Gauge Dependence of the <i>S̃</i> Molecular Orbital Space Decomposition of Optical Rotation

Balduf, Ty; Caricato, Marco

doi:10.1021/acs.jpca.1c01653

“…Grimme et al suggested a simplified TDDFT (sTDDFT), which is so cheap to allow many calculations on several snapshots taken from a preliminary molecular dynamics (MD) 8 calculation, or an automated procedure to treat flexible molecules 9 . From a different perspective, Caricato et al have studied the problem of the gauge choice in optical rotation 10–14 . Mennucci et al worked on excitonic models 15 while Cappelli on the chiroptical properties in aqueous solution 16 .…”

Section: Introductionmentioning

confidence: 99%

A computational approach for modeling electronic circular dichroism of solvated chromophores

Monti

¹

,

Stener

²

,

Aschi

³

2022

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The present study consists in a novel computational protocol to model the UV-circular dichroism spectra of solvated species. It makes use of quantum-chemical calculations on a series of conformations of a flexible chromophore or on a series of chromophore/solvent clusters extracted from molecular dynamic simulations. The protocol is described and applied to the aqueous cationic tripeptide GAG + and to the aqueous neutral decapeptide (GVGVP) 2 . The protocol has proven able to: (i) properly consider the conformational motion of solute in the given environment; (ii) give the actual statistical weight of each conformational state; (iii) provide a reliable quantum mechanical method able to reproduce the spectral features. Temperature effects on conformations and spectral properties are properly taken into account. The role of explicit solvent on the conformational analysis and the spectra calculation is discussed. The comparison of the calculated circular dichroism spectra with experimental ones recorded at different temperatures represents a strict validation test of the method.

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“…The latter can then be used for a detailed analysis of the electron density redistribution for these relevant transitions as done in our previous studies. 1,[7][8][9] Further studies will investigate whether these formulations can be extended to the length gauge approach, which does not have the spurious static limit issue but where the whole tensor is origin dependent. 11,28…”

Section: Discussionmentioning

confidence: 99%

“…9; we write them here in terms of the response matrix as this makes it easier to present how the origin dependence emerges (and can be removed). We have previously shown that, in general, SMVG-M ia ≠ SMVG-E ia ; however, the Sia values for each choice of perturbation are associated with the same physical process and the relative contribution of this process to the observed OR is roughly the same 9 . A feature of the Sia definition in Eq.…”

Section: Theorymentioning

confidence: 90%

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Origin Invariant Molecular Orbital Decomposition of Optical Rotation

Balduf

¹

,

Caricato

²

2022

Preprint

0

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Optical rotation (OR) is a sensitive electronic property for which there are no clear structure-property relations. We proposed an approach to decompose the OR tensor in terms of one-electron transitions between occupied-virtual molecular orbital pairs, called the Sia method. This method allows to select the transitions with the largest magnitude that determine the overall value of the OR for a specific molecule, thus providing useful insights for characterization. However, the individual Sia values are origin-dependent even if the total OR is origin invariant. In this work, we explicitly identify the reason for the origin dependence of the Sia original formulations and we propose two ways to eliminate this spurious effect and define an origin invariant S ̃ia within the modified velocity gauge formalism. One approach is based on averaging the electric and magnetic-perturbed density Sia definitions (which have equal and opposite origin dependence that cancels out in the average), while the second approach is based on the equal distribution of the electronic response to an external field via Cholesky decomposition of the response matrix. Numerical results prove that the new Sia definitions are indeed origin invariant and they provide the same physical picture for the OR tensor decomposition. At the same time, we show that setting the origin of the coordinate system at the center of mass of the molecule also provides the same physical picture when using the original Sia formulation, which confirms that this is a robust approach for investigating structure-property relations in chiral molecules.

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“…These vectors can be visualized and superimposed to the molecular structure to determine what types of one-electron (1e) transition contribute the most to the OR. 1,[7][8][9] This vector analysis holds for the MVG approach because one can define an MVG perturbed density vector that is dotted with the vector of the paired perturbation…”

Section: Theorymentioning

confidence: 99%

Origin Invariant Molecular Orbital Decomposition of Optical Rotation

Balduf

¹

,

Caricato

²

2022

Preprint

0

View full text Add to dashboard Cite

Optical rotation (OR) is a sensitive electronic property for which there are no clear structure-property relations. We proposed an approach to decompose the OR tensor in terms of one-electron transitions between occupied-virtual molecular orbital pairs, called the Sia method. This method allows to select the transitions with the largest magnitude that determine the overall value of the OR for a specific molecule, thus providing useful insights for characterization. However, the individual Sia values are origin-dependent even if the total OR is origin invariant. In this work, we explicitly identify the reason for the origin dependence of the Sia original formulations and we propose two ways to eliminate this spurious effect and define an origin invariant S ̃ia within the modified velocity gauge formalism. One approach is based on averaging the electric and magnetic-perturbed density Sia definitions (which have equal and opposite origin dependence that cancels out in the average), while the second approach is based on the equal distribution of the electronic response to an external field via Cholesky decomposition of the response matrix. Numerical results prove that the new Sia definitions are indeed origin invariant and they provide the same physical picture for the OR tensor decomposition. At the same time, we show that setting the origin of the coordinate system at the center of mass of the molecule also provides the same physical picture when using the original Sia formulation, which confirms that this is a robust approach for investigating structure-property relations in chiral molecules.

show abstract

Gauge Dependence of the S̃ Molecular Orbital Space Decomposition of Optical Rotation

Cited by 8 publications

References 39 publications

A computational approach for modeling electronic circular dichroism of solvated chromophores

A computational approach for modeling electronic circular dichroism of solvated chromophores

Origin Invariant Molecular Orbital Decomposition of Optical Rotation

Origin Invariant Molecular Orbital Decomposition of Optical Rotation

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