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Sahoo J, Mahapatra S. Electronic nonadiabatic effects in the state-to-state dynamics of the H + H 2 → H 2 + H exchange reaction with a vibrationally excited reagent. Phys Chem Chem Phys 2023; 25:28309-28325. [PMID: 37840347 DOI: 10.1039/d3cp02409a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.
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Affiliation(s)
- Jayakrushna Sahoo
- School of Chemistry, University of Hyderabad, Hyderabad, 500 046, India.
| | - S Mahapatra
- School of Chemistry, University of Hyderabad, Hyderabad, 500 046, India.
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2
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Larrégaray P, Bonnet L. Including tunneling into the classical cross sections and rate constants for the N(2D) + H2 (v = 0, j = 0) reaction. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02749-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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3
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Goswami S, Sahoo J, Paul SK, Rao TR, Mahapatra S. Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H 2 → H 2 + H. J Phys Chem A 2020; 124:9343-9359. [PMID: 33124827 DOI: 10.1021/acs.jpca.0c06707] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
State-to-state dynamics of the benchmark hydrogen exchange reaction H + H2 (v = 0-4, j = 0-3) → H2 (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.
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Affiliation(s)
- Sugata Goswami
- School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Jayakrushna Sahoo
- School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Suranjan K Paul
- School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - T Rajagopala Rao
- School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - S Mahapatra
- School of Chemistry, University of Hyderabad, Hyderabad 500046, India
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4
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Bonnet L. Semiclassical initial value representation: From Møller to Miller. J Chem Phys 2020; 153:174102. [PMID: 33167624 DOI: 10.1063/5.0023137] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The initial value representation (IVR) was proposed five decades ago by Miller [J. Chem. Phys. 53, 3578 (1970)] in order to improve the feasibility and accuracy of semiclassical (SC) scattering calculations. Møller operators, which play a fundamental role in quantum scattering theory, do not appear in his formulation based on action-angle coordinates. These operators were introduced much later by Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)] in SC-IVR calculations performed in Cartesian coordinates within the Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] formulation of quantum scattering theory. Remarkably, Møller operators were found to boost the numerical efficiency of SC-IVR calculations. The purpose of this work is to show within a simple model of light-induced rotational transitions that, in fact, Møller operators were already underlying Miller's pioneering formulation. In line with the results of Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)], removing the action of these operators in Miller's theory strongly decreases its numerical efficiency.
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Rodríguez-Fernández A, Bonnet L, Crespos C, Larrégaray P, Díez Muiño R. When classical trajectories get to quantum accuracy: II. The scattering of rotationally excited H2 on Pd(111). Phys Chem Chem Phys 2020; 22:22805-22814. [DOI: 10.1039/d0cp02655g] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The classical trajectory method in a quantum spirit assigns statistical weights to classical paths on the basis of two semiclassical corrections: Gaussian binning and the adiabaticity correction.
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Affiliation(s)
| | | | | | | | - Ricardo Díez Muiño
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU)
- 20018 Donostia-SanSebastián
- Spain
- Donostia International Physics Center (DIPC)
- 20018 Donostia-SanSebastián
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6
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Kendrick BK. Nonadiabatic Ultracold Quantum Reactive Scattering of Hydrogen with Vibrationally Excited HD( v = 5-9). J Phys Chem A 2019; 123:9919-9933. [PMID: 31647679 DOI: 10.1021/acs.jpca.9b07318] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The results from electronically non-adiabatic and adiabatic quantum reactive scattering calculations are presented for the H + HD(v = 5-9) → H + HD(v', j') reaction at ultracold collision energies from 10 nK to 60 K. Several experimentally verifiable signatures of the geometric phase are reported in the total and vibrationally and rotationally resolved rate coefficients. Most notable is the predicted 2 orders of magnitude enhancement of the rotationally resolved ultracold rates of odd symmetry relative to those of even symmetry. Prominent shape resonances appear at higher collision energies (100 mK to 20 K), which could be measured experimentally. Significant geometric phase effects are also reported on the resonance energies and lifetimes. In particular, an enhancement (suppression) of the l = 1 (l = 2) shape resonances for HD(v = 5, 6) is predicted for even symmetry relative to those of odd symmetry.
