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# The ezSpectra suite: An easy‐to‐use toolkit for spectroscopy modeling

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Abstract A molecule's spectrum encodes information about its structure and electronic properties. It is a unique fingerprint that can serve as a molecular ID. Quantum chemistry calculations provide key ingredients for interpreting spectra, but modeling the spectra rarely ends there; it requires additional steps that entail combined treatments of electronic and nuclear degrees of freedom and account for specifics of the experimental setup (light energy, polarization, averaging over molecular orientations, temperature, etc.). This Software Focus article describes the ezSpectra suite, which currently comprises two stand‐alone open‐source codes: ezFCF and ezDyson. ezFCF calculates Franck–Condon factors, which yield vibrational progressions for polyatomic molecules, within the double‐harmonic approximation. ezDyson calculates absolute cross‐sections for photodetachment/photoionization processes and photoelectron angular distributions using Dyson orbitals computed by a quantum chemistry program. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods
Spectroscopic measurements (red panel) yield encrypted messages, which can be decoded using electronic structure calculations (blue panels) to reveal detailed information about molecular structure (black panel)
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Experimental (symbols) and computed (solid lines) β values for the ionization of 3a1 orbitals of gas‐phase (red) and liquid‐phase (blue) water. Gas‐phase data are from Truesdale et al.94 (red triangles), Banna et al.95 (red rhombuses), and from Gozem, Seidel et al.80 (red circles), liquid‐phase experimental data are from Gozem, Seidel et al.80 (blue circles). Computed anisotropies are shown as lines using a Coulomb wave with Belkić's charges for the description of the photoelectron. Liquid β calculations were performed on pentamer structures extracted from the molecular dynamics simulation of water using: (1) a multi‐center model with expansion centers on individual water molecules (blue solid line); (2) the multi‐center model including empirical scattering corrections (blue dashed line); and (3) a single‐center model with the expansion center placed at the centroid of the pentamer cluster Dyson orbital (blue dotted line)
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Plots of the experimental (circles) and computed (solid lines) β as a function of the electron kinetic energy (eKE) for the lowest detachment channel for (a) para‐methyl phenolate, pMP; (b) para‐ethyl phenolate, pEP; and (c) para‐vinyl phenolate, pVP. For pEP, two computed PADs are shown, corresponding to global (red) and local (blue) minimum‐energy structures. The respective Dyson orbitals are shown on the right.Source: Reprinted with permission from Ref. 93. Copyright (2017) American Chemical Society
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Absolute photoionization cross section from molecular hydrogen (a) and formaldehyde (b) using a plane‐wave (black line) and a Coulomb‐wave (blue line) descriptions of the photoelectron and Dyson orbitals computed with EOM‐IP‐CCSD/aug‐cc‐pVTZ. In formaldehyde, neither the plane wave nor Coulomb wave reproduce the experimental total cross section, but a Coulomb wave with a partial effective charge of Zeff = 0.25 (orange) does. The solid and dashed orange lines in panel (b) show the calculations with and without FCFs, respectively. By including the FCFs, the calculation reproduces the small rise in cross section around 11 eV.Source: Adapted with permission from Ref. 85. Copyright (2015) American Chemical Society
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(a) Absolute photodetachment cross section from H using a plane wave description of the photoelectron and the Dyson orbital computed with EOM‐IP‐CCSD/aug‐cc‐pVTZ. The cross section computed using the Hartree–Fock canonical molecular orbital is shown with a dashed line. (b) Absolute photoionization cross section from He using a plane wave (black line) and a Coulomb wave (blue line) descriptions of the photoelectron and the Dyson orbital computed with EOM‐IP‐CCSD/aug‐cc‐pVTZ. The plane‐wave treatment neglects interactions between the photoelectron and ionized core, which is a reasonable approximation for photodetachment. The Coulomb wave accounts for an interaction with a +1 charge placed at the orbital centroid, which is a reasonable description for atomic photoionization. Source: Adapted with permission from Ref. 85. Copyright (2015) American Chemical Society
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β values for H and F as a function of energy of the photoelectron kinetic energy
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ezDyson input parameters, options, and output. The gray box indicates options and features implemented in the code, which the user controls. The main information printed in the output are in yellow
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A schematic illustration of FCFs revealing the differences between excited‐state methods that are not captured by vertical energy calculations. Different excited‐state geometries (compare panels a and b) give rise to different FCF intensity pattern and band position. Different excited‐state curvatures (compare panels a and c) give rise to different spacings between the vibrational peaks
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(a) Experimental and computed (stick spectra) Franck–Condon pattern of the excitation and emission spectra of flavin.37 (c) Experimental (black, for flavin mononucleotide in iLOV41) and computed (red) spectra for flavin in condensed phase. The FCFs were computed for a gas‐phase lumiflavin model using ezFCF with B3LYP/cc‐pVTZ (red stick spectra and solid red line broadened spectrum) and by Davari et. al using a slightly different approach (dashed red line).41 The adiabatic and vertical excitation energies are indicated with vertical dashed lines.Source: Panel (a) reprinted with permission from Ref. 37. Copyright (2012) Elsevier B.V. Panel (b) adapted with permission from Ref. 41. Copyright (2016) American Chemical Society
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Photoelectron stick spectrum of the phenolate anion computed in double‐harmonic parallel normal mode approximation at T = 300 K (red sticks). The experimental33 photoelectron spectrum is shown in black. The structure and displacement vectors indicate the primary Franck–Condon active mode responsible for the well‐resolved vibrational peaks. Source: Reprinted with permission from Ref. 34. Copyright (2013) American Chemical Society
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The effect of rotations of the normal coordinates on FCFs within the parallel‐mode approximation. (a) The correct overlap between wave functions of the lower (Q) and upper (Q′′) surfaces. (b) The overlap when the lower normal coordinates are rotated to coincide with the upper coordinates. (c) The overlap when the upper normal coordinates are rotated to coincide with the lower coordinates. Source: Reprinted with permission from Ref. 21. Copyright (2009) American Chemical Society
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ezFCF input parameters, options, and output. The gray box indicates selected features implemented in the code. The output contains information listed in yellow box
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Factors determining the spectral line shape for electronic transitions. The ground state (red), the first excited state (blue), and the second excited state (green) are represented by one‐dimensional harmonic potentials along a normal mode Q. The change in the excited‐state equilibrium geometry relative to the ground state is denoted by ΔQ and ΔQ′′. The main progression is determined by the overlap of the initial state ν = 0 wave function (red translucent area curve) and each of the excited‐state vibrational wave functions (blue or green translucent area curves). If T ≠ 0, hot bands may appear, such as peaks resulting from the ν = 1 transitions indicated by dotted lines on the right. The total spectrum is an overlay of the main progression and hot bands. Instrumental broadening and interactions with the environment (e.g., inhomogeneous broadening in condensed phase) results in a broadened spectrum like the one shown by black dashed lines on the right. The definition of electronic vertical () and adiabatic () excitation energies are shown for the first excited state
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