On the Correspondence between Molecular Orbital Energies and Empirical Force Field Potential Terms

In order to avoid the difficulty associated with the parameterization of molecular mechanics (MM) potential functions for mole-· cules containing hetero-atoms, a possibility of switching the standard from experimental to theoretical is suggested. Advantages and disadvantages of the ab initio MO-based, transferable force field. are discussed. As the first step toward this goal, the correspondence between the MM potential energy terms and quantities resulting from molecular orbital (MO) calculations has been investigated with the emphasis on extracting the general trend. Stretch, angle bending and electrostatic interaction energy terms can be computed without serious difficulties by MO methods. It is suggested that nonbonded interactions by the through-bond mechanism, especially of the 1,4-type, have been overlooked in the existing MM schemes. Prospects of improving the performance of MM by incorporating these and other features are discussed

RO-VIBRATIONALLY AVERAGED STRUCTURE OF 2Π NCS: RE-INTERPRETATION OF THE B0 VALUES

We have constructed \textit{ab initio} 3D potential energy surfaces (PESs) for \tilde{X}\;^{2}\Pi NCS in core-valence SDCI+$Q$/[aCVQZ(N,C,S)] calculations. The $B_{0}$ value predicted from these PESs deviates only 0.05\%\ from the corresponding experimental values for NC$^{32}$S and NC$^{34}$S. Since we have quite accurate 3D PESs, we can determine both the equilibrium structure and the $r_0$ structure accurately: $r_{\rm e}$(N--C) = 1.1778~\AA, $r_{\rm e}$(C--S) = 1.6335~\AA, and $\angle_{\rm e}$(N--C--S) = 180$^\circ$. The ro-vibrationally averaged structure, determined as expectation values over DVR3D wavefunctions, has $\langle r$(N--C)$\rangle_0$ = 1.1836~\AA, $\langle r$(C--S)$\rangle_0$ = 1.6356~\AA, and $\langle \angle$(N--C--S)$\rangle_0$ = 172.5$^\circ$. The 3D PESs show that the \tilde{X}\, ^2\Pi NCS has its potential energy minimum at a linear configuration, and hence it is a ``linear molecule.'' Experimentally, $B_{0}$ values are reported for two isotopologues only.\footnote{A.~Maeda, H.~Habara, T.~Amano, {\it Mol. Phys.}, {\bf 105}, 477--495 (2007).} Using the expectation values given above as the initial guess, a bent $r_{0}$ structure having an $\langle \angle$(N--C--S)$\rangle_0$ of 172.2$^\circ$ is deduced from the experimentally reported $B_{0}$ values for NC$^{32}$S and NC$^{34}$S. It shows that the linear molecule NCS has a ``bent'' ro-vibrationally averaged structure, confirming our previous predictions:\footnote{T.~Hirano, U.~Nagashima, {\it J. Mol. Spectrosc.}, {\bf 314}, 35--47 (2015); % T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} {\bf 343}, 54--61 (2018).} any linear molecule is observed as being bent on ro-vibrational average. See Ref.~$c$ \footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} (2018), https://doi.org/10.1016/j.jms.2017.12.011.} for further discussion of this molecule. $^{2}\Pi$ NCS is a typical Renner molecule. The Renner spectroscopy of this molecule will be presented in a separate talk.\footnote{J.~Freund et al, ``Computational spectroscopy of NCS in the Renner-degenerate Electronic state \tilde{X}\, ^2\Pi.''