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Affiliation(s)
- Brian K Kendrick
- Theoretical Division , Los Alamos National Laboratory , Group T-1, Mail Stop B221, Los Alamos , New Mexico 87544 , United States
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Shi HM, Guo GH, Sun ZG. Numerical convergence of the Sinc discrete variable representation for solving molecular vibrational states with a conical intersection in adiabatic representation. CHINESE J CHEM PHYS 2019. [DOI: 10.1063/1674-0068/cjcp1812275] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Hai-mei Shi
- School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Guang-hai Guo
- School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
| | - Zhi-gang Sun
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
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Sun Z, Wang C, Zhao W, Yang C. Geometric phase effects on photodissociation dynamics of diatomics. J Chem Phys 2018; 149:224307. [PMID: 30553243 DOI: 10.1063/1.5052514] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigated the effect of the geometric phase (GP) on photodissociation dynamics at a light-induced conical intersection (LICI) through exact quantum dynamical calculations. By taking the one-photon photodissociation of H 2 + ionic molecules as an example, we explored the conditions wherein the LICI associated GP affects dissociation dynamics. We found that GP leads to a phase shift between the angular distributions of GP included and GP excluded photofragments. This effect is more pronounced when the energy of the initial vibrational level is above the energy of the LICI point.
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Affiliation(s)
- Zhaopeng Sun
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Chunyang Wang
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Wenkai Zhao
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Chuanlu Yang
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
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Yuan D, Guan Y, Chen W, Zhao H, Yu S, Luo C, Tan Y, Xie T, Wang X, Sun Z, Zhang DH, Yang X. Observation of the geometric phase effect in the H + HD → H2+ D reaction. Science 2018; 362:1289-1293. [DOI: 10.1126/science.aav1356] [Citation(s) in RCA: 73] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2018] [Accepted: 11/02/2018] [Indexed: 11/02/2022]
Abstract
Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD → H2+ D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state–resolved differential cross sections in the forward scattering direction for H2products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.
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Bouakline F. Unambiguous Signature of the Berry Phase in Intense Laser Dissociation of Diatomic Molecules. J Phys Chem Lett 2018; 9:2271-2277. [PMID: 29649364 DOI: 10.1021/acs.jpclett.8b00607] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We report strong evidence of Berry phase effects in intense laser dissociation of D2+ molecules, manifested as Aharonov-Bohm-like oscillations in the photofragment angular distribution (PAD). Our calculations show that this interference pattern strongly depends on the parity of the diatom initial rotational state, (-1) j. Indeed, the PAD local maxima (minima) observed in one case ( j odd) correspond to local minima (maxima) in the other case ( j even). Using simple topological arguments, we clearly show that such interference conversion is a direct signature of the Berry phase. The sole effect of the latter on the rovibrational wave function is a sign change of the relative phase between two interfering components, which wind in opposite senses around a light-induced conical intersection (LICI). Therefore, encirclement of the LICI leads to constructive ( j odd) or destructive ( j even) self-interference of the initial nuclear wavepacket in the dissociative limit. To corroborate our theoretical findings, we suggest an experiment of strong-field indirect dissociation of D2+ molecules, comparing the PAD of the ortho and para molecular species in directions nearly perpendicular to the laser polarization axis.
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Affiliation(s)
- Foudhil Bouakline
- Institut für Chemie , Universität Potsdam , Karl-Liebknecht-Str. 24-25 , D-14476 Potsdam-Golm , Germany
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Kendrick BK, Hazra J, Balakrishnan N. Geometric Phase Appears in the Ultracold Hydrogen Exchange Reaction. PHYSICAL REVIEW LETTERS 2015; 115:153201. [PMID: 26550721 DOI: 10.1103/physrevlett.115.153201] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2015] [Indexed: 06/05/2023]
Abstract
Quantum reactive scattering calculations for the hydrogen exchange reaction H+H_{2}(v=4,j=0)→H+H_{2}(v^{'}, j^{'}) and its isotopic analogues are reported for ultracold collision energies. Because of the unique properties associated with ultracold collisions, it is shown that the geometric phase effectively controls the reactivity. The rotationally resolved rate coefficients computed with and without the geometric phase are shown to differ by up to 4 orders of magnitude. The effect is also significant in the vibrationally resolved and total rate coefficients. The dynamical origin of the effect is discussed and the large geometric phase effect reported here might be exploited to control the reactivity through the application of external fields or by the selection of a particular nuclear spin state.
