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The use of Δ-self-consistent field (SCF) approaches for studying excited electronic states has received a renewed interest in recent years. In this work, the use of this scheme for calculating excited-state vibrational frequencies is examined. Results from Δ-SCF calculations for a set of representative molecules are compared with those obtained using configuration interaction with single substitutions (CIS) and time-dependent density functional theory (TD-DFT) methods. The use of an approximate spin purification model is also considered for cases where the excited-state SCF solution is spin-contaminated. The results of this work demonstrate that an SCF-based description of an excited-state potential energy surface can be an accurate and cost-effective alternative to CIS and TD-DFT methods.

Evidence of strong photoelectron-valence electron (PEVE) interactions has been observed in the anion photoelectron (PE) spectra of several lanthanide suboxide clusters, which are exceptionally complex from an electronic structure standpoint and are strongly correlated systems. The PE spectrum of Gd2O-, which should have relatively simple electronic structure because of its half-filled 4f subshell, exhibits numerous electronic transitions. The electron affinity determined from the spectrum is 0.26 eV. The intensities of transitions to excited states increase relative to the lower-energy states with lower photon energy, which is consistent with shakeup transitions driven by time-dependent electron-neutral interactions. A group of intense spectral features that lie between electron binding energies of 0.7 and 2.3 eV are assigned to transitions involving detachment of an electron from outer-valence σu and σg orbitals that have large Gd 6s contributions. The spectra show parallel transition manifolds in general, which is consistent with detachment from these orbitals. However, several distinct perpendicular transitions are observed adjacent to several of the vertical transitions. A possible explanation invoking interaction between the ejected electron and the high-spin neutral is proposed. Specifically, the angular momentum of electrons ejected from σu or σg orbitals, which is l = 1, can switch to l = 0, 2 with an associated change in the Ms of the remnant neutral, which is spin-orbit coupling between a free electron and the spin of a neutral.

Photoelectron spectra of Gd2O2– obtained with photon energies ranging from 2.033 to 3.495 eV exhibit numerous close-lying neutral states with photon-energy-dependent relative intensities. Transitio...

The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S

We present here a massively parallel implementation of the recently developed CPS(D-3) excitation energy model that is based on cluster perturbation theory. The new algorithm extends the one developed in Baudin et al. [J. Chem. Phys., 150, 134110 (2019)] to leverage multiple nodes and utilize graphical processing units for the acceleration of heavy tensor contractions. Furthermore, we show that the extended algorithm scales efficiently with increasing amounts of computational resources and that the developed code enables CPS(D-3) excitation energy calculations on large molecular systems with a low time-to-solution. More specifically, calculations on systems with over 100 atoms and 1000 basis functions are possible in a few hours of wall clock time. This establishes CPS(D-3) excitation energies as a computationally efficient alternative to those obtained from the coupled-cluster singles and doubles model.

Simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited states. In this report, we show that utilization of such a procedure within an adiabatic linear response theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent eld method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical excitation procedures, such as those computed from a vertical gradient or molecular dynamics trajectory-based approach. For the methylene blue chromophore, we compare vibronic absorption spectra computed with: an adiabatic Hessian approach with linear response theory optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method optimized structures, and excitation energy time correlation functions generated from a molecular dynamics trajectory. Due to mixing between the bright S1 and dark S2 surfaces near the S1 minimum, computing the adiabatic Hessian with linear response theory time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in linear response theory strongly couples to the optical excitation while showing S1/ S2 state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited state adiabatic Hessian of linear response theory optimized structures and also showcases three alternatives that are not as subject to adiabatic state mixing effects.

Evidence of strong photoelectron-valence electron (PEVE) interactions has been observed in the anion photoelectron (PE) spectra of several lanthanide suboxide clusters, which are exceptionally complex from an electronic structure standpoint and are strongly correlated systems. The PE spectrum of Gd

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.

Photoelectron spectra of Gd2O2− obtained with photon energies from 2.033 eV to 3.495 eV exhibit numerous close-lying neutral states with photon-energy-dependent relative intensities. Transitions to states falling within the electron binding energy window of 0.9 and 1.6 eV are attributed to one- or two-electron transitions to the ground and low-lying excited neutral states. An additional, manifold of electronic states observed in the 2.1 to 2.8 eV window cannot be assigned to any simple one-electron transitions. Because of the relatively simple electronic structure from the half-filled 4f7 subshell occupancy in Gd2O2–, the numerous transitions observed in the spectra are fairly well-resolved, allowing a detailed view of the changes in relative intensities of individual transitions with photon energy. With supporting calculations on the numerous close-lying electronic states, we suggest a description of strong photoelectron-valence electron interactions that result in the photon-energy dependent shake-up transitions and switching between ferro- and antiferromagnetic coupling.

