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Ben-Nun M, Mills JD, Hinde RJ, Winstead CL, Boatz JA, Gallup GA, Langhoff PW. Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions. J Phys Chem A 2009; 113:7687-97. [PMID: 19552480 DOI: 10.1021/jp901427x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H(2), CH) and triatomic (H(3), CH(2)) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently.
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Affiliation(s)
- M Ben-Nun
- San Diego Supercomputer Center and Department of Chemistry & Biochemistry, University of California, 9500 Gilman Drive, La Jolla, California 92093-0505, USA
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Hemmers O, Guillemin R, Rolles D, Wolska A, Lindle DW, Kanter EP, Krässig B, Southworth SH, Wehlitz R, Zimmermann B, McKoy V, Langhoff PW. Low-energy nondipole effects in molecular nitrogen valence-shell photoionization. Phys Rev Lett 2006; 97:103006. [PMID: 17025814 DOI: 10.1103/physrevlett.97.103006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2006] [Indexed: 05/12/2023]
Abstract
Observations are reported for the first time of significant nondipole effects in the photoionization of the outer-valence orbitals of diatomic molecules. Measured nondipole angular-distribution parameters for the 3sigma(g), 1pi(u), and 2sigma(u) shells of N2 exhibit spectral variations with incident photon energies from thresholds to approximately 200 eV which are attributed via concomitant calculations to particular final-state symmetry waves arising from (E1)multiply sign in circle(M1,E2) radiation-matter interactions first-order in photon momentum. Comparisons with previously reported K-edge studies in N2 verify linear scaling with photon momentum, accounting in part for the significantly enhanced nondipole behavior observed in inner-shell ionization at correspondingly higher momentum values in this molecule.
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Affiliation(s)
- O Hemmers
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154-4003, USA
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Abstract
Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive methods which avoid explicit construction the metric matrix and do not require storage of the full Hamiltonian matrix to isolate the antisymmetric subspace of the spectral-product representation. Calculations of the lowest-lying singlet and triplet electronic states of the covalent electron pair bond (H(2)) illustrate the various theorems devised and demonstrate the degree of convergence achieved to values obtained employing conventional prior antisymmetrization. Concluding remarks place the atomic spectral-product development in the context of currently employed approaches for ab initio construction of adiabatic electronic eigenfunctions and potential energy surfaces, provide comparisons with earlier related approaches, and indicate prospects for more general applications of the method.
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Affiliation(s)
- P W Langhoff
- San Diego Supercomputer Center, University of California, La Jolla, California 92093-0505, USA.
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Spotts JM, Wong CK, Johnson MS, Okumura M, Boatz JA, Hinde RJ, Sheehy JA, Langhoff PW. Multiphoton Ionization Spectroscopy of AlArN Clusters. J Phys Chem A 2003. [DOI: 10.1021/jp030399o] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Guillemin R, Hemmers O, Lindle DW, Shigemasa E, Le Guen K, Ceolin D, Miron C, Leclercq N, Morin P, Simon M, Langhoff PW. Nondipolar electron angular distributions from fixed-in-space molecules. Phys Rev Lett 2002; 89:033002. [PMID: 12144388 DOI: 10.1103/physrevlett.89.033002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2002] [Indexed: 05/23/2023]
Abstract
The first indication of nondipole effects in the azimuthal dependence of photoelectron angular distributions emitted from fixed-in-space molecules is demonstrated in N (2). Comparison of the results with angular distributions observed for randomly oriented molecules and theoretical derivations for the nondipole correction first order in photon momentum suggests that higher orders will be needed to describe distributions measured in the molecular frame.
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Affiliation(s)
- R Guillemin
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154-4003, USA
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Hemmers O, Wang H, Focke P, Sellin IA, Lindle DW, Arce JC, Sheehy JA, Langhoff PW. Large nondipole effects in the angular distributions of K-shell photoelectrons from molecular nitrogen. Phys Rev Lett 2001; 87:273003. [PMID: 11800877 DOI: 10.1103/physrevlett.87.273003] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2001] [Revised: 10/25/2001] [Indexed: 05/23/2023]
Abstract
Measurements of angular distributions of K-shell electrons photoejected from molecular nitrogen are reported which reveal large deviations at relatively low photon energies (Planck's omega < or = 500 eV) from emission patterns anticipated from the dipole approximation to interactions between radiation and matter. A concomitant theoretical analysis incorporating the effects of electromagnetic retardation attributes the observed large nondipole behaviors in N2 to bond-length-dependent terms in the E1 [multiply sign in circle] (E2,M1) photoelectron emission amplitudes which are indicative of a potentially universal nondipole behavior in molecular photoionization.