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Affiliation(s)
- B K Kendrick
- Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Jisha Hazra
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154, USA
| | - N Balakrishnan
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154, USA
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Kendrick BK, Hazra J, Balakrishnan N. The geometric phase controls ultracold chemistry. Nat Commun 2015; 6:7918. [PMID: 26224326 PMCID: PMC4532881 DOI: 10.1038/ncomms8918] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2015] [Accepted: 06/22/2015] [Indexed: 11/16/2022] Open
Abstract
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
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Affiliation(s)
- B. K. Kendrick
- Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Jisha Hazra
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154, USA
| | - N. Balakrishnan
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154, USA
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Gao H, Sneha M, Bouakline F, Althorpe SC, Zare RN. Differential Cross Sections for the H + D2 → HD(v′ = 3, j′ = 4–10) + D Reaction above the Conical Intersection. J Phys Chem A 2015; 119:12036-42. [DOI: 10.1021/acs.jpca.5b04573] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hong Gao
- Department
of Chemistry, Stanford University, Stanford, California 94305-5080, United States
| | - Mahima Sneha
- Department
of Chemistry, Stanford University, Stanford, California 94305-5080, United States
| | | | - Stuart C. Althorpe
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Richard N. Zare
- Department
of Chemistry, Stanford University, Stanford, California 94305-5080, United States
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14
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Bouakline F. Investigation of geometric phase effects in photodissociation dynamics at a conical intersection. Chem Phys 2014. [DOI: 10.1016/j.chemphys.2014.02.010] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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15
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Joubert-Doriol L, Ryabinkin IG, Izmaylov AF. Geometric phase effects in low-energy dynamics near conical intersections: A study of the multidimensional linear vibronic coupling model. J Chem Phys 2013; 139:234103. [DOI: 10.1063/1.4844095] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Jankunas J, Sneha M, Zare RN, Bouakline F, Althorpe SC. Hunt for geometric phase effects in H + HD → HD(v′, j′) + H. J Chem Phys 2013; 139:144316. [DOI: 10.1063/1.4821601] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abedi A, Maitra NT, Gross EKU. Correlated electron-nuclear dynamics: exact factorization of the molecular wavefunction. J Chem Phys 2013; 137:22A530. [PMID: 23249067 DOI: 10.1063/1.4745836] [Citation(s) in RCA: 132] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It was recently shown [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] that the complete wavefunction for a system of electrons and nuclei evolving in a time-dependent external potential can be exactly factorized into an electronic wavefunction and a nuclear wavefunction. The concepts of an exact time-dependent potential energy surface (TDPES) and exact time-dependent vector potential emerge naturally from the formalism. Here, we present a detailed description of the formalism, including a full derivation of the equations that the electronic and nuclear wavefunctions satisfy. We demonstrate the relationship of this exact factorization to the traditional Born-Oppenheimer expansion. A one-dimensional model of the H(2)(+) molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: we show how features of its structure indicate the mechanism of dissociation. We compare the exact TDPES with potential energy surfaces from the time-dependent Hartree-approach, and also compare traditional Ehrenfest dynamics with Ehrenfest dynamics on the exact TDPES.
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Affiliation(s)
- Ali Abedi
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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SARKAR BIPLAB, VARANDAS AJC. Dynamics study of a three-fold pseudo-Jahn–Teller system using the extended Longuet–Higgins formalism. J CHEM SCI 2012. [DOI: 10.1007/s12039-011-0192-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Sarkar B, Varandas A. A study of the geometrical phase effect on scattering processes: Validity of the extended-Longuet–Higgins formalism for a four-fold Jahn–Teller type model system. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.08.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Shan X, Connor JNL. Angular scattering using parameterized Smatrix elements for the H + D2(vi= 0, ji= 0) → HD(vf= 3, jf= 0) + D reaction: an example of Heisenberg's Smatrix programme. Phys Chem Chem Phys 2011; 13:8392-406. [DOI: 10.1039/c0cp01354d] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Xiahou C, Connor JNL, Zhang DH. Rainbows and glories in the angular scattering of the state-to-state F + H2 reaction at Etrans = 0.04088 eV. Phys Chem Chem Phys 2011; 13:12981-97. [DOI: 10.1039/c1cp21044k] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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