101:. It allows comparing the theoretical results to experimental measurements. There are many theoretical methods for simulating spectra. Some are simple approximations (like stick spectra); others are high-level, accurate approximations (like those based on Fourier-transform of wavepacket propagations). The NEA lies in between. On the one hand, it is intuitive and straightforward to apply, providing much improved results compared to the stick spectrum. On the other hand, it does not recover all spectral effects and delivers a limited spectral resolution.
474:
80:(NEA) is a general method for simulations of diverse types of molecular spectra. It works by sampling an ensemble of molecular conformations (nuclear geometries) in the source state, computing the transition probabilities to the target states for each of these geometries, and performing a sum over all these transitions convoluted with shape function. The result is an incoherent spectrum containing absolute band shapes through inhomogeneous broadening.
160:
25:
113:, ensembles of geometries started to be also used to estimate the spectra through incoherent sums. Thus, different from the reflection principle, which is usually done via direct integration of analytical functions, the NEA is a numerical approach. In 2012, a formal account of NEA showed that it corresponded to an approximation to the time-dependent spectrum simulation approach, employing a
1279:
841:
84:
469:{\displaystyle \sigma \left(E\right)={\frac {\pi {{e}^{2}}\hbar }{2mc{{\epsilon }_{0}}E}}\sum \limits _{n}^{{N}_{fs}}{{\frac {1}{{N}_{p}}}\sum \limits _{i}^{{N}_{p}}{\Delta {{E}_{0n}}\left({{\mathbf {x} }_{i}}\right){{f}_{0n}}\left({{\mathbf {x} }_{i}}\right)g\left(E-\Delta {{E}_{0n}}\left({{\mathbf {x} }_{i}}\right),\delta \right)}},}
1015:
136:
and temperature, the molecular geometry has a distribution around the equilibrium geometry. From a classical point of view, supposing that the photon absorption is an instantaneous process, each time a molecule is excited, it does so from a different geometry. As a consequence, the transition energy
87:
NEA simulates the spectrum in three steps: firstly an ensemble of molecular geometries is generated. 2)Secondly the transition probability between the initial and final states is computed for each geometry. Lastly a sum over all transition probabilities is done convoluted with a shape
626:
1327:
in the absorption spectrum will not appear in the simulations, only the band envelope around them, because these peaks depend on the wavefunction overlap between the ground and excited state. NEA can be, however, coupled to excited-state dynamics to recover these effects.
973:
1331:
NEA may be too computationally expensive for large molecules. The spectrum simulation requires the calculation of transition probabilities for hundreds of different nuclear geometries, which may become prohibitive due to the high computational costs.
1274:{\displaystyle \Gamma (E)={\frac {e^{2}}{2\pi \hbar mc^{3}\epsilon _{0}}}{\frac {1}{N_{p}}}\sum _{i}^{N_{p}}\Delta E_{1,0}(\mathbf {x} _{i})^{2}\left|f_{1,0}(\mathbf {x} _{i})\right|g\left(E-\Delta E_{1,0}(\mathbf {x} _{i}),\delta \right)}
836:{\displaystyle g\left(E-\Delta {{E}_{0n}},\delta \right)={\frac {1}{\sqrt {2\pi {{\left(\delta /2\right)}^{2}}}}}\exp \left(-{\frac {{\left(E-\Delta {{E}_{0n}}\right)}^{2}}{2{{\left(\delta /2\right)}^{2}}}}\right).}
1625:
Segarra-Martí J, Segatta F, Mackenzie TA, Nenov A, Rivalta I, Bearpark MJ, Garavelli M (December 2019). "Modeling multidimensional spectral lineshapes from first principles: application to water-solvated adenine".
1322:
By construction, NEA does not include information about the target (final) states. For this reason, any spectral information that depends on these states cannot be described in the framework of NEA. For example,
849:
is an arbitrary parameter, it must be much narrower than the band width, not to interfere in its description. As the average value of band widths is around 0.3 eV, it is a good practice to adopt
884:
1679:
Polli D, Altoè P, Weingart O, Spillane KM, Manzoni C, Brida D, et al. (September 2010). "Conical intersection dynamics of the primary photoisomerization event in vision".
109:
The NEA is a multidimensional extension of the reflection principle, an approach often used for estimating spectra in photodissociative systems. With popularization
1570:"Probing electronic and vibrational dynamics in molecules by time-resolved photoelectron, Auger-electron, and X-ray photon scattering spectroscopy"
1366:(June 2012). "Spectrum simulation and decomposition with nuclear ensemble: formal derivation and application to benzene, furan and 2-phenylfuran".
1297:
NEA can be used for many types of steady-state and time-resolved spectrum simulations. Some examples beyond absorption and emission spectra are:
1428:
866:
1444:
Bergsma JP, Berens PH, Wilson KR, Fredkin DR, Heller EJ (February 1984). "Electronic spectra from molecular dynamics: a simple approach".
1731:
41:
63:
34:
1850:"Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories"
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140:
The NEA captures this effect by creating an ensemble of geometries reflecting the zero-point energy, the temperature, or both.
