49 research outputs found
Electronic States of the Benzene Dimer: A Simple Case of Complexity
Electronic structure calculations of the excited states of the benzene dimer using equation-of-motion coupled-cluster method are reported. The calculations reveal large density of electronic states, including multiple valence, Rydberg, and mixed Rydberg-valence states. The calculations of the oscillator strengths for the transitions between the excimer state (i.e., the lowest excited state of the dimer, 1<sup>1</sup><i>B</i><sub>1<i>g</i></sub>) and other excited states allowed us to identify the target state responsible for the excimer absorption as the E<sub>1<i>u</i></sub> state of a mixed Rydberg-valence character at 3.04 eV above the excimer (1<sup>1</sup><i>B</i><sub>1<i>g</i></sub>). Although at <i>D</i><sub>6<i>h</i></sub> the 1<sup>1</sup><i>B</i><sub>1<i>g</i></sub> ā <i>E</i><sub>1<i>u</i></sub> transition is symmetry-forbidden, small geometric displacements (to <i>D</i><sub>2<i>h</i></sub>) that have a negligible effect on the excitation energy split this degenerate state into the dark (4<i>B</i><sub>3<i>u</i></sub>) and bright (4<i>B</i><sub>2<i>u</i></sub>) components (oscillator strength of 0.3 au). The excitation energy for this transition depends strongly on the dimer structure, which explains the broad character of the experimentally observed excimer absorption spectrum
Non-Condon Effects in the One- and Two-Photon Absorption Spectra of the Green Fluorescent Protein
We report calculations of one and two photon absorption (OPA and TPA, respectively) spectra of the green fluorescent protein (GFP) chromophore using the double-harmonic parallel-mode approximation and including explicit dependence of the electronic transition moments on nuclear geometry. The non-Condon effects are found to be more significant for TPA resulting in a different shape of the spectra and a blue shift of 500 cm<sup>ā1</sup> of the TPA peak absorption relative to OPA. The computed shift is in excellent agreement with the experimentally observed 700 cm<sup>ā1</sup>
Visualizing the Contributions of Virtual States to Two-Photon Absorption Cross Sections by Natural Transition Orbitals of Response Transition Density Matrices
Observables
such as two-photon absorption cross sections cannot be computed from
the wave functions of initial and final states alone because of their
nonlinear nature. Rather, they depend on the entire manifold of the
excited states, which follows from the familiar sum-over-states expressions
of second- and higher-order properties. Consequently, the interpretation
of the computed nonlinear optical properties in terms of molecular
orbitals is not straightforward and usually relies on approximate
few-states models. Here, we show that the two-photon absorption (2PA)
transitions can be visualized using response one-particle transition
density matrices, which are defined as transition density matrices
between the zero-order and first-order perturbed states. We also extend
the concept of natural transition orbitals to 2PA transitions. We
illustrate the utility of this new tool, which provides a rigorous
black box alternative to traditional qualitative few-states analysis,
by considering 2PA transitions in ethylene, <i>trans</i>-stilbene, and <i>para</i>-nitroaniline
On the Nature of an Extended Stokes Shift in the mPlum Fluorescent Protein
Far-red fluorescent proteins (FPs)
enable deep-tissue in vivo imaging.
