berquist

Is there a physical reason for why the coupling constant $\beta < 0$? I tried to read the section in your paper but didn't see anything relevant.

Mathematically, it should be clear that as $\beta > 0$, the symmetric stretch becomes higher in energy than the asymmetric stretch. This is a consequence of how the linear combination of eigenvectors works out.

Physically,

The bend in the $\ce{CO2}$ determines the change in the coupling constant between the local modes, $\beta$. The motion of the central carbon atom is the primary motion that couples the two carbonyls. When they are collinear, the motion of one carbonyl directly influences the other. Bending the $\ce{CO2}$ means the carbonyls are no longer collinear, which means that the projection of one local vibration on the other decreases. This decrease, in turn, decreases the effective coupling constant.

The fit I found was

berquist

# Maintainer: Yann Leprince <yann dot leprince at ylep dot fr>
pkgname=blitz
pkgver=0.10
pkgrel=1
pkgdesc="C++ Class library for scientific computing"
arch=('i686' 'x86_64')
url="http://www.sourceforge.net/projects/blitz/"
# The user is free to choose the license among ('Artistic2.0' 'BSD' 'LGPL3'),
# but we cannot express it here so we only mention the most permissive.
license=('BSD')

berquist

# -*- mode: python -*-

from __future__ import print_function

import numpy as np


Nprim = 6
Ncntr = 2

berquist

Warning: Unbrewed dylibs were found in /usr/local/lib.
If you didn't put them there on purpose they could cause problems when
building Homebrew formulae, and may need to be deleted.

Unexpected dylibs:
  /usr/local/lib/libaspell.15.1.4.dylib
  /usr/local/lib/libpspell.15.1.4.dylib

Warning: Unbrewed .la files were found in /usr/local/lib.
If you didn't put them there on purpose they could cause problems when

berquist

#!/usr/bin/env bash

#PBS -N s01.PBE0_def2-QZVPP
#PBS -q mem48g
#PBS -l nodes=1:ppn=4
#PBS -l walltime=4:00:00
#PBS -l qos=low
#PBS -j oe
#PBS -m abe
#PBS -M erb74@pitt.edu

berquist

#!/usr/bin/env python

"""cclib_extract_geom.py: Extract geometries from a quantum chemical
output file using cclib.
"""


from __future__ import print_function

import os.path

berquist

Welcome to Chemistry.SE! This appears to be a homework question. Please share your thoughts and attempts towards the solution, otherwise your question may be closed.

Welcome to Chemistry! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using LaTeX syntax. If you receive useful answers, consider accepting one.

Welcome to Chemistry.SE! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. This appears to be a homework

berquist

javascript:(function(){if(window.MathJax===undefined){var%20script=document.createElement("script");script.type="text/javascript";script.src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML";var%20config='MathJax.Ajax.config.path["mhchem"]="https://cdnjs.cloudflare.com/ajax/libs/mathjax-mhchem/3.2.0";MathJax.Hub.Config({extensions:%20["tex2jax.js"],tex2jax:{inlineMath:[["$","$"],["\\\\\\\\\\\\(","\\\\\\\\\\\\)"]],displayMath:[["$$","$$"],["\\\\[","\\\\]"]],processEscapes:true},TeX:{extensions:["[mhchem]/mhchem.js","cancel.js"]},jax:["input/TeX","output/HTML-CSS"]});MathJax.Hub.Startup.onload();';if(window.opera){script.innerHTML=config}else{script.text=config}document.getElementsByTagName("head")[0].appendChild(script);window.setInterval(function(){MathJax.Hub.Queue(["Typeset",MathJax.Hub]);},1000);}else{MathJax.Hub.Queue(["Typeset",MathJax.Hub]);}})();

berquist

\documentclass[12pt]{article}

\usepackage[
    colorlinks = true,
]{hyperref}

\begin{document}

\section*{Post 1}

berquist

Keybase proof

I hereby claim:

• I am berquist on github.
• I am berquist (https://keybase.io/berquist) on keybase.
• I have a public key ASAyuz17NNVTDhQfiFn4nTAO8qw1zT84vLdMvZ3BI6B-vQo

To claim this, I am signing this object: