%0 Journal Article
%J The Journal of Chemical Physics
%D 2018
%T Combining the ensemble and Franck-Condon approaches for calculating spectral shapes of molecules in solution
%A T. J. Zuehlsdorff
%A Isborn, C. M.
%B The Journal of Chemical Physics
%V 148
%P 024110
%G eng
%U https://doi.org/10.1063/1.5006043
%R 10.1063/1.5006043
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2017
%T Absorption Spectra for Disordered Aggregates of Chromophores Using the Exciton Model
%A Kocherzhenko, Aleksey A.
%A Sosa Vazquez, XochitlA
%A Milanese, Joel M.
%A Isborn, Christine M
%X Optimizing the optical properties of large chromophore aggregates and molecular solids for applications in photovoltaics and nonlinear optics is an outstanding challenge. It requires efficient and reliable computational models that must be validated against accurate theoretical methods. We show that linear absorption spectra calculated using the molecular exciton model agree well with spectra calculated using time-dependent density functional theory and configuration interaction singles for aggregates of strongly polar chromophores. Similar agreement is obtained for a hybrid functional (B3LYP), a long-range corrected hybrid functional (ωB97X), and configuration interaction singles. Accounting for the electrostatic environment of individual chromophores in the parametrization of the exciton model with the inclusion of atomic point charges significantly improves the agreement of the resulting spectra with those calculated using all-electron methods; different charge definitions (Mulliken and ChelpG) yield similar results. We find that there is a size-dependent error in the exciton model compared with all-electron methods, but for aggregates with more than six chromophores, the errors change slowly with the number of chromophores in the aggregate. Our results validate the use of the molecular exciton model for predicting the absorption spectra of bulk molecular solids; its formalism also allows straightforward extension to calculations of nonlinear optical response.
%B Journal of Chemical Theory and Computation
%V 13
%P 3787-3801
%G eng
%U http://dx.doi.org/10.1021/acs.jctc.7b00477
%R 10.1021/acs.jctc.7b00477
%0 Journal Article
%J The Journal of Physical Chemistry B
%D 2017
%T Combining Explicit Quantum Solvent with a Polarizable Continuum Model
%A Provorse Long, Makenzie R.
%A Isborn, Christine M
%X A promising approach for accurately modeling both short-range and long-range solvation effects is to combine explicit quantum mechanical (QM) solvent with a classical polarizable continuum model (PCM), but the best PCM for these combined QM/classical calculations is relatively unexplored. We find that the choice of the solvation cavity is very important for obtaining physically correct results since unphysical double counting of solvation effects from both the QM solvent and the classical dielectric can occur with a poor choice of cavity. We investigate the dependence of electronic excitation energies on the definition of the PCM cavity and the self-consistent reaction field method, comparing results to large-scale explicit QM solvent calculations. For excitation energies, we identify the difference between the ground and excited state dipole moments as the key property determining the sensitivity to the PCM cavity. Using a linear response PCM approach combined with QM solvent, we show that excitation energies are best modeled by a solvent excluded surface or a scaled van der Waals surface. For the aqueous solutes studied here, we find that a scaled van der Waals surface defined by universal force field radii scaled by a factor of 1.5 gives reasonable excitation energies. When using an external iteration state-specific PCM approach, however, the excitation energies are most accurate with a larger PCM cavity, such as a solvent accessible surface.
%B The Journal of Physical Chemistry B
%V 121
%P 10105-10117
%G eng
%U http://dx.doi.org/10.1021/acs.jpcb.7b06693
%R 10.1021/acs.jpcb.7b06693
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2017
%T Convergence of Computed Aqueous Absorption Spectra with Explicit Quantum Mechanical Solvent
%A Milanese, Joel M.
%A Provorse, Makenzie R
%A Alameda, Enrique
%A Isborn, Christine M
%X For reliable condensed phase simulations, an accurate model that includes both short- and long-range interactions is required. Short- and long-range interactions can be particularly strong in aqueous solution, where hydrogen-bonding may play a large role at short range and polarization may play a large role at long range. Although short-range solute–solvent interactions such as charge transfer, hydrogen bonding, and solute–solvent polarization can be taken into account with a quantum mechanical (QM) treatment of the solvent, it is unclear how much QM solvent is necessary to accurately model interactions with different solutes. In this work, we investigate the effect of explicit QM solvent on absorption spectra computed for a series of solutes with decreasing polarity. By adjusting the boundary between QM and classical molecular mechanical solvent to include up to 400 QM water molecules, convergence of the calculated absorption spectra with respect to the size of the QM region is achieved. We find that the rate of convergence does not correlate with solute polarity when excitation energies are calculated using time-dependent density functional theory with a range-separated hybrid functional, but it does correlate with solute polarity when using configuration interaction singles. We also find that larger basis sets converge the computed spectrum with fewer QM solvent molecules. To optimize the computational cost with respect to convergence, we test a mixed basis set with more basis functions for atoms of the chromophore and the solvent molecules that are nearest to it and fewer basis functions for the atoms of the remaining solvent molecules in the QM region. Our results show that using a mixed basis set is a potentially effective way to significantly lower the computational cost while reproducing the results computed with larger basis sets.
%B Journal of Chemical Theory and Computation
%V 13
%P 2159-2171
%G eng
%U http://dx.doi.org/10.1021/acs.jctc.7b00159
%R 10.1021/acs.jctc.7b00159
%0 Book Section
%B Computational Approaches for Studying Enzyme Mechanism Part A
%D 2016
%T Chapter Fifteen - Simulating Nuclear and Electronic Quantum Effects in Enzymes
%A L. Wang
%A Isborn, C. M.
