Ground State Potential Research Articles

Counting monster potentials

We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model.We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.

Accurate ground state potential of Cu2 up to the dissociation limit by perturbation assisted double-resonant four-wave mixing.

Perturbation facilitated double-resonant four-wave mixing is applied to access high-lying vibrational levels of the X 1Σg + (0g +) ground state of Cu2. Rotationally resolved transitions up to v″ = 102 are measured. The highest observed level is at 98% of the dissociation energy. The range and accuracy of previous measurements are significantly extended. By applying the near dissociation equation developed by Le Roy [R. J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186, 197 (2017)], a dissociation energy of De = 16 270(7) hc cm-1 is determined, and an accurate potential energy function for the X 1Σg + (0g +) ground state is obtained. Molecular constants are determined from the measured transitions and by solving the radial Schrödinger equation using this function and are compared with results from earlier measurements. In addition, benchmark multi-reference configuration interaction computations are performed using the Douglas-Kroll-Hess Hamiltonian and the appropriate basis of augmented valence quadruple ζ type. Coupled-cluster single, double, and perturbative triple calculations were performed for comparison.

Phenazine-Based Donor Acceptor Systems as Organic Photocatalysts for "Metal-free" C-N/C-C Cross-Coupling.

With an aim to achieve a balance between ground-state and excited-state reduction potential of donor acceptor systems for efficient C-N/C-C cross-coupling, a series of donor acceptor systems DA1-DA4 have been synthesized by varying the donor strength and connecting positions. With an increase in donor strength, systematic elevation in the ground-state reduction potential and decrease in the HOMO-LUMO gap was observed. Interestingly, all the derivatives DA1-DA4 could catalyze the C-N bond formation reaction between activated aryl halides and amines at low catalytic loading under metal-free conditions without the need of any external base upon irradiation with white LED. A balance was realized in the case of derivative DA2, which exhibits high efficiency in C-N couplings. Different control experiments support the validity of the energy as well as electron transfer pathways in the visible light-mediated C-N bond formation. This study further reveals the potential of derivative DA1 in "metal-free" Sonogashira coupling involving activated aryl halides which is attributed to its high excited-state reduction potential.

Gluonic-excitation energies and Abelian dominance in SU(3) QCD

We present the first study of the Abelian-projected gluonic-excitation energies for the static quark-antiquark (Q$\bar{\rm Q}$) system in SU(3) lattice QCD at the quenched level, using a $32^4$ lattice at $\beta = 6.0$. We investigate ground-state and three excited-state Q$\bar{\rm Q}$ potentials, using smeared link variables on the lattice. We find universal Abelian dominance for the quark confinement force of the excited-state Q$\bar{\rm Q}$ potentials as well as the ground-state potential. Remarkably, in spite of the excitation phenomenon in QCD, we find Abelian dominance for the first gluonic-excitation energy of about 1 GeV at long distances in the maximally Abelian gauge. On the other hand, no Abelian dominance is observed for higher gluonic-excitation energies even at long distances. This suggests that there is some threshold between 1 and 2 GeV for the applicable excitation-energy region of Abelian dominance. Also, we find that Abelian projection significantly reduces the short-distance $1/r$-like behavior in gluonic-excitation energies.

The shape of the electric dipole function determines the sub-picosecond dynamics of anharmonic vibrational polaritons

Vibrational strong coupling has emerged as a promising route for manipulating the reactivity of molecules inside infrared cavities. We develop a full-quantum methodology to study the unitary dynamics of a single anharmonic vibrational mode interacting with a quantized infrared cavity field. By comparing multi-configurational time-dependent Hartree simulations for an intracavity Morse oscillator with an equivalent formulation of the problem in Hilbert space, we describe for the first time the essential role of permanent dipole moments in the femtosecond dynamics of vibrational polariton wavepackets. We classify molecules into three general families according to the shape of their electric dipole function de(q) along the vibrational mode coordinate q. For polar species with a positive slope of the dipole function at equilibrium, an initial diabatic light-matter product state without vibrational or cavity excitations evolves into a polariton wavepacket with a large number of intracavity photons for interaction strengths at the conventional onset of ultrastrong coupling. This buildup of the cavity photon amplitude is accompanied by an effective lengthening of the vibrational mode that is comparable with a laser-induced vibrational excitation in free space. In contrast, polar molecules with a negative slope of the dipole function experience an effective mode shortening, under equivalent coupling conditions. We validate our predictions using realistic ab initio ground state potentials and dipole functions for HF and CO2 molecules. We also propose a non-adiabatic state preparation scheme to generate vibrational polaritons with molecules near infrared nanoantennas for the spontaneous radiation of infrared quantum light.