ARE LINEAR MOLECULES REALLY LINEAR? I. THEORETICAL PREDICTIONS

In spectroscopic parlance, a linear triatomic molecule is one whose potential energy minimum occurs at a linear geometry. We have recently discussed\footnote{T.~Hirano, U.~Nagashima, {\it J. Mol. Spectrosc.}, {\bf 314}, 35--47 (2015)}$^,$% \footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} {\bf 343}, 54--61 (2018).}$^,$\footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.} that any linear triatomic molecule will be observed as being ``bent'' on ro-vibronic average in any ro-vibronic state. As quantum mechanics asserts, we have to characterize Nature through ``observation.'' Theoretically we make observations of molecular structures by calculating the expectation values of the structural parameters over the relevant ro-vibronic wavefunctions. In computational molecular spectroscopy studies, we have shown that for many linear triatomic molecules such as $^{6}\Delta$ FeNC, $^{6}\Delta$ FeCN, $^{2}\Pi$ BrCN$^{+}$, $^{3}\Phi$ CoCN, $^{2}\Delta$ NiCN, $^{1}\Sigma^{+}$ CsOH, $^{3}\Sigma^{-}$ FeCO, and $^{2}\Pi$ NCS, the ro-vibrationally averaged structure (zero-point structure, for example) is slightly bent with a bond angle supplement 180$^\circ$ $-$ $\angle$(A-B-C) [where $\angle$(A-B-C) is the bond angle] in the range from 7.5$^{\circ}$ (NCS) to 22.5$^{\circ}$ (C$_{3}$). We have also described the theoretical background$^{b}$ for this fact using a Laguerre-Gauss type wavefunction for the doubly degenerate bending oscillator; the average ``bentness'' is basically caused by the inseparability of the bending motion from the free rotation about the molecular axis. Our finding is in contradiction to the well-established paradigm in spectroscopy that the ro-vibrationally averaged structure of a linear molecule is linear. In particular, it throws doubt on the so-called $r_0$ structures routinely determined for linear triatomic molecules under the \textit{a priori} assumption that ro-vibrationally averaged bond-angle of a linear molecule should be 180$^{\circ}$. In the following talk, we discuss how experimentally derived rotational-constant values are to be interpreted

ARE LINEAR MOLECULES REALLY LINEAR? II. RE-INTERPRETATION OF EXPERIMENTAL B0-VALUES.

As discussed in the preceding talk, any linear triatomic molecule will be observed as being ``bent'' on ro-vibronic average in any ro-vibronic state.\footnote{T.~Hirano, U.~Nagashima, {\it J. Mol. Spectrosc.}, {\bf 314}, 35--47 (2015)}$^{,}$% \footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} {\bf 343}, 54--61 (2018).}$^{,}$\footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.} Experimentally derived $B_{0}$ constants are the results of the ``observation'' of Nature. This suggests that the observed $B_{0}$ values are in fact those for the ro-vibrationally averaged bent structures. The easiest way to check this proposition is to interpret the set of $B_{0}$ values of isotopologues taking the bond-angle as a ``variable,'' discarding the preconceived, conventional notion that the ro-vibrationally averaged bond angle of a linear molecule is 180$^{\circ}$. We have shown in previous publications$^a$ that bond length values derived from a set of experimental $B_{0}$ values under the assumption of a linear $r_0$ structure, is not the ro-vibrationally averaged bond lengths, but their projections onto the molecular axis. Therefore, when the projection angle is not accounted for, the bond length values obtained from the $B_0$ values may differ significantly from the averaged bond lengths. We will show how we can derive physically sound ro-vibrational structures from the experimentally reported $B_{0}$ values, taking the FeCO, NCS, HCO$^{+}$, HCN, and C$_{3}$ molecules as examples. The averaged bond-angle deviations from the linearity, derived from experimentally reported $B_{0}$ values of multiple isotopologues, are 7.8$^\circ$, 9.5$^\circ$, 12.5$^\circ$, 14.3$^\circ$, and 23.4$^\circ$, respectively, for NCS, FeCO, HCO$^{+}$, HCN, and C$_{3}$ in their respective vibrational ground states. Thus, we can conclude that both theoretically (as described in the preceding talk) and experimentally (as shown here), the ro-vibrationally averaged structure of a linear molecule is observed as being bent

Assessment of Lower-limb Vascular Endothelial Function Based on Enclosed Zone Flow-mediated Dilation

This paper proposes a novel non-invasive method for assessing the vascular endothelial function of lower-limb arteries based on the dilation rate of air-cuff plethysmograms measured using the oscillometric approach. The principle of evaluating vascular endothelial function involves flow-mediated dilation. In the study conducted, blood flow in the dorsal pedis artery was first monitored while lower-limb cuff pressure was applied using the proposed system. The results showed blood flow was interrupted when the level of pressure was at least 50 mmHg higher than the subject’s lower-limb systolic arterial pressure and that blood flow velocity increased after cuff release. Next, values of the proposed index, %ezFMDL, for assessing the vascular endothelial function of lower-limb arteries were determined from 327 adult subjects: 87 healthy subjects, 150 subjects at high risk of arteriosclerosis and 90 patients with cardiovascular disease (CAD). The mean values and standard deviations calculated using %ezFMDL were 30.5 ± 12.0% for the healthy subjects, 23.6 ± 12.7% for subjects at high risk of arteriosclerosis and 14.5 ± 15.4% for patients with CAD. The %ezFMDL values for the subjects at high risk of arteriosclerosis and the patients with CAD were significantly lower than those for the healthy subjects (p < 0.01). The proposed method may have potential for clinical application.This work was supported by JSPS KAKENHI Grant Number 16K21076

