# Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics.

19 Jul 2011-Journal of Chemical Physics (American Institute of Physics)-Vol. 135, Iss: 3, pp 034107-034107

TL;DR: The ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na(3) cluster and the adiabatic PESs for the electronic states 2( 2)E' and 1(2)A(1)', and the non-adiabatic coupling (NAC) terms among those states are presented.

Abstract: We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na3 cluster and present the adiabatic PESs for the electronic states 22E′ and 12A1′, and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 22E′ and 12A1′ demonstrate the numerical validity of so called “Curl Condition,” such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the “adiabatic-diabatic transformation (ADT)” equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development o...

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TL;DR: The molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states of Na3 cluster is presented, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO).

Abstract: We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (22E′ and 12A1′) of Na3 cluster, where the adiabatic potential ener...

52 citations

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TL;DR: The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities.

Abstract: The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H3+ system (11A', 21A', and 31A') using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D+ + H2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H3+. We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results.

47 citations

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TL;DR: The beyond Born-Oppenheimer approach could incorporate the effect of NACTs accurately and construct single-valued, continuous, smooth, and symmetric diabatic PESs.

Abstract: We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non-Adiabatic Coupling Terms (NACTs) for the three lowest singlet states of H3 (+) in hyperspherical coordinates as functions of hyperangles (θ and ϕ) for a grid of fixed values of hyperradius (1.5 ⩽ ρ ⩽ 20 bohrs) using the MRCI level of methodology employing ab initio quantum chemistry package (MOLPRO). The NACT between the ground and the first excited state translates along the seams on the θ - ϕ space, i.e., there are six Conical Intersections (CIs) at each θ (60° ⩽ θ ⩽ 90°) within the domain, 0 ⩽ ϕ ⩽ 2π. While transforming the adiabatic PESs to the diabatic ones, such surfaces show up six crossings along those seams. Our beyond Born-Oppenheimer approach could incorporate the effect of NACTs accurately and construct single-valued, continuous, smooth, and symmetric diabatic PESs. Since the location of CIs and the spatial amplitudes of NACTs are most prominent around ρ = 10 bohrs, generally only those results are depicted.

44 citations

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TL;DR: In this article, the development on beyond Born-Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years are reviewed.

Abstract: We review our development on beyond Born–Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years. The theoretical f...

33 citations

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TL;DR: The analytic expressions for the adiabatic PESs and ADT angles are provided to represent a two-state three-mode diabatic Hamiltonian of NO2 for performing nuclear dynamics to calculate the photo-electron spectra of its anion.

Abstract: A thorough investigation has been performed for electronic structure, topological effect, and nuclear dynamics of NO2 molecule, where the adiabatic potential energy surfaces (PESs), conical intersections between the ground (X2A1) and the first excited state (A2B2), and the corresponding non-adiabatic coupling terms between those states are recalculated [Chem. Phys. 416, 11 (2013)] to achieve enough accuracy in dynamics. We employ beyond Born-Oppenheimer theory for these two state sub-Hilbert space to carry out adiabatic to diabatic transformation (ADT) to obtain the ADT angles and thereby, to construct single-valued, smooth, and continuous diabatic PESs. The analytic expressions for the adiabatic PESs and ADT angles are provided to represent a two-state three-mode diabatic Hamiltonian of NO2 for performing nuclear dynamics to calculate the photo-electron spectra of its anion. It appears that not only Jahn-Teller type coupling but also Renner-Teller interaction contributes significantly on the overall spectrum. The coupling between the electronic states (X2A1 and A2B2) of NO2 is essentially through the asymmetric stretching mode, where the functional form of such interaction is distinctly symmetric and non-linear.

23 citations

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01 Jan 1954

TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.

Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.

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TL;DR: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird as discussed by the authors.

Abstract: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird. Mehratomige Molekeln werden in entsprechender Weise als starre „Kreisel“ angesehen.2) Dieser Standpunkt erlaubt es, die einfachsten Gesetze der Bandenspektren und der spezifischen Warme mehratomiger Gase zu erklaren. Das nachste Stadium1) last die Annahme starrer Verbindungen zwischen den Atomen fallen und berucksichtigt die Kernschwingungen, zunachst als harmonische Schwingungen; dabie ergenben sich nach Sponer3) und Kratzer4) Zusammenhange zwischen den einzelnen Banden eines Bandensystems.

4,131 citations

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[...]

TL;DR: In this article, it was shown that the force on a nucleus in an atomic system is just the classical electrostatic force that would be exerted on this nucleus by other nuclei and by the electrons' charge distribution.

Abstract: Formulas have been developed to calculate the forces in a molecular system directly, rather than indirectly through the agency of energy. This permits an independent calculation of the slope of the curves of energy vs. position of the nuclei, and may thus increase the accuracy, or decrease the labor involved in the calculation of these curves. The force on a nucleus in an atomic system is shown to be just the classical electrostatic force that would be exerted on this nucleus by other nuclei and by the electrons' charge distribution. Qualitative implications of this are discussed.

2,832 citations

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856 citations

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TL;DR: In this paper, the Born-Oppenheimer separation into electronic and heavy-particle coordinates is re-examined, and the coupled equations that result for the heavyparticle motion are expressed in a particularly simple form.

Abstract: The equations of the general Born-Oppenheimer separation into electronic and heavy-particle coordinates are re-examined, and the coupled equations that result for the heavy-particle motion are expressed in a particularly simple form. This is accomplished by introducing a generalized matrix operator for the effective momentum associated with the heavy particles; the matrix portion of this operator represents a coupling of the nuclear momentum with the electronic motion. The commutator between the momentum and potential matrices is a force matrix, which provides an alternative means of evaluating the momentum matrix. The momentum coupling has both radial and angular parts; the angular momentum coupling agrees with Thorson's expression. In the usual adiabatic molecular representation, the potential energy matrix is diagonalized, and all the coupling is thrown into the radial and angular momentum matrices. For collision problems it is often more important to diagonalize the radial momentum matrix, putting the radial off-diagonal coupling into the potential matrix; this generates a family of diabatic representations, the most important of which dissociates to unique separated atom states. This standard diabatic representations has the properties called for by Lichten, is uniquely defined even with the inclusion of configuration interaction, and leads immediately to the Landau-Zener-Stueckelberg limiting case under appropriate conditions.

711 citations