Electron Density Difference Analysis on the Oxidative and Reductive Quenching Cycles of Classical Iridium and Ruthenium Photoredox Catalysts.

In this study a detailed scrutiny of the electronic structure changes during the redox events of the oxidative and reductive quenching cycles of the representative homoleptic and heteroleptic octahedral iridium [Ir(bpy)x(ppy)3-x]x+ (x = 0, 1, 2, and 3) and ruthenium [Ru(bpy)x(ppy)3-x]x-1+ (x = 1, 2, and 3) photoredox catalysts is provided through the corresponding electron density difference Δρ(r) distributions. The systematic analysis of the Δρ(r) distributions provides intuitive insights into the details of the metal- and ligand-centered electron transfer processes that take place in the different excited- and ground-state redox steps of classical photoredox catalysis. In addition to the structural metrics, the measured ground-state reduction potentials were also reproduced with great accuracy, typically within 0.15 V, when using the TPSSh functional in combination with the Def2-TZVP basis set coupled to reparameterized implicit solvation model (SMD). We computed the excited-state reduction potentials of these ruthenium and iridium complexes without using TD-DFT, but by directly computing the solution-state Gibbs free energy of the triplet 3MLCT state, giving good agreement with respective experiments. The analyzed Δρ(r) maps reveal the characteristic features of metal- and ligand-centered reductions and oxidations in both ground- and excited states and metal-to-ligand charge transfers (MLCT), sometimes perturbed by additional ligand-to-ligand charge transfer (LLCT) contributions. One of the most interesting features of ligand-centered redox processes is the localization of the accumulated electron density at one redox-active ligand in the case of heteroleptic systems [Ir(bpy)(ppy)2]+ and [Ru(bpy)(ppy)2]0, which is in contrast to the delocalized nature of the ligands-hosted charge in homoleptic photoredox catalysts, such as the classical [Ru(bpy)3]2+ system.

Ground-State Redox Potentials Calculations of D-π-A and D-A-π-A Organic Dyes for DSSC and Visible-Light-Driven Hydrogen Production

The prediction of ground-state redox potentials by quantum chemical methods has a prominent role in the rational design of novel organic photosensitizers both for dye-sensitized solar cells (DSSCs) and photocatalytic systems for the production of H2. Indeed, the ground-state redox potential of the photosensitizers is one of the key parameters to identify the most promising candidates for such applications. Here, the ground-state redox potentials of 16 organic donor-π-acceptor D-π-A and donor-acceptor-π-acceptor D-A-π-A dyes having a medium to large size of the conjugated scaffold are evaluated, using the methods of the Density Functional Theory (DFT), in terms of free energy differences between their neutral and oxidized ground-state forms. These results are compared to the available experimental data and to the computed highest occupied molecular orbital energy −ε(HOMO) values as an approximation of ground-state redox potentials according to Koopmans’ theorem. Using the MPW1K functional in combination with the 6-31+G* basis set, the strategy based on the free energy cycle, including solvent effects, reproduces with a good level of accuracy the observed values (mean absolute error (MAE) < 0.2 eV) and trend of redox potentials within related families of dyes. On the other hand, the −ε(HOMO) values are only able to capture the experimental trends in redox potential values.

A DFT Study on the Redox Active Behavior of Carbene and Pyridine Ligands in the Oxidative and Reductive Quenching Cycles of Ruthenium Photoredox Catalysts

In this study, a detailed look at the electronic structure changes induced by photon absorption and of the succeeding redox events of the oxidative and reductive quenching cycles of ruthenium–carbene and ruthenium–pyridine photoredox catalysts is provided through an arsenal of density functional theory-based techniques including electron density difference Δρ(r) maps, spin-density distributions, and the non-covalent interaction analysis. We introduced an efficient computational protocol to obtain accurate equilibrium structures and ground-state reduction potentials for these types of complexes, substantiated via a direct comparison to empirical X-ray structures and cyclic voltammetry measurements, respectively. Moreover, we demonstrated the utility of a hitherto unexplored approach to compute excited-state redox potentials based on the Gibbs free energy of the triplet metal-to-ligand charge transfer state (3MLCT). The analyzed Δρ(r) maps revealed the characteristic features of, for example, metal- and ligand-centered reductions and oxidations in both ground and excited states and MLCT processes, disclosing the active participation of carbene ligands in the redox events of homoleptic systems. Beyond analyzing ligand–ligand non-covalent interactions and redox-active behaviors of carbene and pyridine ligands side by side, the effect of such groups on the kinetics of 3MLCT to 3MC transition was scrutinized.

