the in-situ UV-vis and EPR spectroelectrochemical techniques. The three other derivatives for comparison were parent diphenylisobenzofuran (1), direct dimer (3) and methylene bridged dimer (4). The main goal of this deeper study was to characterize properly not only electrochemical properties of the molecules, but also their absorbance and fluorescence properties and stability in solvents. Acknowledgement This work was supported by the grant 21-23261S (Grant Agency of the Czech Republic) and by the institutional support RVO: 61388955.

Vibronic and Cationic Features of 2-Fluorobenzonitrile and 3-Fluorobenzonitrile Studied by REMPI and MATI Spectroscopy and Franck-Condon Simulations.

Fluorinated organic compounds have superior physicochemical properties than general organic compounds due to the strong C-F single bond; they are widely used in medicine, biology, pesticides, and materials science. In order to gain a deeper understanding of the physicochemical properties of fluorinated organic compounds, fluorinated aromatic compounds have been investigated by various spectroscopic techniques. 2-fluorobenzonitrile and 3-fluorobenzonitrile are important fine chemical intermediates and their excited state S1 and cationic ground state D0 vibrational features remain unknown. In this paper, we used two-color resonance two photon ionization (2-color REMPI) and mass analyzed threshold ionization (MATI) spectroscopy to study S1 and D0 state vibrational features of 2-fluorobenzonitrile and 3-fluorobenzonitrile. The precise excitation energy (band origin) and adiabatic ionization energy were determined to be 36,028 ± 2 cm-1 and 78,650 ± 5 cm-1 for 2-fluorobenzonitrile and 35,989 ± 2 cm-1 and 78,873 ± 5 cm-1 for 3-fluorobenzonitrile, respectively. The density functional theory (DFT) at the levels of RB3LYP/aug-cc-pvtz, TD-B3LYP/aug-cc-pvtz, and UB3LYP/aug-cc-pvtz were used to calculate the stable structures and vibrational frequencies for the ground state S0, excited state S1, and cationic ground state D0, respectively. Franck-Condon spectral simulations for transitions of S1 ← S0 and D0 ← S1 were performed based on the above DFT calculations. The theoretical and experimental results were in good agreement. The observed vibrational features in S1 and D0 states were assigned according to the simulated spectra and the comparison with structurally similar molecules. Several experimental findings and molecular features were discussed in detail.

Electron affinities and lowest triplet and singlet state properties of para-oligophenylenes (n = 3-5): theory and experiment.

We apply photodetachment-photoelectron spectroscopy to measure the electron affinities and the energetics of the lowest excited electronic states of the neutral molecules para-terphenyl (p3P), para-quaterphenyl (p4P) and para-quinquephenyl (p5P), including especially the triplet states below S1. The interpretation of the experimental data is based on the comparison to calculated 0-0 energies and Dyson norms, using density functional theory and multireference configuration interaction methods, as well as Franck-Condon patterns. The comparison between calculated and experimental vibrational fine-structures reveals a twisted benzoid-like molecular structure of the S0 ground state and nearly planar quinoid-like nuclear arrangements in the S1 and T1 excited states as well as in the D0 anion ground state. For all para-oligophenylenes (ppPs) in this series, at least two triplet states have been identified in the energy regime below the S1 state. The large optical S0-S1 cross sections of the ppPs are rationalised by the nodal structure of the molecular orbitals involved in the transition. The measured electron affinities range from 380 meV (p3P) over 620 meV (p4P) to 805 meV (p5P). A saturation of the electron binding energy with the increasing number of phenyl units is thus not yet in sight.