1959:
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45:
872:
968:{\displaystyle \sigma =\ln(10){\frac {10^{3}}{N_{\text{A}}}}\varepsilon \approx 3.82353216\times 10^{-21}\,\varepsilon .}
865:
can be generated by any method able to describe the ground state distribution. Two of the most employed are dynamics and
586:) states are computed. Each transition in the ensemble is convoluted with a normalized line shape function centered at Δ
1954:
1899:"Predicting the emission wavelength of organic molecules using a combinatorial QSAR and machine learning approach"
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1415:. Cambridge Monographs on Atomic, Molecular and Chemical Physics (1 ed.). Cambridge University Press.
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McFarland BK, Farrell JP, Miyabe S, Tarantelli F, Aguilar A, Berrah N, et al. (June 2014).
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1533:"Effects of different initial condition samplings on photodynamics and spectrum of pyrrole"
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Photodissociation
Dynamics: Spectroscopy and Fragmentation of Small Polyatomic Molecules
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It may require cleanup to comply with
Knowledge (XXG)'s content policies, particularly
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The line shape function may be, for instance, a normalized
Gaussian function given by
1948:
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1395:
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Heller EJ (December 1981). "The semiclassical way to molecular spectroscopy 2".
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is a vector collecting the cartesian components of the geometries of each atom.
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997:, NEA is a post-Condon approximation, and it can predict dark vibronic bands.
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has not always the same value, but is a function of the nuclear coordinates.
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1732:"Steady and Time-Resolved Photoelectron Spectra Based on Nuclear Ensembles"
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Ye ZR, Huang IS, Chan YT, Li ZJ, Liao CC, Tsai HR, et al. (2020).
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544:. For each of such geometries in the ensemble, transition energies Δ
1774:"Ultrafast X-ray Auger probing of photoexcited molecular dynamics"
143:
In the NEA, the absorption spectrum (or absorption cross section)
83:
82:
1336:
methods coupled to NEA have been proposed to reduce these costs.
1730:
Arbelo-González W, Crespo-Otero R, Barbatti M (October 2016).
129:. Initially, all molecules are in the ground electronic state
18:
97:
Spectrum simulation is one of the most fundamental tasks in
16:
Semiclassical approach for molecular spectrum simulations.
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can be obtained from absorption cross section through
33:
A major contributor to this article appears to have a
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629:
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835:
468:
1476:"Machine Learning for Absorption Cross Sections"
1289:, with emission from the first excited state.
1009:, the differential emission rate is given by
8:
1285:This expression assumes the validity of the
1568:Bennett K, Kowalewski M, Mukamel S (2015).
1474:Xue BX, Barbatti M, Dral PO (August 2020).
1739:Journal of Chemical Theory and Computation
1540:International Journal of Quantum Chemistry
582:) between the ground (0) and the excited (
117:of the wavepacket overlap time evolution.
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64:Learn how and when to remove this message
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1848:Petit AS, Subotnik JE (October 2014).
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1480:The Journal of Physical Chemistry A
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125:Consider an ensemble of molecules
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127:absorbing radiation in the UV/vis
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44:. Please discuss further on the
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1854:The Journal of Chemical Physics
1293:NEA for other types of spectrum
1531:Barbatti M, Sen K (May 2016).
1368:Theoretical Chemistry Accounts
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1823:Accounts of Chemical Research
978:Because of the dependence of
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1325:vibronically resolved peaks
563:) and oscillator strengths
121:NEA for absorption spectrum
1976:
1380:10.1007/s00214-012-1237-4
1304:differential transmission
1001:NEA for emission spectrum
132:Because of the molecular
78:Nuclear Ensemble Approach
1751:10.1021/acs.jctc.6b00704
1500:10.1021/acs.jpca.0c05310
1421:10.1017/cbo9780511586453
1409:Schinke R (April 1993).
519:reduced Planck constant
151:) at excitation energy
115:Monte Carlo integration
1313:X-ray photo-scattering
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42:neutral point of view
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521:. The sums run over
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1915:2020RSCAd..1023834Y
1909:(40): 23834–23841.
1866:2014JChPh.141o4108P
1835:10.1021/ar00072a002
1790:2014NatCo...5.4235M
1701:10.1038/nature09346
1693:2010Natur.467..440P
1628:Faraday Discussions
1586:2015FaDi..177..405B
1574:Faraday Discussions
1492:2020JPCA..124.7199X
1458:10.1021/j150647a055
867:Wigner distribution
535:nuclear geometries
528:excited states and
511:vacuum permittivity
111:molecular mechanics
1924:10.1039/D0RA05014H
1799:10.1038/ncomms5235
1640:10.1039/C9FD00072K
1594:10.1039/C4FD00178H
1318:Limitations of NEA
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1955:Quantum chemistry
1875:10.1063/1.4897258
1745:(10): 5037–5049.
1552:10.1002/qua.25049
1486:(35): 7199–7210.
1430:978-0-521-48414-5
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54:October 2020
51:
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1634:: 219–244.
1374:(6): 1237.
853:≤ 0.05 eV.
1949:Categories
1580:: 405–28.
1364:Barbatti M
1340:References
940:3.82353216
105:Historical
93:Motivation
1666:196857298
1388:1432-881X
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1122:Δ
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1425:ISBN
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490:and
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1870:doi
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