The Experts below are selected from a list of 183 Experts worldwide ranked by ideXlab platform
Katharine L C Hunt - One of the best experts on this subject based on the ideXlab platform.
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the interaction induced dipole of h2 h new ab initio results and spherical tensor analysis
Journal of Chemical Physics, 2019Co-Authors: Xiaoping Li, Evangelos Miliordos, Katharine L C HuntAbstract:We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree–Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree–Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r,...
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the interaction induced dipole of h2 h new ab initio results and spherical tensor analysis
Journal of Chemical Physics, 2019Co-Authors: Huakuang Lee, Evangelos Miliordos, Katharine L C HuntAbstract:We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree-Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.
Evangelos Miliordos - One of the best experts on this subject based on the ideXlab platform.
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the interaction induced dipole of h2 h new ab initio results and spherical tensor analysis
Journal of Chemical Physics, 2019Co-Authors: Xiaoping Li, Evangelos Miliordos, Katharine L C HuntAbstract:We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree–Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree–Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r,...
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the interaction induced dipole of h2 h new ab initio results and spherical tensor analysis
Journal of Chemical Physics, 2019Co-Authors: Huakuang Lee, Evangelos Miliordos, Katharine L C HuntAbstract:We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree-Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.
Chung-kuan Cheng - One of the best experts on this subject based on the ideXlab platform.
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circuit simulation using matrix Exponential method
International Conference on ASIC, 2011Co-Authors: Shih-hung Weng, Quan Chen, Chung-kuan ChengAbstract:We propose a stable explicit numerical integration method based on matrix Exponential Operator that enables accurate large time stepping for transient analysis. We utilize Krylov subspace projection to reduce the computational complexity of matrix Exponential. Numerical experiments show the advantages of the proposed method over backward Euler in terms of accuracy and performance.
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A fast and stable explicit integration method by matrix Exponential Operator for large scale circuit simulation
2011 IEEE International Symposium of Circuits and Systems (ISCAS), 2011Co-Authors: Shih-hung Weng, Peng Du, Chung-kuan ChengAbstract:In this paper, we present a fast and stable explicit numerical integration method. Our method utilizes matrix Exponential Operator to compute numerical solution of the ordinary differential equations of circuits to avoid the stability issue. A matrix partition algorithm and a numerical approximation are proposed to reduce the complexity of matrix Exponential and matrix inverse operation. Experimental results show that our method is stable and efficient. Our method is over two times faster than backward Euler on average.
Mechthild Thalhammer - One of the best experts on this subject based on the ideXlab platform.
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efficient time integration methods based on Operator splitting and application to the westervelt equation
Ima Journal of Numerical Analysis, 2015Co-Authors: Barbara Kaltenbacher, Vanja Nikolic, Mechthild ThalhammerAbstract:formulation. Employ compact formulation of Westervelt equation as nonlinear evolution equation and define nonlinear Operators A,B d dt u(t ) = F ( u(t ) )= A(u(t ))+B(u(t )) , t ∈ (0,T ) , A(v) = ( v2 α ( 1−δv2 )−1 ∆v2 ) , B(v) = ( 0 β ( 1−δv2 )−1 ∆v1 ) . Subproblem (Nonlinear diffusion equation). Resolution of subproblem associated with A { ∂tΨ1(x, t ) =Ψ2(x, t ) , ∂tΨ2(x, t ) =α ( 1−δΨ2(x, t ) )−1 ∆Ψ2(x, t ) , amounts to solution of nonlinear diffusion equation for second componentΨ2 = ∂tψ ∂tΨ2(x, t ) =α ( 1−δΨ2(x, t ) )−1 ∆Ψ2(x, t ) . First componentΨ1 =ψ then retained by (pointwise) integration Ψ1(x, t ) =Ψ1(x,0)+ ∫ t 0 Ψ2(x,τ) dτ . Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Associated subproblems (Decomposition I) Abstract formulation. Employ compact formulation of Westervelt equation as nonlinear evolution equation and define nonlinear Operators A,B d dt u(t ) = F ( u(t ) )= A(u(t ))+B(u(t )) , t ∈ (0,T ) , A(v) = ( v2 α ( 1−δv2 )−1 ∆v2 ) , B(v) = ( 0 β ( 1−δv2 )−1 ∆v1 ) .formulation. Employ compact formulation of Westervelt equation as nonlinear evolution equation and define nonlinear Operators A,B d dt u(t ) = F ( u(t ) )= A(u(t ))+B(u(t )) , t ∈ (0,T ) , A(v) = ( v2 α ( 1−δv2 )−1 ∆v2 ) , B(v) = ( 0 β ( 1−δv2 )−1 ∆v1 ) . Subproblem (Explicit representation). For subproblem associated with B { ∂tΨ1(x, t ) = 0, ∂tΨ2(x, t ) =β ( 1−δΨ2(x, t ) )−1 ∆Ψ1(x, t ) , first component remains constant on considered time interval Ψ1(x, t ) =Ψ1(x,0) . Consequently, second component is (pointwise) solution to ODE with explicit representation ∂tΨ2(x, t ) =β ( 1−δΨ2(x, t ) )−1 ∆Ψ1(x,0) , Ψ2(x, t ) = 1 δ ( 1− √( 1−δΨ2(x,0) )2 −2βδ t∆Ψ1(x,0) ) . Suitable choice of time increment t > 0 ensures (1−δΨ2(x,0)) −2βδ t∆Ψ1(x,0) > 0 and henceΨ2(x, t ) ∈R. Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour) Operator splitting methods for Westervelt equation Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour) Calculus of Lie-derivatives Formal calculus. Calculus of Lie-derivatives suggestive of less involved linear case, see for instance HAIRER, LUBICH, WANNER (2002), SANZ-SERNA, CALVO (1994). Problem. Consider nonlinear evolution equation on Banach space involving unbounded nonlinear Operator F : D(F ) ⊂ X → X d dt u(t ) = F ( u(t ) ) , t ∈ (0,T ) . Employ formal notation for exact solution u(t ) = EF ( t ,u(0) )= e tDF u(0) , t ∈ [0,T ] . Evolution Operator, Lie-derivative. For (unbounded) nonlinear Operator G : D(G) ⊆ X → X define evolution Operator and Lie-derivative by e tDF G v =G(EF (t , v)) , t ∈ (0,T ) , DF G v =G ′(v)F (v) . Remark. Definition of Lie-derivative naturally extends identity L = d dt ∣∣∣ t=0 e tL d dt ∣∣∣ t=0 e tDF G v = d dt ∣∣∣ t=0 G ( EF (t , v) )=G ′(EF (t , v)) F (EF (t , v))∣∣∣t=0 =G ′(v)F (v) = DF G v . Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour) Exponential Operator splitting methods Time-stepping approach. Time integration of nonlinear evolution equation on Banach space (X ,‖ ·‖X ) d dt u(t ) = F ( u(t ) )= A(u(t ))+B(u(t )) , t ∈ (0,T ) , u(0) given. Approximations at time grid points 0 = t0 < ·· · < tN ≤ T with increments τn−1 = tn − tn−1 given by recurrence un =SF (τn−1,un−1) ≈ u(tn ) = EF ( τn−1,u(tn−1) )= eτn−1DF u(tn−1) , n ∈ {1, . . . , N } . Splitting methods. Operator splitting methods rely on suitable decomposition of right-hand side and presumption that associated subproblems solvable in accurate and efficient manner d dt v(t ) = A ( v(t ) ) , v(t ) = etDA v(0) , t ∈ (0,T ) , d dt w(t ) = B ( w(t ) ) , w(t ) = etDB w(0) , t ∈ (0,T ) . General form. High-order splitting methods cast into form SF (t , ·) = s ∏ j=1 es+1− j tDA es+1− j tDB ≈ EF (t , ·) = eF = e (DA+DB ) with real (or complex) coefficients (a j ,b j )j=1 . Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour) Splitting methods for Westervelt equation Splitting methods for Westervelt equation. Recall abstract formulation for Westervelt equation (Decomposition I) d dt u(t ) = F ( u(t ) )= A(u(t ))+B(u(t )) , t ∈ (0,T ) , A(v) = ( v2 α ( 1−δv2 )−1 ∆v2 ) , B(v) = ( 0 β ( 1−δv2 )−1 ∆v1 ) . Solution of subproblem associated with A requires resolution of nonlinear diffusion equation and (pointwise) integration. Explicit (pointwise) representation available for solution to subproblem associated with B . Lower-order splitting methods. First-order Lie–Trotter splitting method s = 1, a1 = 1 = b1 , SF (t , ·) = eA eB , or s = 2, a1 = 0 = b2 , a2 = 1 = b1 , SF (t , ·) = eB eA . Second-order Strang splitting method s = 2, a1 = 1 2 = a2 , b1 = 1, b2 = 0, SF (t , ·) = e 1 2 tDA eB e 1 2 tDA , or s = 2, a1 = 0, a2 = 1, b1 = 1 2 = b2 , SF (t , ·) = e 1 2 tDB eA e 1 2 tDB . Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour) Higher-order splitting methods Higher-order splitting method (Real coefficients). Symmetric fourth-order splitting method by BLANES, MOAN (2002). j aj 1 0 2,7 0.245298957184271 3,6 0.604872665711080 4,5 1/2− (a2 +a3) j bj 1,7 0.0829844064174052 2,6 0.3963098014983680 3,5 −0.0390563049223486 4 1−2(b1 +b2 +b3) Remark. Numerical solution of parabolic problems requires application of splitting methods defined by complex coefficients with positive real part. Higher-order splitting method (Complex coefficients). Variant of fourth-order splitting method by YOSHIDA. j a j 1 0 2,4 0.3243964040201712+0.1345862724908067i 3 0.3512071919596576−0.2691725449816134i j b j 1,4 0.1621982020100856+0.0672931362454034i 2,3 0.3378017979899144−0.0672931362454034i Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour) Stability and error analysis of Lie–Trotter splitting method Mechthild Thalhammer (Universitat Innsbruck, Austria) Operator splitting methods for Westervelt equation Westervelt equation Splitting methods Conclusions Operator splitting methods for Westervelt equation Stability and error analysis for Lie–Trotter splitting method Illustrations (Global error, Solution behaviour)
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the lie trotter splitting for nonlinear evolutionary problems with critical parameters a compact local error representation and application to nonlinear schrodinger equations in the semiclassical regime