%A T.E. Markland
%E Gregory A. Voth
%K Nuclear quantum effects
%X Abstract An accurate treatment of the structures and dynamics that lead to enhanced chemical reactivity in enzymes requires explicit treatment of both electronic and nuclear quantum effects. The former can be captured in ab initio molecular dynamics (AIMD) simulations, while the latter can be included by performing ab initio path integral molecular dynamics (AI-PIMD) simulations. Both \{AIMD\} and AI-PIMD simulations have traditionally been computationally prohibitive for large enzymatic systems. Recent developments in streaming computer architectures and new algorithms to accelerate path integral simulations now make these simulations practical for biological systems, allowing elucidation of enzymatic reactions in unprecedented detail. In this chapter, we summarize these recent developments and discuss practical considerations for applying \{AIMD\} and AI-PIMD simulations to enzymes.
%B Computational Approaches for Studying Enzyme Mechanism Part A
%S Methods in Enzymology
%I Academic Press
%V 577
%P 389 - 418
%G eng
%U http://www.sciencedirect.com/science/article/pii/S0076687916300830
%R http://dx.doi.org/10.1016/bs.mie.2016.05.047
%0 Journal Article
%J The Journal of Physical Chemistry B
%D 2016
%T Convergence of Excitation Energies in Mixed Quantum and Classical Solvent: Comparison of Continuum and Point Charge Models
%A Provorse, Makenzie R
%A Peev, Thomas
%A Xiong, Chou
%A Isborn, Christine M
%X Mixed quantum mechanical (QM)/classical methods provide a computationally efficient approach to modeling both ground and excited states in the condensed phase. To accurately model short-range interactions, some amount of the environment can be included in the QM region, whereas a classical model can treat long-range interactions to maintain computational affordability. The best computational protocol for these mixed QM/classical methods can be determined by examining convergence of molecular properties. Here, we compare molecular mechanical (MM) fixed point charges to a polarizable continuum model (PCM) for computing electronic excitations in solution. We computed the excitation energy of three pairs of neutral/anionic molecules in aqueous solvent, including up to 250 water molecules in the QM region. Interestingly, the convergence is similar for MM point charges and a PCM, with convergence achieved when at least one full solvation shell is treated with QM. Although the van der Waals (VDW) definition of the PCM cavity is adequate with small amounts of QM solvent, larger QM solvent layers had gaps in the VDW PCM cavity, leading to asymptotically incorrect excitation energies. Given that the VDW cavity leads to unphysical solute–solvent interactions, we advise using a solvent-excluded surface cavity for QM/PCM calculations that include QM solvent.
%B The Journal of Physical Chemistry B
%V 120
%P 12148-12159
%G eng
%U http://dx.doi.org/10.1021/acs.jpcb.6b09176
%R 10.1021/acs.jpcb.6b09176
%0 Journal Article
%J International Journal of Quantum Chemistry
%D 2016
%T Electron dynamics with real-time time-dependent density functional theory
%A Provorse, Makenzie R
%A Isborn, Christine M
%K adiabatic approximation
%K charge transfer
%K density functional theory
%K electron dynamics
%K real-time
%K TDDFT
%K time-domain
%X Real-time time-dependent functional theory (RT-TDDFT) directly propagates the electron density in the time domain by integrating the time-dependent Kohn–Sham equations. This is in contrast to the popular linear response TDDFT matrix formulation that computes transition frequencies from a ground state reference. RT-TDDFT is, therefore, a potentially powerful technique for modeling atto- to picosecond electron dynamics, including charge transfer pathways, the response to a specific applied field, and frequency dependent linear and nonlinear properties. However, qualitatively incorrect electron dynamics and time-dependent resonant frequencies can occur when perturbing the density away from the ground state due to the common adiabatic approximation. An overview of the RT-TDDFT method is provided here, including examples of some cases that lead to this qualitatively incorrect behavior. © 2016 Wiley Periodicals, Inc.
%B International Journal of Quantum Chemistry
%V 116
%P 739–749
%G eng
%U http://dx.doi.org/10.1002/qua.25096
%R 10.1002/qua.25096
%0 Journal Article
%J The Journal of Chemical Physics
%D 2015
%T Density-functional errors in ionization potential with increasing system size
%A Whittleton, Sarah R.
%A Sosa Vazquez, XochitlA
%A Isborn, Christine M
%A Johnson, Erin R.
%B The Journal of Chemical Physics
%V 142
%P 184106
%G eng
%U http://scitation.aip.org/content/aip/journal/jcp/142/18/10.1063/1.4920947
%R http://dx.doi.org/10.1063/1.4920947
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2015
%T Peak-Shifting in Real-Time Time-Dependent Density Functional Theory
%A Provorse, Makenzie R
%A Habenicht, Bradley F
%A Isborn, Christine M
%X In recent years, the development and application of real-time time-dependent density functional theory (RT-TDDFT) has gained momentum as a computationally efficient method for modeling electron dynamics and properties that require going beyond a linear response of the electron density. However, the RT-TDDFT method within the adiabatic approximation can unphysically shift absorption peaks throughout the electron dynamics. Here, we investigate the origin of these time-dependent resonances observed in RT-TDDFT spectra. Using both exact exchange and hybrid exchange-correlation approximate functionals, adiabatic RT-TDDFT gives time-dependent absorption spectra in which the peaks shift in energy as populations of the excited states fluctuate, while exact wave function methods yield peaks that are constant in energy but vary in intensity. The magnitude of the RT-TDDFT peak shift depends on the frequency and intensity of the applied field, in line with previous studies, but it oscillates as a function of time-dependent molecular orbital populations, consistent with a time-dependent superposition electron density. For the first time, we provide a rationale for the direction and magnitude of the time-dependent peak shifts based on the molecular electronic structure. For three small molecules, H2, HeH+, and LiH, we give contrasting examples of peak-shifting to both higher and lower energies. The shifting is explained as coupled one-electron transitions to a higher and a lower lying state. Whether the peak shifts to higher or lower energies depends on the relative energetics of these one-electron transitions.
