VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Rosnik, Andreana M.; Polik, William F.

doi:10.1080/00268976.2013.808386

Cited by 91 publications

(138 citation statements)

References 33 publications

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“…The latter step is commonly known as Martin's test . The overall procedure can be summarized as,

Step 1 : | ω_{i} - (ω_{j} + ω_{k}) | + ω_{ω}^{1 - 2}

Step 2 : | 〈 v + 1_{i} | \overset{H}{true}' | v + 1_{j} + 1_{k} 〉 | - true| \frac{k_{i j k}^{2}}{2 [ω_{i} - (ω_{j} + ω_{k})]} true| \geq K^{1 - 2}

where

\overset{H}{true}'

is the contact transformed hamiltonian, which is used here for consistency during the variational correction . Here and in the following, harmonic vibrational states will be represented as vectors of N quanta, noted

bold-italicv

.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…To fulfill the accuracy (for structures and frequencies) and interpretability (for intensities) requirements of vibrational spectra, it is mandatory to go beyond the so‐called double‐harmonic approximation accounting for both mechanical and electric (and more generally property‐related) anharmonic effects. For very small molecules, it is possible to compute ro‐vibrational energy levels using full variational approaches while simplified, less expensive methodologies are necessary for larger molecular systems (see also reference and references therein), either based on variational or perturbative schemes. Here, we will employ the framework of the generalized second‐order vibrational perturbation theory (GVPT2), which permits the computation of thermodynamic properties, vibrational energies, and transition intensities (for infrared (IR), Raman, vibrational circular dichroism and Raman optical activity) from the vibrational ground state to fundamentals, overtones and combination bands up to the three quanta …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Aiming at an accurate prediction of vibrational and electronic spectra for medium‐to‐large molecules: An overview

Bloino

Baiardi

Biczysko

2016

Int J of Quantum Chemistry

182

196

View full text Add to dashboard Cite

In this tutorial review, we present some effective methodologies available for the simulation of vibrational and vibrationally resolved electronic spectra of medium-to-large molecules. They have been integrated into a unified platform and extended to support a wide range of spectroscopies.The resulting tool is particularly useful in assisting the extensive characterization of molecules, often achieved by combining multiple types of measurements. A correct assessment of the reliability of theoretical calculations is a necessary prelude to the interpretation of their results. For this reason, the key concepts of the underlying theories will be first presented and then illustrated through the study of thiophene and its smallest oligomer, bithiophene. While doing so, a complete computational protocol will be detailed, with emphasis on the strengths and potential shortcomings of the models employed here. Guidelines are also provided for performing similar studies on different molecular systems, with comments on the more common pitfalls and ways to overcome them. Finally, extensions to other cases, like chiral spectroscopies or mixtures, are also discussed. K E Y W O R D Sanharmonic vibrational spectroscopy, computational spectroscopy, large amplitude motion, medium-to-large molecules, vibronic spectroscopy | I N T R O D U C T I O NMolecular properties are commonly probed with a wide panel of spectroscopies, which can be combined to offer a unique picture, reflection of the property, its environment, and the experimental conditions. [1][2][3][4][5][6][7][8] The wealth of information contained in the recorded spectrum or spectra can become complex to analyze in a purely phenomenological way and theoretical models can provide a valuable aid in understanding the origin of the features observed in the band-shapes. [9][10][11] As a matter of fact, the predictive and interpretative power of computational spectroscopy has been clearly demonstrated already for small molecular systems in the gas phase, by comparison with the most sophisticated experimental techniques. [1,[12][13][14] However, depending on the target system and the required accuracy, the theoretical spectroscopic models can vary greatly in complexity. The situation is even more challenging when considering their actual implementation, often done in ad hoc, standalone programs, whose levels of completion, versatility and ease of use may be very different. As a result, getting an extensive picture of the experimental spectra can become a challenge as it may require multiple packages with their own usage and peculiarities.Hence, to facilitate the simulation and interpretation of multiple spectra, several conditions need to be met. A first challenge is to provide a simple interface, lowering the barrier to the broad adoption of state-of-the-art methods able to produce accurate data for the problems at hand. [11,[15][16][17] This can be achieved by automatizing most aspects of the calculations. Due to the inherent complexity of some theoretical models, such ...

