\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}



\usepackage{float}








\begin{document}

\title{Bond Flexing, Twisting, Anharmonicity and Responsivity for the IR-active
modes of Benzene}



\author[1]{Yong Yang}%
\author[1]{Tianlv Xu}%
\author[1]{Steven Kirk}%
\author[1]{Samantha Jenkins}%
\affil[1]{Hunan Normal University}%


\vspace{-1em}



  
  \date{June 13, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
In this investigation we have used NG-QTAIM to fully quantity the
response to the four IR-active modes of all the bonding in benzene in
terms of bond-flexing, bond-torsion and bond-anharmonicity that includes
the tendencies towards IR-responsivity and IR-non-responsivity.
Bond-anharmonicity is found to be lacking for the C-C bonds comprising
the lowest frequency mode (721.57 cm-1) measured as the absence of bond
critical point (BCP) sliding. Additionally, bond-flexing was absent for
this mode harmonic-like variation of the profile of the variation of the
wrapping (torsion) of the \{p,p'\} path-packet, referred to as the
Precession K, along the conventional QTAIM bond-path, the remaining
three IR-active mode possessed step-like variations in the K profiles.
The presence of non-nuclear attractors was detected for the IR-active
mode with frequency 1573.93 cm-1 with C-C K profiles that most closely
resemble those of the relaxed benzene. We quantified the C-H bonds in
terms of bond-flexing and bond-anharmonicity and IR-responsivity and
IR-non-responsivity.%
\end{abstract}%



\sloppy




\selectlanguage{english}
\FloatBarrier
\end{document}