%B Journal of Chemical Theory and Computation
%V 11
%P 4791-4802
%G eng
%U http://dx.doi.org/10.1021/acs.jctc.5b00559
%R 10.1021/acs.jctc.5b00559
%0 Journal Article
%J The Journal of Chemical Physics
%D 2015
%T Size-dependent error of the density functional theory ionization potential in vacuum and solution
%A Sosa Vazquez, XochitlA
%A Isborn, Christine M
%B The Journal of Chemical Physics
%V 143
%P 244105
%G eng
%U http://scitation.aip.org/content/aip/journal/jcp/143/24/10.1063/1.4937417
%R http://dx.doi.org/10.1063/1.4937417
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2014
%T Optimum Exchange for Calculation of Excitation Energies and Hyperpolarizabilities of Organic Electro-optic Chromophores
%A Garrett, Kerry
%A Sosa Vazquez, XochitlA
%A Egri, Shawn B
%A Wilmer, Jacob
%A Johnson, Lewis E
%A Robinson, Bruce H
%A Isborn, Christine M
%X Organic electro-optic (OEO) materials integrated into silicon–organic hybrid devices afford significant improvements in size, weight, power, and bandwidth performance of integrated electronic/photonic systems critical for current and next generation telecommunication, computer, sensor, transportation, and defense technologies. Improvement in molecular first hyperpolarizability (β), and in turn electro-optic activity, is crucial to optimizing device performance. Common hybrid density functional theory (DFT) methods, while attractive due to their computational scaling, often perform poorly for optical properties in systems with substantial intramolecular charge-transfer character, such as OEO chromophores. This study evaluates the utility of the long-range corrected (LC) DFT methods for computation of the molecular second-order nonlinear optical response. We compare calculated results for a 14-molecule benchmark set of OEO chromophores with the corresponding experimentally measured β and one-photon absorption energy, λmax. We analyze the distance dependence of the fraction of exact exchange in LC-DFT methods for accurately computing these properties for OEO chromophores. We also examine systematic tuning of the range-separation parameter to enforce Koopmans’/ionization potential theorem. This tuning method improves prediction of excitation energies but is not reliable for predicting the hyperpolarizabilities of larger chromophores since the tuning parameter value can be too small, leading to instabilities in the computation of βHRS. Additionally, we find that the size dependence of the optimal tuning parameter for the ionization potential has the opposite size dependence of optimal tuning parameter for best agreement with the experimental λmax, suggesting the tuning for the ionization potential is unreliable for extended conjugated systems.
%B Journal of Chemical Theory and Computation
%V 10
%P 3821-3831
%G eng
%U http://dx.doi.org/10.1021/ct500528z
%R 10.1021/ct500528z
%0 Journal Article
%J The Journal of Chemical Physics
%D 2014
%T Two-electron Rabi oscillations in real-time time-dependent density-functional theory
%A Habenicht, Bradley F
%A Tani, Noriyuki P
%A Provorse, Makenzie R
%A Isborn, Christine M
%B The Journal of Chemical Physics
%V 141
%P 184112
%G eng
%U http://scitation.aip.org/content/aip/journal/jcp/141/18/10.1063/1.4900514
%R http://dx.doi.org/10.1063/1.4900514
%0 Journal Article
%J Journal of Physical Chemistry Letters
%D 2013
%T Carbon nanotube chirality determines efficiency of electron transfer to fullerene in all-carbon photovoltaics
%A Isborn, Christine M
%A Tang, Chun
%A Martini, Ashlie
%A Johnson, Erin R.
%A Otero-De-La-Roza, Alberto
%A Tung, Vincent C.
%K carbon nanotubes
%K charge transfer
%K chirality
%K exciton dissociation
%K photovoltaics
%X Nanocarbon-based photovoltaics offer a promising new architecture for the next generation of solar cells. We demonstrate that a key factor determining the efficiency of single-walled carbon nanotube (SWCNT)/fullerene devices is the chirality of the SWCNT. This is shown via current density vs voltage measurements of nanocarbon devices prepared with (9,7), (7,6) and (6,5) SWCNTs, as well as density-functional theory (DFT) density of states calculations of C60 adsorbed onto the corresponding SWCNTs. The trends in efficiency are rationalized in terms of the relative energies of the fullerene and SWCNT conduction band energy levels.
%B Journal of Physical Chemistry Letters
%V 4
%P 2914–2918
%@ 1948-7185
%G eng
%R 10.1021/jz401369s
%0 Journal Article
%J The Journal of Physical Chemistry B
%D 2013
%T The charge transfer problem in density functional theory calculations of aqueously solvated molecules.
%A Isborn, Christine M
%A Mar, Brendan D
%A Curchod, Basile F E
%A Tavernelli, Ivano
%A Mart\'ınez, Todd J
%X Recent advances in algorithms and computational hardware have enabled the calculation of excited states with time-dependent density functional theory (TDDFT) for large systems of O(1000) atoms. Unfortunately, the aqueous charge transfer problem in TDDFT (whereby many spuriously low-lying charge transfer excited states are predicted) seems to become more severe as the system size is increased. In this work, we concentrate on the common case where a chromophore is embedded in aqueous solvent. We examine the role of exchange-correlation functionals, basis set effects, ground state geometries, and the treatment of the external environment in order to assess the root cause of this problem. We conclude that the problem rests largely on water molecules at the boundary of a finite cluster model, i.e., "edge waters." We also demonstrate how the TDDFT problem can be related directly to ground state problems. These findings demand caution in the commonly employed strategy that rests on "snapshot" cutout geometries taken from ground state dynamics with molecular mechanics. We also find that the problem is largely ameliorated when the range-separated hybrid functional LC-$ømega$PBEh is used.
%B The Journal of Physical Chemistry B
%V 117
%P 12189–201
%G eng
%U http://www.ncbi.nlm.nih.gov/pubmed/23964865
%R 10.1021/jp4058274
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2012
%T Electronic absorption spectra from MM and ab initio QM/MM molecular dynamics: Environmental effects on the absorption spectrum of photoactive yellow protein
%A Isborn, Christine M
%A Götz, Andreas W.
%A Clark, Matthew a.
%A Walker, Ross C.
