Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy

Yamaguchi, Yukio; Schaefer, Henry F.

doi:10.1002/9780470749593.hrs006

Cited by 18 publications

(13 citation statements)

References 214 publications

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“…Modern techniques pertaining to specific ab initio calculations of dynamically important regions of PESs such as local minima or transition structures for reaction dynamics are discussed by Yamaguchi et al (1994), Yamaguchi and Schaefer (2011): Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy, this handbook and reviewed by Dunning (1990). Applications of such techniques to derive accurate PESs for systems larger than five-atomic molecules involving not more than 50 electrons are hardly found, however.…”

Section: Ab Initio Calculations Of Potential Energy Surfacesmentioning

confidence: 99%

“…In the Born-Oppenheimer approximation, the first step is to solve the molecular Schrödinger equation for the electronic states at fixed nuclear geometries. This procedure is based on first principles and is carried out in many modern computer codes for ab initio calculations (see also Yamaguchi and Schaefer 2011: Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy; Tew et al 2011 Wörner and Merkt 2011: Fundamentals of Electronic Spectroscopy, this handbook). Despite the great advances made in computer technology since the early days of quantum mechanics, traditional ab initio calculations can yield only approximate values of electronic energies because many-electron molecular systems are highly correlated (Löwdin 1959).…”

Section: Ab Initio Calculations Of Potential Energy Surfacesmentioning

confidence: 99%

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Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Marquardt¹,

Qüack²

2011

Handbook of High‐resolution Spectroscopy

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Analytical representations of potential energy hypersurfaces for the nuclear motion in polyatomic molecules from ab initio theory and experiment are discussed in a general way. The qualification of potential hypersurface representations from ab initio theory regarding the description of experimental data from rovibrational high-resolution spectroscopy and chemical reaction kinetics is analyzed in more detail for a restricted group of molecules including methane, CH 4 , ammonia, NH 3 , H 2 O 2 , and (HF) 2 . Current methods for the derivation of analytical representations of potential energy surfaces as well as some applications are reviewed.

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Section: Ab Initio Calculations Of Potential Energy Surfacesmentioning

confidence: 99%

Section: Ab Initio Calculations Of Potential Energy Surfacesmentioning

confidence: 99%

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Marquardt¹,

Qüack²

2011

Handbook of High‐resolution Spectroscopy

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“…As the application to the simplest hydrogen problem suggests, the Newton‐Raphson optimization procedure can be extended to general many‐electron and multi‐center problems using the analytic derivative method, which is widely used for molecular geometry optimizations and also for orbital exponent optimizations …”

Section: Computation and Resultsmentioning

confidence: 99%

Optimization of complex slater‐type functions with analytic derivative methods for describing photoionization differential cross sections

Matsuzaki

Yabushita

2017

J Comput Chem

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The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc.

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“…For a detailed discussion on the subject, we refer the reader to the review by Yamaguchi and Schaefer. 76 We start with the electronic Hamiltonian in second quantization:…”

Section: B Gradients Of Hciscf Wave Functionsmentioning

confidence: 99%

Near-Exact Nuclear Gradients of Complete Active Space Self-Consistent Field Wave Functions

Smith,

Lee,

Sharma

2022

Preprint

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In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that the HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant error. The ability of HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems which require a larger active space than possible with complete active space self-consistent field (CASSCF). Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and show that the triplet potential energy surface is much more sensitive to the nuclear coordinates than the singlet surface.

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Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy

Cited by 18 publications

References 214 publications

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Optimization of complex slater‐type functions with analytic derivative methods for describing photoionization differential cross sections

Near-Exact Nuclear Gradients of Complete Active Space Self-Consistent Field Wave Functions

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