Dyson orbitals are overlaps between states with N and N±1 electrons and provide conceptual links between transition probabilities of electron detachment or attachment, density matrices, total energ...

Vertical excitation energies belonging to several Rydberg series of MgH have been inferred from 3+ electron-propagator calculations of the electron affinities of MgH+ and are in close agreement with experiment. Many electronically excited states with n > 3 are reported for the first time and new insight is given on the assignment of several Rydberg series. Valence and Rydberg excited states of MgH are distinguished respectively by high and low pole strengths corresponding to Dyson orbitals of electron attachment to the cation. By applying the Molecular Quantum Defect Orbital method, oscillator strengths for electronic transitions involving Rydberg states also have been determined.

Electron binding energies and Dyson orbitals may be obtained from the poles and residues of the electron propagator. The Dyson quasiparticle equation provides a convenient route to computing this information. Systematic approximations to the latter equation's self-energy, wherein electron correlation and final-state orbital relaxation are described, may be expressed in terms of the elements of the superoperator Hamiltonian matrix. Perturbative methods of electron propagator theory in wide use are based on a reference determinant constructed with canonical, Hartree–Fock orbitals. Generalised matrix elements of the superoperator Hamiltonian that accommodate non-integer occupation numbers associated with general, orthogonal spin orbitals are presented for the first time. Non-Hermitian terms may be systematically eliminated with perturbative corrections to generalised reference density operators. The structure of self-energy approximations that are complete through second, third, fourth or fifth order...

Ab initio electron propagator methods are efficient and accurate means of calculating vertical electron detachment energies of closed-shell, molecular anions with nuclei from the first three periods. Basis set extrapolations enable definitive comparisons between electron propagator results and benchmarks defined by total energy differences obtained with coupled-cluster, single, double, plus perturbative triple substitution theory. The best compromises of accuracy and efficiency are provided by the renormalized, partial third-order, diagonal (P3+) self-energy and by the nondiagonal, renormalized, second-order (NR2) approximation. The outer-valence Green function, the two-particle-one-hole Tamm-Dancoff approximation, the third-order algebraic diagrammatic construction, and the renormalized third-order methods also are examined. A detailed analysis of errors for small anions is performed. Case studies include F-(H2O) and Cl-(H2O) complexes, C5H5-, two P2N3- pentagonal rings, and a superhalide, Al(BO2)4-, whose electron detachment energy is more than double those of the halide anions. These applications illustrate the versatility of electron propagator methods, their utility for interpreting negative-ion photoelectron spectra, and their promise in the discovery of unusual properties and patterns of chemical bonding. Composite methods, which combine basis set effects calculated at the relatively efficient diagonal, second-order level and higher correlation effects calculated with small basis sets, provide excellent estimates of basis set-extrapolated P3+ or NR2 results and facilitate applications to large molecules. In the P3+ and NR2 methods, a judicious choice of low-order couplings between hole operators that correspond to the assumptions of Koopmans's theorem and operators that describe final-state relaxation and polarization and initial-state correlation leads to predictive accuracy, computational efficiency, and interpretive lucidity.

Two accurate and computationally efficient electron-propagator (EP) methods for calculating the valence, vertical ionization energies (VIEs) of closed-shell molecules have been identified through comparisons with related approximations. VIEs of a representative set of closed-shell molecules were calculated with EP methods using 10 basis sets. The most easily executed method, the diagonal, second-order (D2) EP approximation, produces results that steadily rise as basis sets are improved toward values based on extrapolated coupled-cluster singles and doubles plus perturbative triples calculations, but its mean errors remain unacceptably large. The outer valence Green function, partial third-order and renormalized partial third-order methods (P3+), which employ the diagonal self-energy approximation, produce markedly better results but have a greater tendency to overestimate VIEs with larger basis sets. The best combination of accuracy and efficiency with a diagonal self-energy matrix is the P3+ approximation, which exhibits the best trends with respect to basis-set saturation. Several renormalized methods with more flexible nondiagonal self-energies also have been examined: the two-particle, one-hole Tamm-Dancoff approximation (2ph-TDA), the third-order algebraic diagrammatic construction or ADC(3), the renormalized third-order (3+) method, and the nondiagonal second-order renormalized (NR2) approximation. Like D2, 2ph-TDA produces steady improvements with basis set augmentation, but its average errors are too large. Errors obtained with 3+ and ADC(3) are smaller on average than those of 2ph-TDA. These methods also have a greater tendency to overestimate VIEs with larger basis sets. The smallest average errors occur for the NR2 approximation; these errors decrease steadily with basis augmentations. As basis sets approach saturation, NR2 becomes the most accurate and efficient method with a nondiagonal self-energy.