%A Martinez, Todd J
%X We describe a new interface of the GPU parallelized TeraChem electronic structure package and the Amber molecular dynamics package for quantum mechanical (QM) and mixed QM and molecular mechanical (MM) molecular dynamics simulations. This QM/MM interface is used for computation of the absorption spectra of the photoactive yellow protein (PYP) chromophore in vacuum, aqueous solution, and protein environments. The computed excitation energies of PYP require a very large QM region (hundreds of atoms) covalently bonded to the chromophore in order to achieve agreement with calculations that treat the entire protein quantum mechanically. We also show that 40 or more surrounding water molecules must be included in the QM region in order to obtain converged excitation energies of the solvated PYP chromophore. These results indicate that large QM regions (with hundreds of atoms) are a necessity in QM/MM calculations.
%B Journal of Chemical Theory and Computation
%V 8
%P 5092–5106
%@ 1549-9618
%G eng
%R 10.1021/ct3006826
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2011
%T Excited-state electronic structure with configuration interaction singles and Tamm-Dancoff time-dependent density functional theory on graphical processing units
%A Isborn, Christine M
%A Luehr, Nathan
%A Ufimtsev, Ivan S.
%A Martinez, Todd J
%X Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm–Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).
%B Journal of Chemical Theory and Computation
%V 7
%P 1814–1823
%@ 1549-9618
%G eng
%R 10.1021/ct200030k
%0 Journal Article
%J Journal of Chemical Physics
%D 2011
%T On the gauge invariance of nonperturbative electronic dynamics using the time-dependent Hartree-Fock and time-dependent Kohn-Sham
%A Ding, Feizhi
%A Liang, Wenkel
%A Chapman, Craig T.
%A Isborn, Christine M
%A Li, Xiaosong
%X Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.
%B Journal of Chemical Physics
%V 135
%P 164101
%G eng
%R 10.1063/1.3655675
%0 Journal Article
%J Journal of the American Chemical Society
%D 2010
%T {Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals}
%A Bing, Yonghong
%A Selassie, David
%A Paradise, Ruthanne H.
%A Isborn, Christine
%A Kramer, Nicholas
%A Sadilek, Martin
%A Kaminsky, Werner
%A Kahr, Bart
%X In 1919, Perucca reported anomalous optical rotatory dispersion from chiral NaClO(3) crystals that were colored by having been grown from a solution containing an equilibrium racemic mixture of a triarylmethane dye (Perucca, E. Nuovo Cimento 1919, 18, 112-154). Perucca's chiroptical observations are apparently consistent with a resolution of the propeller-shaped dye molecules by NaClO(3) crystals. This implies that Perucca achieved the first enantioselective adsorption of a racemic mixture on an inorganic crystal, providing evidence of the resolution of a triarylmethyl propeller compound lacking bulky ortho substituents. Following the earlier report, NaClO(3) crystals dyed with aniline blue are described herein. The rich linear optical properties of (001), (110), and (111) sections of these mixed crystals are described via their absorbance spectra in polarized light as well as images related to linear dichroism, linear birefringence, circular dichroism, and anomalous circular extinction. The linear dichroism fixes the transition electric dipole moments in the aromatic plane with respect to the growth faces of the NaClO(3) cubes. Likewise, circular dichroism measurements of four orientations of aniline blue in NaClO(3) fix a bisignate tensor with respect to the crystal growth faces. Electronic transition moments and circular dichroism tensors were computed ab initio for aniline blue. These calculations, in conjunction with the crystal-optical properties, establish a consistent mixed-crystal model. The nature of the circular extinction depends upon the crystallographic direction along which the crystals are examined. Along 100, the crystals evidence circular dichroism. Along 110, the crystals evidence mainly anomalous circular extinction. These two properties, while measured by the differential transmission of left and right circularly polarized light, are easily distinguished in their transformation properties with respect to reorientations of the sample plates. Circular dichroism is symmetric with respect to the wave vector, whereas anomalous circular extinction is antisymmetric. Analysis of Perucca's raw data reveals that he was observing a convolution of linear and circular optical properties. The relatively large circular dichroism should in principle establish the absolute configuration of the propeller-shaped molecules associated with d- or l-NaClO(3) crystals. However, this determination was not as straightforward as it appeared at the outset. In the solid state, unlike in solution, a strong chiroptical response is not in and of itself evidence of enantiomeric resolution. It is shown how it is possible to have a poor resolution-even an equal population of P and M propellers-within a given chiral NaClO(3) crystal and still have a large circular dichroism.
%B Journal of the American Chemical Society
%V 132
%P 7454–7465
%G eng
%0 Journal Article
%J Journal of Physical Chemistry Letters
%D 2010
%T {Multiple exciton generation in small Si clusters: A high-level, ab initio study}
%A Fischer, Sean A.
%A Madrid, Angeline B.
%A Isborn, Christine M
%A Prezhdo, Oleg V.
%K Clusters
%K Dynamics
%K Excited states
%X The electron hole excitonic nature of high energy states is investigated in neutral and charged Si clusters, motivated by the multiple exciton generation (MEG) process that is highly debated in photovoltaic literature, Silicon forms the basis for-much of the photovoltaic industry, and our high-level, first principles calculations show that at 2-3 times the lowest excitation energy, the majority of optically excited states in neutral Si, and Si 10 take on multiple exciton (ME) character. The transition from single excitons (SEs) to MEs is not as sharp in Si as in PbSe clusters, but it is much more pronounced than in CdSe. The closer similarity of Si to PbSe than CdSe is unexpected, since Si clusters are less symmetric than PbSe clusters. Charging suppresses MEG in Si clusters; however, the suppression is less pronounced than in PbSe. A strong ME signal is seen already at 5 X E(g) upon charging. The low ME thresholds and nearly complete switch from SEs to MEs create a good possibility for efficient MEG in neutral Si nanoclusters and reveal hope that reasonable quantum yields can still be obtained despite charging.
%B Journal of Physical Chemistry Letters
%V 1
%P 232–237
%@ 1948-7185
%G eng
%R 10.1021/jz900097e
%0 Journal Article
%J Journal of Physical Chemistry A
%D 2010
%T {Time-dependent density functional theory calculations of ehrenfest dynamics of laser controlled dissociation of NO+: Pulse length and sequential multiple single-photon processes}
%A Liang, Wenkel
%A Isborn, Christine M
%A Lindsay, Alex
%A Li, Xiaosong
%A Smith, Stanley M.