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Affiliation(s)
- O Hemmers
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154-4003, USA
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Weber W, Helms V, McCammon JA, Langhoff PW. Shedding light on the dark and weakly fluorescent states of green fluorescent proteins. Proc Natl Acad Sci U S A 1999; 96:6177-82. [PMID: 10339561 PMCID: PMC26855 DOI: 10.1073/pnas.96.11.6177] [Citation(s) in RCA: 273] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Recent experiments on various similar green fluorescent protein (GFP) mutants at the single-molecule level and in solution provide evidence of previously unknown short- and long-lived "dark" states and of related excited-state decay channels. Here, we present quantum chemical calculations on cis-trans photoisomerization paths of neutral, anionic, and zwitterionic GFP chromophores in their ground and first singlet excited states that explain the observed behaviors from a common perspective. The results suggest that favorable radiationless decay channels can exist for the different protonation states along these isomerizations, which apparently proceed via conical intersections. These channels are suggested to rationalize the observed dramatic reduction of fluorescence in solution. The observed single-molecule fast blinking is attributed to conversions between the fluorescent anionic and the dark zwitterionic forms whereas slow switching is attributed to conversions between the anionic and the neutral forms. The predicted nonadiabatic crossings are seen to rationalize the origins of a variety of experimental observations on a common basis and may have broad implications for photobiophysical mechanisms in GFP.
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Affiliation(s)
- W Weber
- Departments of Chemistry and Biochemistry, and Pharmacology, University of California, San Diego, La Jolla, CA 92093-0365, USA
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Affiliation(s)
- P. W. Langhoff
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-4001
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Winstead C, Langhoff PW. Feshbach–Fano formalism in Hilbert space: Application to shape resonances in molecular photoionization. J Chem Phys 1991. [DOI: 10.1063/1.460868] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sheehy JA, Gil TJ, Winstead CL, Farren RE, Langhoff PW. Correlation of molecular valence‐ andK‐shell photoionization resonances with bond lengths. J Chem Phys 1989. [DOI: 10.1063/1.457085] [Citation(s) in RCA: 111] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Saha HP, Froese-Fischer C, Langhoff PW. Numerical multiconfiguration Hartree-Fock studies of atomic photoionization cross sections: Dynamical core-polarization effects in atomic sodium. Phys Rev A Gen Phys 1988; 38:1279-1285. [PMID: 9900502 DOI: 10.1103/physreva.38.1279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lindle DW, Cowan PL, LaVilla RE, Jach T, Deslattes RD, Karlin B, Sheehy JA, Gil TJ, Langhoff PW. Polarization of molecular x-ray fluorescence. Phys Rev Lett 1988; 60:1010-1013. [PMID: 10037918 DOI: 10.1103/physrevlett.60.1010] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Diercksen GHF, Kraemer WP, Rescigno TN, Bender CF, McKoy BV, Langhoff SR, Langhoff PW. Theoretical studies of photoexcitation and ionization in H2O. J Chem Phys 1982. [DOI: 10.1063/1.443072] [Citation(s) in RCA: 112] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Padial N, Csanak G, McKoy BV, Langhoff PW. Photoexcitation and ionization in ozone: Stieltjes–Tchebycheff studies in the separated‐channel static‐exchange approximation. J Chem Phys 1981. [DOI: 10.1063/1.441647] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Orel AE, Rescigno TN, McKoy BV, Langhoff PW. Photoexcitation and ionization in molecular fluorine: Stieltjes–Tchebycheff calculations in the static‐exchange approximation. J Chem Phys 1980. [DOI: 10.1063/1.439187] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gerwer A, Asaro C, McKoy BV, Langhoff PW. Photoexcitation and ionization in molecular oxygen: Theoretical studies of electronic transitions in the discrete and continuous spectral intervals. J Chem Phys 1980. [DOI: 10.1063/1.438908] [Citation(s) in RCA: 89] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Langhoff PW, Orel AE, Rescigno TN, McKoy BV. Photoabsorption in formaldehyde: Intensities and assignments in the discrete and continuous spectral intervals. J Chem Phys 1978. [DOI: 10.1063/1.436422] [Citation(s) in RCA: 34] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Padial N, Csanak G, McKoy BV, Langhoff PW. Photoabsorption in carbon monoxide: Stieltjes–Tchebycheff calculations in the separated‐channel static‐exchange approximation. J Chem Phys 1978. [DOI: 10.1063/1.437017] [Citation(s) in RCA: 138] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rescigno TN, Bender CF, McKoy BV, Langhoff PW. Photoabsorption in molecular nitrogen: A moment analysis of discrete‐basis‐set calculations in the static‐exchange approximation. J Chem Phys 1978. [DOI: 10.1063/1.435836] [Citation(s) in RCA: 123] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Langhoff PW, Gordon RG, Karplus M. Comparisons of Dispersion Force Bounding Methods with Applications to Anisotropic Interactions. J Chem Phys 1971. [DOI: 10.1063/1.1676384] [Citation(s) in RCA: 168] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lyons JD, Langhoff PW, Hurst RP. Uniform-Electric-Field Quadrupole Polarizabilities and Shielding Factors forS-State Atoms and Ions. ACTA ACUST UNITED AC 1966. [DOI: 10.1103/physrev.151.60] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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