Structures, isomerization energies, and electron binding energies of 5-azauracil and its anions have been calculated ab initio with perturbative, coupled-cluster, and electron-propagator methods. Tautomeric structures, including those produced by proton transfer to a CH group, have been considered. Dyson orbitals and pole strengths from electron-propagator calculations validated a simple, molecular-orbital picture of anion formation. In one case, an electron may enter a delocalized π orbital, yielding a valence-bound (VB) anion with a puckered ring structure. The corresponding electron affinity is 0.27 eV; the vertical electron detachment energy (VEDE) of this anion 1.05 eV. An electron also may enter a molecular orbital that lies outside the nuclear framework, resulting in a diffuse-bound (DB) anion. In the latter case, the electron affinity is 0.06 eV and the VEDE of the DB anion is 0.09 eV. Another VB isomer that is only 0.02 eV more stable than the neutral molecule has a VEDE of 2.0 eV.

Electron propagator theory is an efficient means to accurately calculating electron binding energies and associated Dyson orbitals that is systematically improvable and easily interpreted in terms of familiar concepts of valence theory. After a brief discussion of the physical meaning of the poles and residues of the electron propagator, the Dyson quasiparticle equation is derived. Practical approximations of the self-energy operator in common use are defined in terms of the elements of the Hermitian superoperator Hamiltonian matrix. Methods that retain select self-energy terms in all orders of the fluctuation potential include the two-particle-one-hole Tamm–Dancoff approximation, the renormalized third-order method, the third-order algebraic diagrammatic construction, and the renormalized, nondiagonal second-order approximation. Methods based on diagonal second-order and third-order elements of the self-energy matrix, such as the diagonal second-order, diagonal third-order, outer valence Green's function, partial third-order, and renormalized partial third-order approximations, provide efficient alternatives. Recent numerical tests on valence, vertical ionization energies of representative, small molecules, and a comparison of arithmetic and memory requirements provide guidance to users of electron propagator software. A survey of recent applications and extensions illustrates the versatility and interpretive power of electron propagator methodology.

Valence, vertical ionization energies of a representative set of closed-shell molecules were calculated with the symmetry-adapted-cluster, configuration-interaction (SAC-CI) method using ten basis sets for its level 1 and level 2 operator inclusion criteria, whereas for its more stringent level 3 scheme, 15 basis sets were used. SAC-CI level 3 is capable of producing mean unsigned errors of approximately 0.2 eV with quadruple $$\zeta$$ correlation-consistent basis sets. Fortuitously better results may be obtained when smaller basis sets are used. Anomalous behavior with respect to the basis set size may occur when the level 1 and level 2 options are employed.

The synthesis of a p-terphenyl-based macrocycle, containing a p-phenylene unit with 42.6 kcal/mol of strain energy (SE), is reported. The conversion of a macrocyclic 1,4-diketone to a highly strained arene system takes place over five synthetic steps, featuring iterative dehydrative reactions in the aromatization protocol. Spectroscopic data of the deformed benzenoid macrocycle are in excellent agreement with other homologues that have been reported, indicating that the central p-phenylene ring of 9 is aromatic.

A series of p-terphenyl-based macrocycles, containing highly distorted p-phenylene units, have been synthesized. Biaryl bonds of the nonplanar p-terphenyl nuclei were constructed in the absence of Pd-catalyzed or Ni-mediated cross-coupling reactions, using 1,4-diketones as surrogates to strained arene units. A streamlined synthetic protocol for the synthesis of 1,4-diketo macrocycles has been developed, using only 2.5 mol % of the Hoveyda-Grubbs second-generation catalyst in both metathesis and transfer hydrogenation reactions. Under protic acid-mediated dehydrative aromatization conditions, the central and most strained benzene ring of the p-terphenyl systems was susceptible to rearrangement reactions. To overcome this, a dehydrative aromatization protocol using the Burgess reagent was developed. Under these conditions, no strain-induced rearrangement reactions occur, delivering p-phenylene units with up to 28.4 kcal/mol strain energy and deformation angles that sum up to 40°.

The standard deviations and Shannon information entropies of the probability densities for a particle in a quantum corral are compared and contrasted to determine their effectiveness in measuring particle (de)localization. We illustrate how the two measures emphasize different aspects of the underlying distributions which can lead to inconsistent interpretations. Among these, we show that the Shannon entropy is able to distinguish between the presence of an attractive or repulsive effective potential in the radial Schrodinger equation while the standard deviation does not. The analysis of this radial model is then extended to momentum space where the dependence of the measures, entropic sum and uncertainty product on the effective potential, is examined.

The localization–delocalization of a particle in a cyclic box is studied by examination of its Shannon information entropy and standard deviation. These results are compared to the particle in a box model, in ground and also in excited states. We show how a cyclic symmetry imposes that the ground state is more delocalized in the cyclic box as compared to the particle in a box. However, excited states in both models exhibit the same localization. The differences between the Shannon entropy and the standard deviation are discussed and the analysis is then extended to consider multiple particles in both models.