%A Levis, Robert J.
%X Intense laser field controlled dissociation reactions of the nitric oxide cation (NO(+)) are studied by ab initio Ehrenfest dynamics with time-dependent density functional theory. Intense electric fields with five different pulse lengths are compared, combined with potential energy surface and density of state analysis, to reveal the effect of pulse length on the control mechanism. Controllable dissociative charge states are observed, and the correlation between the laser pulse length and the probability of sequential multiple single-photon processes is presented. This work introduces a concept of using laser pulse length to control the sequential multiple single-photon process.
%B Journal of Physical Chemistry A
%V 114
%P 6201–6206
%G eng
%R 10.1021/jp102013b
%0 Journal Article
%J Journal of Physical Chemistry C
%D 2009
%T {Charging quenches multiple exciton generation in semiconductor nanocrystals: first-principles calculations on small PbSe clusters}
%A Isborn, Christine M
%A Prezhdo, Oleg V.
%X We demonstrate using symmetry adapted cluster theory with configuration$\backslash$ninteraction \{(SAC-CI)\} that charging of small \{PbSe\} nanocrystals$\backslash$n\{(NCs)\} greatly modifies their electronic states and optical excitations.$\backslash$nConduction and valence band transitions that are not available in$\backslash$nneutral \{NCs\} dominate low energy electronic excitations and show$\backslash$nweak optical activity. At higher energies these transitions mix with$\backslash$nboth single excitons \{(SEs)\} and multiple excitons \{(MEs)\} associated$\backslash$nwith transitions across the band-gap. As a result, both \{SEs\} and$\backslash$n\{MEs\} are significantly blue-shifted, and \{ME\} generation is drastically$\backslash$nhampered. The overall contribution of \{MEs\} to the electronic excitations$\backslash$nof the charged \{NCs\} is small even at very high energies. The calculations$\backslash$nsupport the recent view that the observed strong dependence of the$\backslash$n\{ME\} yields on the experimental conditions is likely due to the effects$\backslash$nof \{NC\} charging.
%B Journal of Physical Chemistry C
%V 113
%P 12617–12621
%@ 1932-7447
%G eng
%R 10.1021/jp902621a
%0 Journal Article
%J The journal of physical chemistry. A
%D 2009
%T {Laser-controlled dissociation of C2H2(2+): Ehrenfest dynamics using time-dependent density functional theory.}
%A Liang, Wenkel
%A Isborn, Christine M
%A Li, Xiaosong
%X Intense laser field dissociations of the acetylene dication C(2)H(2)(2+) are studied by an ab initio Ehrenfest dynamics method with time-dependent density functional theory. Various field frequencies (9.5 to approximately 13.6 eV) and field directions are applied to a Boltzmann ensemble of C(2)H(2)(2+) molecules. With the laser field perpendicular to the molecular axis, four fragmentation channels are observed at high frequency with no dominant pathway. With the field parallel to the molecular axis, fragmentations occur at all frequencies and the amount of C-H bond breakage increases with laser frequency. Selective dissociation patterns are observed with low-frequency fields parallel to the molecular axis. A systematic analysis of excited-state potential energy surfaces is used to rationalize the simulation results.
%B The journal of physical chemistry. A
%V 113
%P 3463–3469
%G eng
%R 10.1021/jp811431u
%0 Journal Article
%J Journal of Chemical Physics
%D 2009
%T {Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search}
%A Liang, Wenkel
%A Isborn, Christine M
%A Li, Xiaosong
%X The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the alpha and beta electrons to achieve the two-electron excited states of minimal basis H(2) and HeH(+) [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H(2), HeH(+), lithium hydride, ethylene, and butadiene.
%B Journal of Chemical Physics
%V 131
%@ 0021-9606
%G eng
%R 10.1063/1.3266564
%0 Journal Article
%J Journal of Chemical Physics
%D 2009
%T {Representation independent algorithms for molecular response calculations in time-dependent self-consistent field theories}
%A Tretiak, Sergei
%A Isborn, Christine M
%A Niklasson, Anders M N
%A Challacombe, Matt
%X Four different numerical algorithms suitable for a linear scaling implementation of time-dependent Hartree-Fock and Kohn-Sham self-consistent field theories are examined. We compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures to solve the random-phase approximation (RPA) (non-Hermitian) and Tamm-Dancoff approximation (TDA) (Hermitian) eigenvalue equations in the molecular orbital-free framework. Semiempirical Hamiltonian models are used to numerically benchmark algorithms for the computation of excited states of realistic molecular systems (conjugated polymers and carbon nanotubes). Convergence behavior and stability are tested with respect to a numerical noise imposed to simulate linear scaling conditions. The results single out the most suitable procedures for linear scaling large-scale time-dependent perturbation theory calculations of electronic excitations.
%B Journal of Chemical Physics
%V 130
%@ 0021-9606
%G eng
%R 10.1063/1.3068658
%0 Journal Article
%J Journal of Chemical Theory and Computation
%D 2009
%T {Singlet− Triplet Transitions in Real-Time Time-Dependent Hartree− Fock/Density Functional Theory}
%A Isborn, Christine M
%A Li, Xiaosong
%X Real-time time-dependent Hartree-Fock (TDHF)/density functional theory (TDDFT) has been gaining in popularity because of its ability to treat phenomena beyond the linear response and because it has the potential to be more computationally powerful than frequency domain TDHF/TDDFT. Within real-time TDHF/TDDFT, we present a method that gives the excited state triplet energies starting from a singlet ground state. Using a spin-dependent field, we break the spin-symmetry of the R and ? density matrices, which incorporates a triplet contribution into the superposition state. The R electron density follows the applied field, and the ? electron density responds to the perturbation from the changing R electron density. We examine the individual R/? responses during the electron density propagation. Singlet-triplet transitions appear as ‘dark’ states: they are present in the R/? responses but are absent from the total electron density response
%B Journal of Chemical Theory and Computation
%V 5
%P 2415–2419
%G eng
%U http://pubs.acs.org/doi/abs/10.1021/ct900264b
%0 Journal Article
%J Journal of Physical Chemistry C
%D 2009
%T {Theoretical Characterization of Electronic Transitions in Co 2+ - and Mn 2+ -Doped ZnO Nanocrystals}
%A Badaeva, Ekaterina
%A Isborn, Christine M
%A Feng, Yong
%A Ochsenbein, Stefan T.