Combining FPs with large and small Stokes shifts enables single-excitation/dual-emission
multicolor applications. Using a quantum mechanics/molecular mechanics
(QM/MM) scheme, we carried out a series of simulations to identify
the origin of an extended Stokes shift (0.2 eV) observed in mPlum,
one of the most far-red-shifted FPs. We demonstrated that the red
shift of emission is largely due to the excited-state relaxation of
the chromophore itself. Rigid protein environment suppresses the relaxation;
however, if the hydrogen-bond network around the chromophore is sufficiently
flexible, it can rearrange upon electronic excitation, allowing the
chromophore to relax. The reorganization of the hydrogen-bond network
is driven by changes in bonding and charge distributions of the chromophore
in the excited state. The ILE65 and GLU16 residues play the most important
role. The MD simulations reveal two ground-state populations with
the direct (Chro-ILE65Ā·Ā·Ā·GLU16) and water-mediated
(Chro-ILE65Ā·Ā·Ā·Wat321Ā·Ā·Ā·GLU16) hydrogen-bond
patterns. In the excited state, both populations relax to a single
emitting state with the water-mediated (Chro-ILE65Ā·Ā·Ā·Wat321Ā·Ā·Ā·GLU16)
hydrogen-bond pattern, which provides a better match for the excited-state
charge distribution (the acylimineās oxygen has a larger negative
charge in S<sub>1</sub> than in S<sub>0</sub>). The extended Stokes
shift arises due to the conversion of the direct hydrogen-bond pattern
to the water-mediated one accompanied by large structural relaxation
of the electronically excited chromophore. This conclusion is supported
by calculations for the GLU16LEU mutant, which has only one hydrogen-bond
pattern. Consequently, no interconversion is possible, and the computed
Stokes shift is small, in agreement with the experiment. Our theoretical
findings provide support to a recent study of the Stokes shifts in
mPlum and its mutants
Real and Imaginary Excitons: Making Sense of Resonance Wave Functions by Using Reduced State and Transition Density Matrices
Within
non-Hermitian quantum mechanics, metastable electronic states
can be represented by isolated <i>L</i><sup>2</sup>-integrable
complex-valued wave functions with complex energies. An analysis scheme
of the real and imaginary parts of resonance wave functions by using
reduced transition density matrices and natural transition orbitals
is presented. While the real parts of excitons describe changes in
the electron density corresponding to the bound part of the resonance,
the imaginary excitons can be interpreted as virtual states facilitating
one-electron decay into the continuum. The different nature of real
and imaginary excitons is revealed by exciton descriptors, in particular
hole-particle separation and their correlation. Singular values and
respective participation ratios quantify the extent of collectivity
of the excitation and a number of distinct decay channels. The utility
of the new tool is illustrated by the analysis of bound and metastable
excited states of cyanopolyyne anions
Modeling Photoelectron Spectra of CuO, Cu<sub>2</sub>O, and CuO<sub>2</sub> Anions with Equation-of-Motion Coupled-Cluster Methods: An Adventure in Fock Space
The
experimental photoelectron spectra of di- and triatomic copper
oxide anions have been reported previously. We present an analysis
of the experimental spectra of the CuO<sup>ā</sup>, Cu<sub>2</sub>O<sup>ā</sup>, and CuO<sub>2</sub><sup>ā</sup> anions using equation-of-motion coupled-cluster
(EOM-CC) methods. The open-shell electronic structure of each molecule
demands a unique combination of EOM-CC methods to achieve an accurate
and balanced representation of the multiconfigurational anionic- and neutral-state manifolds. Analysis of the Dyson orbitals associated
with photodetachment from CuO<sup>ā</sup> reveals the strong
non-Koopmans character of the CuO states. For the lowest detachment
energy, a good agreement between theoretical and experimental values
is obtained with CCSDĀ(T) (coupled-cluster with single and double excitations
and perturbative account of triple excitations). The (T) correction
is particularly important for Cu<sub>2</sub>O<sup>ā</sup>.
Use of a relativistic pseudopotential and matching basis set improves
the quality of results in most cases. EOM-DIP-CCSD analysis of the
low-lying states of CuO<sub>2</sub><sup>ā</sup> reveals multiple singlet and triplet anionic states
near the triplet ground state, adding an extra layer of complexity
to the interpretation of the experimental CuO<sub>2</sub><sup>ā</sup> photoelectron spectrum
Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method Yields Smooth and Internally Consistent Potential Energy Surfaces and Lifetimes for Molecular Resonances
The recently developed equation-of-motion
electron-attachment coupled-cluster
singles and doubles (EOM-EA-CCSD) method augmented by a complex absorbing
potential (CAP) is applied to the <sup>2</sup>Ī <sub>g</sub> resonance
of N<sub>2</sub><sup>ā</sup> and the <sup>2</sup>Ī£<sub>u</sub><sup>+</sup> resonance of H<sub>2</sub><sup>ā</sup> at various internuclear distances.