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“…The latter step is commonly known as Martin's test . The overall procedure can be summarized as,

Step 1 : | ω_{i} - (ω_{j} + ω_{k}) | + ω_{ω}^{1 - 2}

Step 2 : | 〈 v + 1_{i} | \overset{H}{true}' | v + 1_{j} + 1_{k} 〉 | - true| \frac{k_{i j k}^{2}}{2 [ω_{i} - (ω_{j} + ω_{k})]} true| \geq K^{1 - 2}

where

\overset{H}{true}'

bold-italicv

.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Aiming at an accurate prediction of vibrational and electronic spectra for medium‐to‐large molecules: An overview

Bloino

Baiardi

Biczysko

2016

Int J of Quantum Chemistry

182

196

View full text Add to dashboard Cite

show abstract

“…It has already been widely discussed in the literature that variational corrections are particularly relevant for resonant states. 28,29,101 For this reason, a higher number of renormalized block states m is required to obtain converged energies.…”

Section: Higher-order Expansion Of the Potential Energy Surface: Ementioning

confidence: 99%

Vibrational Density Matrix Renormalization Group

Baiardi

Stein

Barone

et al. 2017

J. Chem. Theory Comput.

123

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Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.

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“…, with the difference that, now, we impose that the terms

〈 ϕ_{A_{a}}^{(0)} | {\overset{true˜}{scriptH}}^{(2)} | ϕ_{B_{b}}^{(0)} 〉

vanish and

i [{scriptS}^{(1)}, {scriptH}^{(1)}] - [{scriptS}^{(1)}, [{scriptS}^{(1)}, {scriptH}^{(0)}]] / 2

is the perturbation correction to

{scriptH}^{(2)}

that derives from the cancellation of the off‐diagonal terms of

{scriptH}^{(1)}

. It can be shown that the general matrix element of

{\overset{true˜}{scriptH}}^{(2)}

is given by the expression,

\begin{matrix} left \\ 〈 ϕ_{A_{a}}^{(0)} | {\overset{H}{true}}^{(2)} | ϕ_{B_{b}}^{(0)} 〉 = 〈 ϕ_{A_{a}}^{(0)} | {scriptH}^{(2)} | ϕ_{B_{b}}^{(0)} 〉 \\ - \frac{1}{2} \sum_{C \neq A, B}^{*} [\frac{1}{E_{C}^{(0)} - E_{A}^{(0)}} +<...> \end{matrix}

…”

Section: Theorymentioning

confidence: 99%

“…According to the classification of the total change of quanta, there are 1‐1, 2‐2 and 1‐3 second‐order resonances. For asymmetric tops, a detailed description of all these off‐diagonal terms has been recently given by Rosnik and Polik . The total number of non‐zero second‐order off‐diagonal elements becomes very large when doubly degenerate normal modes are also taken into account, because of the large number of combinations of nondegenerate/doubly degenerate normal modes that can be obtained when considering all states involved in the matrix elements.…”

Section: Theorymentioning

confidence: 99%

Generalized vibrational perturbation theory for rotovibrational energies of linear, symmetric and asymmetric tops: Theory, approximations, and automated approaches to deal with medium‐to‐large molecular systems

Piccardo

Bloino

Barone

2015

Int J of Quantum Chemistry

101

129

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Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc.

show abstract

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Abstract: VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Cited by 91 publications

References 33 publications

Aiming at an accurate prediction of vibrational and electronic spectra for medium‐to‐large molecules: An overview

Aiming at an accurate prediction of vibrational and electronic spectra for medium‐to‐large molecules: An overview

Vibrational Density Matrix Renormalization Group

Generalized vibrational perturbation theory for rotovibrational energies of linear, symmetric and asymmetric tops: Theory, approximations, and automated approaches to deal with medium‐to‐large molecular systems

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