New Insights into the Lamb Shift: The Spectral Density of the Shift

In an atom, the interaction of a bound electron with the vacuum fluctuations of the electromagnetic field leads to complex shifts in the energy levels of the electron, with the real part of the shift corresponding to a shift in the energy level and the imaginary part to the width of the energy level. The most celebrated radiative shift is the Lamb shift between the 2s1/2 and the 2p1/2 levels of the hydrogen atom. The measurement of this shift in 1947 by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy levels were degenerate was incorrect. Hans Bethe’s non-relativistic calculation of the shift using second-order perturbation theory demonstrated the renormalization process required to deal with the divergences plaguing the existing theories and led to the understanding that it was essential for theory to include interactions with the zero-point quantum vacuum field. This was the birth of modern quantum electrodynamics (QED). Numerous calculations of the Lamb shift followed including relativistic and covariant calculations, all of which contain a nonrelativistic contribution equal to that computed by Bethe. The semi-quantitative models for the radiative shift of Welton and Power, which were developed in an effort to demonstrate physical mechanisms by which vacuum fluctuations lead to the shift, are also considered here. This paper describes a calculation of the shift using a group theoretical approach which gives the shift as an integral over frequency of a function, which is called the “spectral density of the shift.“ The energy shift computed by group theory is equivalent to that derived by Bethe yet, unlike in other calculations of the non-relativistic radiative shift, no sum over a complete set of states is required. The spectral density, which is obtained by a relatively simple computation, reveals how different frequencies of vacuum fluctuations contribute to the total energy shift. The analysis shows, for example, that half the radiative shift for the ground state 1S level in H comes from virtual photon energies below 9700 eV, and that the expressions of Power and Welton have the correct high-frequency behavior, but not the correct low-frequency behavior, although they do give approximately the correct value for the total shift.

Intersystem Crossing of 2-Methlypyrazine Studied by Femtosecond Photoelectron Imaging.

2-methylpyrazine was excited to the high vibrational dynamics of the S1 state with 260 nm femtosecond laser light, and the evolution of the excited state was probed with 400 nm light. Because it was unstable, the S1 state decayed via intersystem crossing to the triplet state T1, and it may have decayed to the ground state S0 via internal conversion. S1-to-T1 intersystem crossing was observed by combining time-resolved mass spectrometry and time-resolved photoelectron spectroscopy. The crossover time scale was 23 ps. Rydberg states were identified, and the photoelectron spectral and angular distributions indicated accidental resonances of the S1 and T1 states with the 3s and 3p Rydberg states, respectively, during ionization.

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.

Simulation of Ab Initio Optical Absorption Spectrum of β-Carotene with Fully Resolved S0 and S2 Vibrational Normal Modes.

The electronic absorption spectrum of β-carotene (β-Car) is studied using quantum chemistry and quantum dynamics simulations. Vibrational normal modes were computed in optimized geometries of the electronic ground state S0 and the optically bright excited S2 state using the time-dependent density functional theory. By expressing the S2-state normal modes in terms of the ground-state modes, we find that no one-to-one correspondence between the ground- and excited-state vibrational modes exists. Using the ab initio results, we simulated the β-Car absorption spectrum with all 282 vibrational modes in a model solvent at 300 K using the time-dependent Dirac-Frenkel variational principle and are able to qualitatively reproduce the full absorption line shape. By comparing the 282-mode model with the prominent 2-mode model, widely used to interpret carotenoid experiments, we find that the full 282-mode model better describes the high-frequency progression of carotenoid absorption spectra; hence, vibrational modes become highly mixed during the S0 → S2 optical excitation. The obtained results suggest that electronic energy dissipation is mediated by numerous vibrational modes.

Thermal Activation of Valley-Orbit States of Neutral Magnesium in Silicon

Interstitial magnesium acts as a moderately deep double donor in silicon, and is relatively easily introduced by diffusion. Unlike the case of the chalcogen double donors, parameters of the even-parity valley-orbit excited states 1s(T2) and 1s(E) have remained elusive. Here we report on further study of these states in neutral magnesium through temperature dependence absorption measurements. The results demonstrate thermal activation from the ground state 1s(A1) to the valley-orbit states, as observed by transitions from the thermally populated levels to the odd-parity states 2p0 and 2p±. Analysis of the data makes it possible to determine the thermal activation energies of transitions from the donor ground state to 1s(T2) and 1s(E) levels, as well as the binding energies of an electron with the valley-orbit excited states. Keywords: magnesium impurity in silicon, deep center, optical spectroscopy.