The results illustrate the advantages of EOM-CC for treating resonance
states over state-specific approaches. CAP-EOM-EA-CCSD produces smoothly
varying potential energy curves and lifetimes for both Ī£ and
Ī resonances. The computed lifetimes and energy differences
between the neutral and electron-attached states are internally consistent,
that is, the resonance width becomes zero at the same internuclear
distance where the energy of the electron-attached state drops below
that of the neutral state. Such smooth and internally consistent behavior
is only achieved when the perturbation due to the CAP is removed using
the first-order deperturbative correction that we introduced earlier;
the evaluation of resonance positions and widths from raw (uncorrected)
energies leads to unphysical discontinuities and fails to correctly
describe the conversion of a resonance to a bound state at large internuclear
distances
Probing Electronic Wave Functions of Sodium-Doped Clusters: Dyson Orbitals, Anisotropy Parameters, and Ionization Cross-Sections
We
apply high-level ab initio methods to describe the electronic
structure of small clusters of ammonia and dimethyl ether (DME) doped
with sodium, which provide a model for solvated electrons. We investigate
the effect of the solvent and cluster size on the electronic states.
We consider both energies and properties, with a focus on the shape
of the electronic wave function and the related experimental observables
such as photoelectron angular distributions. The central quantity
in modeling photoionization experiments is the Dyson orbital, which
describes the difference between the initial <i>N</i>-electron
and final (<i>N</i>ā1)-electron states of a system.
Dyson orbitals enter the expression of the photoelectron matrix element,
which determines total and partial photoionization cross-sections.
We compute Dyson orbitals for the NaĀ(NH<sub>3</sub>)<sub><i>n</i></sub> and NaĀ(DME)<sub><i>m</i></sub> clusters using correlated
wave functions (obtained with equation-of-motion coupled-cluster model
for electron attachment with single and double substitutions) and
compare them with more approximate Hartree-Fock and Kohn-Sham orbitals.
We also analyze the effect of correlation and basis sets on the shapes
of Dyson orbitals and the experimental observables
On the Photodetachment from the Green Fluorescent Protein Chromophore
Motivated by the discrepancies in
recent experimental and theoretical
studies of photodetachment from isolated model chromophores of the
green fluorescent protein (GFP), this study reports calculations of
the electron detachment energies and photoelectron spectra of the
phenolate and deprotonated <i>p</i>-hydroxybenzylidene-2,3-dimethylimidazolinone
(HBDI) anions. The spectra were computed using double-harmonic parallel
normal mode approximation. High-level coupled-cluster methods as well
as density functional theory were used to compute vertical and adiabatic
detachment energies of the phenolate anion serving as a model system
representing anionic GFP-like chromophores (HBDI). The benchmark calculations
reveal that the basis set has significant effect on the computed detachment
energies, whereas the results are less sensitive to the level of electron
correlation treatment. At least aug-cc-pVTZ basis set is required.
The best ĻB97X-D and CCSDĀ(T) estimates of phenolateās
adiabatic detachment energy are 2.12 and 2.19 eV; these values are
very close to the experimental value, 2.253 eV [Gunion et al. <i>Int. J. Mass Spectrom. Ion Proc.</i> <b>1992</b>, <i>117</i>, 601]. The best estimate of the vertical detachment
energy of deprotonated HBDI is 2.76 eV, which supports bound character
of the bright excited state in the FranckāCondon region. The
most intense transition in the computed photoelectron spectra of both
phenolate and deprotonated HBDI is the 0ā0 S<sub>0</sub>āD<sub>0</sub> transition, which is 0.11 eV below vertical detachment energy.
Therefore, the position of the maximum of the photoelectron spectrum
does not represent vertical detachment energy, and the direct comparison
between theory and experiment must involve spectrum modeling
Supplementary Information Files for: libwfa: Wavefunction analysis tools for excited and openāshell electronic states
Supplementary Information Files for: libwfa: Wavefunction analysis tools for excited and openāshell electronic statesAn open-source software library for wavefunction analysis, libwfa, provides a comprehensive and flexible toolbox for post-processing excited-state calculations, featuring a hierarchy of interconnected visual and quantitative analysis methods. These tools afford compact graphical representations of various excited-state processes, provide detailed insight into electronic structure, and are suitable for automated processing of large data sets. The analysis is based on reduced quantities, such as state and transition density matrices (DMs), and allows one to distill simple molecular orbital pictures of physical phenomena from intricate correlated wavefunctions. The implemented descriptors provide a rigorous link between many-body wavefunctions and intuitive physical and chemical models, for example, exciton binding, double excitations, orbital relaxation, and polyradical character. A broad range of quantum-chemical methods is interfaced with libwfa via a uniform interface layer in the form of DMs. This contribution reviews the structure of libwfa and highlights its capabilities by several representative use cases.<br