Feshbach resonances in Na23+K39 mixtures and refined molecular potentials for the NaK molecule

We present a detailed study of interspecies Feshbach resonances of the bosonic $^{23}\mathrm{Na}+$$^{39}\mathrm{K}$ mixture for magnetic fields up to $750 \, \mathrm{G}$ in various collision channels. A total of fourteen Feshbach resonances are reported, as well as four zero crossings of the scattering length and three inelastic two-body loss features. We use the observed magnetic field locations of the resonant features together with the known data on $^{23}\mathrm{Na}+$$^{40}\mathrm{K}$ to refine the singlet and triplet ground state potentials of NaK and achieve a consistent description of Feshbach resonances for both, the Bose-Bose mixture of $^{23}\mathrm{Na}+$$^{39}\mathrm{K}$ as well as the Bose-Fermi mixture of $^{23}\mathrm{Na}+$$^{40}\mathrm{K}$.

Multi reference studies of gas phase vanadium nitride di- and trications

Using ab initio configuration interaction methodologies, we compute the potentials of the doubly and triply charged vanadium nitride. By performing benchmark calculations, we show that the 4s and 3d AOs are enough for the accurate description of VN multiple ionizations. In VN2+, several deep potential wells are located below the lowest dissociation limit. Within these potential wells, long-lived rovibrational levels may be found. Specifically, we find an unconventional shape for the ground state potential of VN2+ that differs from the volcanic form typical of dications. For VN3+, four shallow potential wells were characterized that may support rovibrational levels, where metastable VN3+ can be found. Accordingly, we predict the existence of VN2+ and VN3+ species in the gas phase as already noticed experimentally for the dication VN2+. For the bound states, we provide a set of accurate spectroscopic parameters. Double and triple ionization energies of VN are computed to be 23.56 and 51.05 eV, respectively.

Spectroscopic properties and cold elastic collisions of alkaline-earth Mg + Mg+ system

In this theoretical work, we calculate molecular potential energy curves, spectroscopic constants and transition dipole moments for the ground and first excited electronic states (A2Πu) of alkaline-earth molecular ion We consider an ab initio multi-reference configuration interaction method using an aug-cc-pv5z Gaussian basis set and compare our results with those obtained by others. The comparison shows a very good agreement. In addition, we investigate the ion-atom elastic collisions for a wide range of energies including the isotopic effect. In close connections, we determine the scattering T-matrix elements for ground-state electronic potentials, which show divergent behavior at a particular energy, indicating the occurrence of scattering resonances. We find that the s-wave scattering length is positive for both ground-state potentials. We also study possible free-bound transitions and Franck–Condon overlap for our system.

Two-photon photoassociation spectroscopy of CsYb: Ground-state interaction potential and interspecies scattering lengths

We perform two-photon photoassociation spectroscopy of the heteronuclear CsYb molecule to measure the binding energies of near-threshold vibrational levels of the $X~^{2}\Sigma_{1/2}^{+}$ molecular ground state. We report results for $^{133}$Cs$^{170}$Yb, $^{133}$Cs$^{173}$Yb and $^{133}$Cs$^{174}$Yb, in each case determining the energy of several vibrational levels including the least-bound state. We fit an interaction potential based on electronic structure calculations to the binding energies for all three isotopologs and find that the ground-state potential supports 77 vibrational levels. We use the fitted potential to predict the interspecies s-wave scattering lengths for all seven Cs+Yb isotopic mixtures.

Optimization of Photocatalyst Excited- and Ground-State Reduction Potentials for Dye-Sensitized HBr Splitting.

Dye-sensitized bromide oxidation was investigated using a series of four ruthenium polypyridyl photocatalysts anchored to SnO2/TiO2 core/shell mesoporous thin films through 2,2'-bipyridine-4,4'-diphosphonic acid anchoring groups. The ground- and excited-state reduction potentials were tuned over 500 mV by the introduction of electron withdrawing groups in the 4 and 4' positions of the ancillary bipyridine ligands. Upon light excitation of the surface-bound photocatalysts, excited-state electron injection yielded an oxidized photocatalyst that was regenerated through bromide oxidation. High injection quantum yields (Φinj) and regeneration quantum yields (Φreg) were essential to obtain efficient bromide oxidation yet required a photocatalyst that is both a potent photoreductant and a strong oxidant after excited-state injection. The four photocatalysts utilized in this manuscript ranged from unity Φinj (1.0) and minimal Φreg (0.037) to minimal Φinj (0.09) and unity Φreg (1.0). The photocatalyst that displayed the highest overall dye-sensitized photoelectrosynthesis cell performances exhibited near unity Φreg (0.99), while a significant Φinj was still preserved (0.59). Thus, these results highlighted the delicate interplay between the ground- and excited-state reduction potentials of photocatalysts for dye-sensitized hydrobromic acid splitting.