Ima Journal of Numerical Analysis, 2013Co-Authors: Stephane Descombes, Mechthild ThalhammerAbstract:In the present work, we investigate the error behaviour of Exponential Operator splitting methods for nonlinear evolutionary problems. In particular, our concern is to deduce an exact local error representation that is suitable in the presence of critical parameters. Essential tools in the theoretical analysis including time-dependent nonlinear Schrodinger equations in the semi-classical regime as well as parabolic initial-boundary value problems with high spatial gradients are an abstract formulation of differential equations on function spaces and the formal calculus of Lie-derivatives. We expose the general mechanism on the basis of the least technical example method, the first-order Lie–Trotter splitting
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embedded Exponential Operator splitting methods for the time integration of nonlinear evolution equations
Applied Numerical Mathematics, 2013Co-Authors: Othmar Koch, Ch Neuhauser, Mechthild ThalhammerAbstract:In this work, we introduce embedded Exponential Operator splitting methods for the adaptive time integration of nonlinear evolution equations. In the spirit of embedded Runge-Kutta methods, such pairs of related higher-order split-step methods provide estimates of the local error with moderate additional computational effort as substeps of the basic integrator are reused to obtain a local error estimator. As illustrations, we construct a split-step pair of orders 4(3) involving real method coefficients, tailored for nonlinear Schrodinger equations, and two order 4(3) split-step pairs with complex method coefficients, appropriate for nonlinear parabolic problems. Our theoretical investigations and numerical examples show that the splitting methods retain their orders of convergence when applied to evolution problems with sufficiently regular solutions. Furthermore, we demonstrate the ability of the new algorithms to serve as a reliable basis for error control in the time integration of nonlinear evolution equations by applying them to the solution of two model problems, the two-dimensional cubic Schrodinger equation with focusing singularity and a three-dimensional reaction-diffusion equation. Moreover, we demonstrate the advantages of our real embedded 4(3) pair of splitting methods over a pair of unrelated schemes for the time-dependent Gross-Pitaevskii equation.
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an exact local error representation of Exponential Operator splitting methods for evolutionary problems and applications to linear schrodinger equations in the semi classical regime
Bit Numerical Mathematics, 2010Co-Authors: Stephane Descombes, Mechthild ThalhammerAbstract:In this paper, we are concerned with the derivation of a local error representation for Exponential Operator splitting methods when applied to evolutionary problems that involve critical parameters. Employing an abstract formulation of differential equations on function spaces, our framework includes Schrodinger equations in the semi-classical regime as well as parabolic initial-boundary value problems with high spatial gradients. We illustrate the general mechanism on the basis of the first-order Lie splitting and the second-order Strang splitting method. Further, we specify the local error representation for a fourth-order splitting scheme by Yoshida. From the given error estimate it is concluded that higher-order Exponential Operator splitting methods are favourable for the time-integration of linear Schrodinger equations in the semi-classical regime with critical parameter 0
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high order Exponential Operator splitting methods for time dependent schrodinger equations
SIAM Journal on Numerical Analysis, 2008Co-Authors: Mechthild ThalhammerAbstract:In this paper, we deduce high-order error bounds for Exponential Operator splitting methods. The employed techniques are specific to linear differential equations of the form $u'(t) = A \, u(t) + B \, u(t)$, $t \geq 0$, involving an unbounded Operator $A$. In particular, evolutionary Schrodinger equations with sufficiently regular initial values are included in the analysis.
Xiaoping Li - One of the best experts on this subject based on the ideXlab platform.
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the interaction induced dipole of h2 h new ab initio results and spherical tensor analysis
Journal of Chemical Physics, 2019Co-Authors: Xiaoping Li, Evangelos Miliordos, Katharine L C HuntAbstract:We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree–Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the Exponential Operator applied to a restricted Hartree–Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r,...