%A Gamelin, D R
%A Li, Xiaosong
%X Linear response time-dependent hybrid density functional theory has been applied for the first time to describe optical transitions characteristic of Co2+- and Mn2+-doped ZnO quantum dots (QDs) with sizes up to 300 atoms (∼1.8 nm diam) and to investigate QD size effects on the absorption spectra. Particular attention is given to charge-transfer (CT or “photoionization”) excited states. For both dopants, CT transitions are calculated to appear at sub-band-gap energies and extend into the ZnO excitonic region. CT transitions involving excitation of dopant d electrons to the ZnO conduction band occur lowest in energy, and additional CT transitions corresponding to promotion of ZnO valence band electrons to the dopant d orbitals are found at higher energies, consistent with experimental results. The CT energies are found to depend on the QD diameter. Analysis of excited-state electron and hole density distributions shows that, for both CT types, the electron and hole are localized to some extent around the impurity ion, which results in “heavier” photogenerated carriers than predicted from simple effective mass considerations. In addition to CT transitions, the Co2+-doped ZnO QDs also exhibit characteristic d-d excitations whose experimental energies are reproduced well and do not depend on the size of the QD.
%B Journal of Physical Chemistry C
%V 113
%P 8710–8717
%G eng
%R 10.1021/jp900392j
%0 Journal Article
%J Journal of Physical Chemistry C
%D 2008
%T {Frequency and solvent dependence of nonlinear optical properties of molecules}
%A Takimoto, Y.
%A Isborn, C. M.
%A Eichinger, B. E.
%A Rehr, J. J.
%A Robinson, B. H.
%X Real-time, time-dependent density functional theory (RT-TDDFT) is used for the evaluation of the frequency dependence of the polarizability and hyperpolarizability of molecules intended for application in electro-optic devices. These first-principles computational methods are powerful but costly. Significantly easier calculations based on a simplified version of second-order time-dependent perturbation theory, the ``two-state model'' (TSM), are here used to provide another estimate of the frequency dependence. Furthermore, the TSM calculations can be done in the presence of a dielectric reaction field (the polarizable continuum model method) to provide estimates of the solvent dependent properties in addition to the frequency-dependent properties. Here we use RT-TDDFT to assess the accuracy of the frequency dependence of the TS, and a ground-state finite field calculation to assess the effect of additional states on the static hyperpolarizability. Both frequency and dielectric responses are important for evaluation of the suitability of molecules in nonlinear optical applications.
%B Journal of Physical Chemistry C
%V 112
%P 8016–8021
%G eng
%R 10.1021/jp800444j
%0 Journal Article
%J Journal of Physical Chemistry C
%D 2008
%T {Generation of multiple excitons in PbSe and CdSe quantum dots by direct photoexcitation: First-principles calculations on small PbSe and CdSe clusters}
%A Isborn, Christine M
%A Kilina, Svetlana V.
%A Li, Xiaosong
%A Prezhdo, Oleg V.
%X We demonstrate for the first time using a combination of the Hartree?Fock approximation and the symmetry adapted cluster theory with configuration interaction (SAC-CI) that multiple excitons (ME) in PbSe and CdSe quantum dots (QD) can be generated directly upon photoexcitation. At energies 2.5?3 times the lowest excitation, almost all optically excited states in Pb4Se4 become MEs, while both single excitons and MEs are seen in Cd6Se6. We analyze the high-level SAC-CI results of the small clusters based on the band structure and then extend our band structure analysis to Pb68Se68, Pb180Se180, Cd33Se33, and Cd111Se111. Our results explain the ultrafast generation of MEs without the need for a phonon relaxation bottleneck and clarify why PbSe is particularly suitable for generation of MEs. Efficient exciton multiplication can be used to considerably increase the efficiency of QD-based solar cells.
%B Journal of Physical Chemistry C
%V 112
%P 18291–18294
%@ 1932-7447
%G eng
%R 10.1021/jp807283j
%0 Journal Article
%J Organic Letters
%D 2008
%T Internal Dynamics and Optical Rotations Predicted for O h - and O-Symmetric Cubanes
%A Hrovat, David
%A Isborn, Christine M
%A Kahr, Bart
%A Borden, Weston Thatcher
%B Organic Letters
%P 85–87
%G eng
%0 Journal Article
%J Journal of Chemical Physics
%D 2008
%T {Modeling the doubly excited state with time-dependent Hartree-Fock and density functional theories}
%A Isborn, Christine M
%A Li, Xiaosong
%X Multielectron excited states have become a hot topic in many cutting-edge research fields, such as the photophysics of polyenes and in the possibility of multiexciton generation in quantum dots for the purpose of increasing solar cell efficiency. However, obtaining multielectron excited states has been a major obstacle as it is often done with multiconfigurational methods, which involve formidable computational cost for large systems. Although they are computationally much cheaper than multiconfigurational wave function based methods, linear response adiabatic time-dependent Hartree-Fock (TDHF) and density functional theory (TDDFT) are generally considered incapable of obtaining multielectron excited states. We have developed a real-time TDHF and adiabatic TDDFT approach that is beyond the perturbative regime. We show that TDHF/TDDFT is able to simultaneously excite two electrons from the ground state to the doubly excited state and that the real-time TDHF/TDDFT implicitly includes double excitation within a superposition state. We also present a multireference linear response theory to show that the real-time electron density response corresponds to a superposition of perturbative linear responses of the S(0) and S(2) states. As a result, the energy of the two-electron doubly excited state can be obtained with several different approaches. This is done within the adiabatic approximation of TDDFT, a realm in which the doubly excited state has been deemed missing. We report results on simple two-electron systems, including the energies and dipole moments for the two-electron excited states of H(2) and HeH(+). These results are compared to those obtained with the full configuration interaction method.