ARE LINEAR MOLECULES REALLY LINEAR? I. THEORETICAL PREDICTIONS

In spectroscopic parlance, a linear triatomic molecule is one whose potential energy minimum occurs at a linear geometry. We have recently discussed\footnote{T.~Hirano, U.~Nagashima, {\it J. Mol. Spectrosc.}, {\bf 314}, 35--47 (2015)}$^,$% \footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} {\bf 343}, 54--61 (2018).}$^,$\footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.} that any linear triatomic molecule will be observed as being ``bent'' on ro-vibronic average in any ro-vibronic state. As quantum mechanics asserts, we have to characterize Nature through ``observation.'' Theoretically we make observations of molecular structures by calculating the expectation values of the structural parameters over the relevant ro-vibronic wavefunctions. In computational molecular spectroscopy studies, we have shown that for many linear triatomic molecules such as $^{6}\Delta$ FeNC, $^{6}\Delta$ FeCN, $^{2}\Pi$ BrCN$^{+}$, $^{3}\Phi$ CoCN, $^{2}\Delta$ NiCN, $^{1}\Sigma^{+}$ CsOH, $^{3}\Sigma^{-}$ FeCO, and $^{2}\Pi$ NCS, the ro-vibrationally averaged structure (zero-point structure, for example) is slightly bent with a bond angle supplement 180$^\circ$ $-$ $\angle$(A-B-C) [where $\angle$(A-B-C) is the bond angle] in the range from 7.5$^{\circ}$ (NCS) to 22.5$^{\circ}$ (C$_{3}$). We have also described the theoretical background$^{b}$ for this fact using a Laguerre-Gauss type wavefunction for the doubly degenerate bending oscillator; the average ``bentness'' is basically caused by the inseparability of the bending motion from the free rotation about the molecular axis. Our finding is in contradiction to the well-established paradigm in spectroscopy that the ro-vibrationally averaged structure of a linear molecule is linear. In particular, it throws doubt on the so-called $r_0$ structures routinely determined for linear triatomic molecules under the \textit{a priori} assumption that ro-vibrationally averaged bond-angle of a linear molecule should be 180$^{\circ}$. In the following talk, we discuss how experimentally derived rotational-constant values are to be interpreted

ARE LINEAR MOLECULES REALLY LINEAR? II. RE-INTERPRETATION OF EXPERIMENTAL B0-VALUES.

As discussed in the preceding talk, any linear triatomic molecule will be observed as being ``bent'' on ro-vibronic average in any ro-vibronic state.\footnote{T.~Hirano, U.~Nagashima, {\it J. Mol. Spectrosc.}, {\bf 314}, 35--47 (2015)}$^{,}$% \footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} {\bf 343}, 54--61 (2018).}$^{,}$\footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} (2018), https://doi.org/10.1016/j.jms.2017.12.011; and references therein.} Experimentally derived $B_{0}$ constants are the results of the ``observation'' of Nature. This suggests that the observed $B_{0}$ values are in fact those for the ro-vibrationally averaged bent structures. The easiest way to check this proposition is to interpret the set of $B_{0}$ values of isotopologues taking the bond-angle as a ``variable,'' discarding the preconceived, conventional notion that the ro-vibrationally averaged bond angle of a linear molecule is 180$^{\circ}$. We have shown in previous publications$^a$ that bond length values derived from a set of experimental $B_{0}$ values under the assumption of a linear $r_0$ structure, is not the ro-vibrationally averaged bond lengths, but their projections onto the molecular axis. Therefore, when the projection angle is not accounted for, the bond length values obtained from the $B_0$ values may differ significantly from the averaged bond lengths. We will show how we can derive physically sound ro-vibrational structures from the experimentally reported $B_{0}$ values, taking the FeCO, NCS, HCO$^{+}$, HCN, and C$_{3}$ molecules as examples. The averaged bond-angle deviations from the linearity, derived from experimentally reported $B_{0}$ values of multiple isotopologues, are 7.8$^\circ$, 9.5$^\circ$, 12.5$^\circ$, 14.3$^\circ$, and 23.4$^\circ$, respectively, for NCS, FeCO, HCO$^{+}$, HCN, and C$_{3}$ in their respective vibrational ground states. Thus, we can conclude that both theoretically (as described in the preceding talk) and experimentally (as shown here), the ro-vibrationally averaged structure of a linear molecule is observed as being bent