Semi-empirical ground-state potential of carbon monoxide with physical behavior in the limits of small and large inter-atomic separations

Recently, several empirical models of the potential energy function (PEF) of the ground electronic state of CO have been developed by Coxon and Hajigeorgiou using the direct-potential-fit (DPF) analysis. These models reproduce more than twenty thousand of observed ro-vibrational line positions within their experimental accuracies and follow the theoretically predicted long-range asymptotic behavior of the potential beyond Le Roy's radius. However, the applicability of these models to calculations of the intensities of weak transitions is not obvious due to limitations discussed in this work. Here, we make the next step by imposing an additional requirement that the model has to display physical behavior outside the region to which the available spectroscopic data pertain. We perform ab initio calculations of the potential in the short-range region r = 0.3–0.8 Å where the potential increases well above the dissociation limit and include these data along with the estimated uncertainties in the DPF analysis. At smaller r, our PEF tends to the well-known united-atom limit. In the long-range region, it follows the ab initio data with their estimated accuracies available in the literature. On top of the above, the model is analytical, i.e. it has continuous derivatives of all orders. The model constructed is a linear function of twenty three adjustable parameters, and a non-linear function of additional five parameters. The properties of the new PEF are investigated in comparison with the previous empirical model due to Coxon and Hajigeorgiou (2004). Our PEF provides reproduction of all observed lines at the same level of accuracy. The new potential changes the intensities of high overtone transitions dramatically. In addition, we find that the anomalies in the purely rotational and ro-vibrational spectra change their intensities between the two PEFs even for the low-v bands.

A screened independent atom model for the description of ion collisions from atomic and molecular clusters

We apply a recently introduced model for an independent-atom-like calculation of ion-impact electron transfer and ionization cross sections to proton collisions from water, neon, and carbon clusters. The model is based on a geometrical interpretation of the cluster cross section as an effective area composed of overlapping circular disks that are representative of the atomic contributions. The latter are calculated using a time-dependent density-functional-theory-based single-particle description with accurate exchange-only ground-state potentials. We find that the net capture and ionization cross sections in p-X$_n$ collisions are proportional to $n^\alpha$ with $2/3 \le \alpha \le 1$. For capture from water clusters at 100 keV impact energy $\alpha$ is close to one, which is substantially different from the value $\alpha=2/3$ predicted by a previous theoretical work based on the simplest-level electron nuclear dynamics method. For ionization at 100 keV and for capture at lower energies we find smaller $\alpha$ values than for capture at 100 keV. This can be understood by considering the magnitude of the atomic cross sections and the resulting overlaps of the circular disks that make up the cluster cross section in our model. Results for neon and carbon clusters confirm these trends. Simple parametrizations are found which fit the cross sections remarkably well and suggest that they depend on the relevant bond lengths.

Challenges in XUV Photochemistry Simulations: A Case Study on Ultrafast Fragmentation Dynamics of the Benzene Radical Cation.

The challenges of simulating extreme ultraviolet (XUV)-induced dissociation dynamics of organic molecules on a multitude of coupled potential energy surfaces are discussed for the prototypical photoionization of benzene. The prospects of Koopmans' theorem-based electronic structure calculations in combination with classical trajectories and Tully's fewest switches surface hopping are explored. It is found that a Koopmans' theorem-based approach overestimates the CH dissociation barrier and thus underestimates the fragmentation yield. However, the nonadiabatic population dynamics are in good agreement with previous approaches, indicating that the Koopmans' theorem based potentials are well described around the Franck-Condon point. This is explicitly tested for the ground state potential of the benzene cation employing CASPT2 calculations, for which very good agreement is found. This work highlights the need for efficient electronic structure approaches that can treat medium-sized organic molecules with a multitude of coupled excited states and several dissociation channels.

Quantum Effects for a Proton in a Low-Barrier, Double-Well Potential: Core Level Photoemission Spectroscopy of Acetylacetone.

We have performed core level photoemission spectroscopy of gaseous acetylacetone, its fully deuterated form, and two derivatives, benzoylacetone and dibenzoylmethane. These molecules show intramolecular hydrogen bonds, with a proton located in a double-well potential, whose barrier height is different for the three compounds. This has allowed us to examine the effect of the double-well potential on photoemission spectra. Two distinct O 1s core hole peaks are observed, previously assigned to two chemical states of oxygen. We provide an alternative assignment of the double-peak structure of O 1s spectra by taking full account of the extended nature of the wave function associated with the nuclear motion of the proton, the shape of the ground and final state potentials in which the proton is located, and the nonzero temperature of the samples. The peaks are explained in terms of an unusual Franck-Condon factor distribution.