%B Journal of Chemical Physics
%V 129
%@ 1089-7690 (Electronic)
%G eng
%R 10.1063/1.3020336
%0 Journal Article
%J Angewandte Chemie - International Edition
%D 2008
%T {Optical rotation of achiral compounds}
%A Claborn, Kacey
%A Isborn, Christine
%A Kaminsky, Werner
%A Kahr, Bart
%K Circular dichroism
%K Crystallography
%K Molecular chirality
%K Optical activity
%K Polarimetry
%X Oriented achiral molecules and crystals with D(2d) symmetry or one of its non-enantiomorphous subgroups, S(4), C(2v), or C(s), can rotate the plane of transmitted polarized light incident in a general direction. This well-established fact of crystal optics is contrary to the teaching of optical activity to students of organic chemistry. This Minireview gives an overview of the measurement and calculation of the chiroptical properties of some achiral compounds and crystals. Methane derivatives with four identical ligands related by reflection symmetry are quintessential optically inactive compounds according to the logic of van't Hoff. Analysis of the optical activity of simple achiral compounds such as H(2)O and NH(3) provides general aspects of chiroptics that are not readily broached when considering chiral compounds exclusively. We show here, through the use of group theoretical arguments, the transformation properties of tensors, and diagrams, why some achiral, acentric compounds are optically active while others are not.
%B Angewandte Chemie - International Edition
%V 47
%P 5706–5717
%@ 1521-3773 (Electronic)$\backslash$r1433-7851 (Linking)
%G eng
%R 10.1002/anie.200704559
%0 Journal Article
%D 2008
%T {Rational Enhancement of Second-Order Nonlinearity : Chromophores : Design , Synthesis , and Electrooptic Activity Rational Enhancement of Second-Order Nonlinearity : Chromophores : Design , Synthesis , and Electrooptic Activity}
%A Davies, Joshua a
%A Elangovan, Arumugasamy
%A Sullivan, Philip a
%A Olbricht, C
%A Bale, Denise H
%A Ewy, Todd R
%A Isborn, Christine M
%A E, Bruce
%A Robinson, Bruce H
%A Reid, Philip J
%A Li, Xiaosong
%A Dalton, Larry R
%A Olbricht, Benjamin C
%A Eichinger, Bruce E
%P 10565–10575
%G eng
%R 10.1021/ja8007424
%0 Journal Article
%J Journal of Physical Chemistry A
%D 2007
%T {Comparison of static first hyperpolarizabilities calculated with various quantum mechanical methods}
%A Isborn, C. M.
%A Leclercq, a.
%A Vila, F. D.
%A Dalton, L. R.
%A Brédas, J. L.
%A Eichinger, B. E.
%A Robinson, B. H.
%X The prediction of nonlinear electro-optic (EO) behavior of molecules with quantum methods is the first step in the development of organic-based electro-optic devices. Typical EO molecules may require calculations with several hundred electrons, which prevents all but the fastest methods (semiempirical and density functional theory (DFT)) from being used for EO estimation. To test the reliability of these methods, we compare dipole moments, polarizabilities, and first-order hyperpolarizabilities for a wide range of structures of experimental interest with Hartree-Fock (HF), intermediate neglect of differential overlap (INDO), and DFT methods. The relative merits of molecules are consistently predictable with every method.
%B Journal of Physical Chemistry A
%V 111
%P 1319–1327
%G eng
%R 10.1021/jp064096g
%0 Journal Article
%J Journal of Physical Chemistry C
%D 2007
%T {Dispersive kinetics from single molecules oriented in single crystals of potassium acid phthalate}
%A Wustholz, Kristin L.
%A Bott, Eric D.
%A Isborn, Christine M
%A Li, Xiaosong
%A Kahr, Bart
%A Reid, Philip J
%B Journal of Physical Chemistry C
%V 111
%P 9146–9156
%G eng
%R 10.1021/jp0713559
%0 Journal Article
%J Journal of Physical Chemistry A
%D 2007
%T {The optical rotatory power of water}
%A Isborn, Christine
%A Claborn, Kacey
%A Kahr, Bart
%X Ab initio molecular orbital calculations of the optical rotatory response of a single oriented water molecule are described. The unique tensor element g(xy) was computed to be -0.047 bohr(3) with CCSD/6-311+G(d,p). A value of -0.033 was obtained with the minimal valence basis that was better suited to parsing the rotatory response among a limited number of excited states. Transition moments were calculated ab initio and qualitatively derived from the wave functions. Rotations were reckoned from the relative dispositions of the transition moments with respect to the wavevectors. In this way, it was possible to intuitively reckon the form of the optical rotation tensor consistent with that from higher levels of theory and to establish which excitations make the most significant contributions.
%B Journal of Physical Chemistry A
%V 111
%P 7800–7804
%G eng
%0 Journal Article
%J Journal of Chemical Physics
%D 2007
%T {Time-dependent density functional theory Ehrenfest dynamics: Collisions between atomic oxygen and graphite clusters}
%A Isborn, Christine M
%A Li, Xiaosong
%A Tully, John C.
%X An ab initio direct Ehrenfest dynamics method with time-dependent density functional theory is introduced and applied to collisions of 5 eV oxygen atoms and ions with graphite clusters. Collisions at three different sites are simulated. Kinetic energy transfer from the atomic oxygen to graphite local vibrations is observed and electron-nuclear coupling resulting in electronic excitation within the graphite surface as well as alteration of the atomic charge is first reported in this paper. The three oxygen species studied, O(3P), O-(2P), and O+(4S), deposit different amounts of energy to the surface, with the highest degree of damage to the pi conjugation of the cluster produced by the atomic oxygen cation. Memory of the initial charge state is not lost as the atom approaches, in contrast to the usual assumption.
%B Journal of Chemical Physics
%V 126
%@ 0021-9606 (Print)$\backslash$r0021-9606 (Linking)
%G eng
%R 10.1063/1.2713391
%0 Journal Article
%J Journal of Physical Chemistry A
%D 2006
%T {Ab initio diradical/zwitterionic polarizabilities and hyperpolarizabilities in twisted double bonds}
%A Isborn, Christine M
%A Davidson, Ernest R.
%A Robinson, Bruce H
%X We investigated the nature of the ground state and static response properties (mu, alpha, and beta) for a promising class of twisted pi-electron system nonlinear optical chromophores at the HF, B3LYP, MP2, and CASSCF levels. We report results for a substituted twisted ethylene and a larger tictoid analogue. Previous work has reported only a zwitterionic character for such tictoid species, however, (14,13) CASSCF calculations predict a ground-state diradical. At the HF, B3LYP, MP2, and (14,13) CASSCF levels, the values of beta are orders of magnitude smaller than those predicted by semiempirical methods.
%B Journal of Physical Chemistry A
%V 110
%P 7189–7196
%G eng
%R 10.1021/jp056580+
%0 Journal Article
%J Journal of Physical Chemistry B
%D 2006
%T {Influence of isomerization on nonlinear optical properties of molecules}
%A Kinnibrugh, T.
%A Bhattacharjee, S.
%A Sullivan, P.
%A Isborn, C.
%A Robinson, B. H.
%A Eichinger, B. E.
%X The influence of rotational and geometrical isomerism on the nonlinear optical (NLO) properties, specifically the first-order hyperpolarizability beta, of chromophores of current interest has been investigated with density functional theory (DFT). In the first of this two-part study, the rotational isomerism of a linear chromophore was explored. Calculation of the torsion potentials about two of the rotatable and conformation-changing single bonds in a chromophore demonstrated the near equality of the molecular energies at 0 degrees and 180 degrees rotational angles. To explore the consequences of this near conformational energy degeneracy to NLO behavior, the eight low energy rotational isomers of FTC [Robinson, B. H.; et al. Chem. Phys. 1999, 245, 35] were investigated. This study provides the first-reported DFT-based calculation of the statistical mechanical average of beta over the conformational space of a molecule having substantial nonlinear optical behavior. The influence of the solvent reaction field on rotameric populations and on the beta tensor is reported. In the second part, two molecules having two donors and two acceptors bonded respectively in ortho and meta positions on a central benzene ring are shown to have substantially different beta tensors. These two so-called molecular Xs have different highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) distributions, and consistent with expectations, it is found that the larger beta(zzz) is associated with a large spatial asymmetry between the HOMOs and LUMOs. Large hyperpolarizability correlates with the HOMO concentrated on the donor groups and the LUMO on the acceptor groups.
%B Journal of Physical Chemistry B
%V 110
%P 13512–13522
%G eng
%0 Journal Article
%J Journal of the American Chemical Society
%D 2006
%T {Optical rotation of achiral pentaerythritol}
%A Claborn, Kacey
%A Cedres, Javier Herreros
%A Isborn, Christine
%A Zozulya, Alexey
%A Weckert, Edgar
%A Kaminsky, Werner
%A Kahr, Bart
%X The optical rotatory power of achiral crystals of achiral pentaerythritol molecules was measured. The maximum rotations were found to be +/-6 degrees /mm. The quantum mechanically computed rotation of pentaerythritol molecules using linear response theory was 6 times larger although the experimental and theoretical tensors were similarly oriented to within 5 degrees .
%B Journal of the American Chemical Society
%V 128
%P 14746–14747
%G eng
%0 Journal Article
%J Journal of the American Chemical Society
%D 2005
%T {Factors controlling the barriers to degenerate hydrogen atom transfers}
%A Isborn, Christine
%A Hrovat, David a
%A Borden, Weston Thatcher
%A Mayer, James M.
%A Carpenter, Barry K.
%X High-level electronic structure calculations have been used to study the factors contributing to the barriers to degenerate hydrogen-atom transfer (HAT) reactions. Understanding of these reactions is a prerequisite to the development of any more general theory of HAT reactions, and yet, the existing models for such reactions perform quite poorly when applied to even simple self-exchanges. The reasons behind these failures are elucidated in the present work. They include a near cancellation of bond-strength effects between reactant and transition state, as well as a strong dependence of the geometry of the transition state on the nature of the heavy atoms.
%B Journal of the American Chemical Society
%V 127
%P 5794–5795
%G eng
%0 Journal Article
%J Journal of Physical Chemistry A
%D 2004
%T {Does Formation of Singlet Propane-1,3-diyl from Propane Deviate from Bond Enthalpy Additivity? Results of Ab Initio Calculations That Bear on the Existence of the Benson Barrier to Diradical Ring Closure}
%A Isborn, Christine
%A Hrovat, David a.
%A Borden, Weston Thatcher
%B Journal of Physical Chemistry A
%V 108
%P 3024–3029
%G eng
%R 10.1021/jp036867b
%0 Journal Article
%J Organic Letters
%D 2002
%T {Aromaticity with a twist: Möbius [4n]annulenes}
%A Castro, Claire
%A Isborn, Christine M
%A Karney, William L.
%A Mauksch, Michael
%A {Von Ragué Schleyer}, Paul
%X Aromatic Möbius [4n]annulenes with 4n pi electrons, originally conceived by Heilbronner, are characterized computationally. These (CH)(12), (CH)(16), and (CH)(20) minima have nearly equal C-C bond lengths, small twist angles around the rings, and magnetic properties (NICS, nucleus-independent chemical shifts–see above at various positions in [16]annulene–and magnetic susceptibility exaltations) indicating significantly diatropic ring currents. The Möbius forms are not the most stable isomers but may contribute significantly to the chemistry of these annulenes. [structure: see text]
%B Organic Letters
%V 4
%P 3431–3434
%@ 1523-7060
%G eng
%R 10.1021/ol026610g