Exploring function activated chlorins using MCD spectroscopy and DFT methods: design of a chlorin with a remarkably intense, red Q band.

The electronic structures of three previously synthesized Ni-coordinated chlorins with β-substituents of thioketone, fluorene, and ketone were investigated using magnetic circular dichroism spectroscopy (MCD) and density functional theory (DFT) for potential application as sensitizers for dye-sensitized solar cells (DSSCs). Computational studies on modeled Zn-coordinated chlorins allowed identification of charge transfer and d-d transitions of the Ni2+ coordinated chlorins. Two fictive Zn chlorins, M1 and M2, were designed with thiophene units based on the fluorene substituted chlorin. Substitution with thiophene altered the typical arrangement of the four Gouterman molecular orbitals (MOs) and red-shifted and greatly intensified the lowest energy absorption band (the Q band). The introduction of the thiophene-based MO as the LUMO below the usual Gouterman LUMO is predicted to increase the efficiency of electron transfer from the dye to the conduction band of the semiconductor in DSSCs. The addition of a donor group on the opposite pyrrole (M2) red-shifted the Q band further and introduced a donor-based MO between the typical Gouterman HOMO and HOMO-1. Despite the relatively small ΔHOMO, M1 and M2 exhibited remarkably intense Q bands. M2 would be a possible candidate for application in DSSCs due to its panchromatic absorption, intense and red-shifted Q band, and the presence of the substituent based MO properties. Another indicator of a successful dye is the alignment of the ground state and excited state oxidation potentials (GSOP and ESOP, respectively) with respect to the conduction band of the semiconductor. The GSOP for M2 lies 0.55 eV below the I-/I3- redox potential and the ESOP lies 0.48 eV above the TiO2 conduction band. The impact of the thiophene dominance in the LUMO also supports the prediction of efficient sensitization properties. The remarkably intense Q band of M2 predicted to be at 777 nm with a ΔHOMO of just 1.04 eV provides a synthetic route to tetrapyrroles with extremely intense, red Q bands without the need for aza nitrogens of the phthalocyanines. This study illustrates the value of guided synthesis using MCD spectral analysis and computational methods for optimizing the design of porphyrin dyes.

A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

The near ultraviolet photodissociation dynamics of 2- and 3-substituted thiophenols: Geometric vs. electronic structure effects.

The near ultraviolet spectroscopy and photodissociation dynamics of two families of asymmetrically substituted thiophenols (2- and 3-YPhSH, with Y = F and Me) have been investigated experimentally (by H (Rydberg) atom photofragment translational spectroscopy) and by ab initio electronic structure calculations. Photoexcitation in all cases populates the 11ππ* and/or 11πσ* excited states and results in S-H bond fission. Analyses of the experimentally obtained total kinetic energy release (TKER) spectra yield the respective parent S-H bond strengths, estimates of ΔE(A∼-X∼), the energy splitting between the ground (X∼) and first excited (A∼) states of the resulting 2-(3-)YPhS radicals, and reveal a clear propensity for excitation of the C-S in-plane bending vibration in the radical products. The companion theory highlights roles for both geometric (e.g., steric effects and intramolecular H-bonding) and electronic (i.e., π (resonance) and σ (inductive)) effects in determining the respective parent minimum energy geometries, and the observed substituent and position-dependent trends in S-H bond strength and ΔE(A∼-X∼). 2-FPhSH shows some clear spectroscopic and photophysical differences. Intramolecular H-bonding ensures that most 2-FPhSH molecules exist as the syn rotamer, for which the electronic structure calculations return a substantial barrier to tunnelling from the photoexcited 11ππ* state to the 11πσ* continuum. The 11ππ* ← S0 excitation spectrum of syn-2-FPhSH thus exhibits resolved vibronic structure, enabling photolysis studies with a greater parent state selectivity. Structure apparent in the TKER spectrum of the H + 2-FPhS products formed when exciting at the 11ππ* ← S0 origin is interpreted by assuming unintended photoexcitation of an overlapping resonance associated with syn-2-FPhSH(v33 = 1) molecules. The present data offer tantalising hints that such out-of-plane motion influences non-adiabatic coupling in the vicinity of a conical intersection (between the 11πσ* and ground state potentials at extended S-H bond lengths) and thus the electronic branching in the eventual radical products.