Complex dynamics and multistability of driven diatomic molecules revealed by numerical modeling of shifted molecular potentials

We have explored the nonlinear dynamics of six common, driven, diatomic molecules using a shifted Tietz-Wei (sTW) model of their molecular potential functions. We focused on the variations in their resonances, bifurcations and multistability with changes in the spectroscopic and driving force parameters, namely the dissociation energy (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>V</a:mi><a:mn>0</a:mn></a:msub></a:math>), the potential function optimization parameters (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>b</b:mi><b:mi>h</b:mi></b:msub></b:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>c</c:mi><c:mi>h</c:mi></c:msub></c:math>), driving frequency (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>ω</d:mi></d:math>), and amplitude (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>F</e:mi><e:mn>0</e:mn></e:msub></e:math>). We used the method of multiple timescales to obtain frequency response curves for the primary and secondary superharmonic resonances. The primary resonances were larger for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi mathvariant="normal">I</f:mi><f:mn>2</f:mn></f:msub></f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>Cl</h:mi><h:mn>2</h:mn></h:msub></h:math> than for CO or <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi mathvariant="normal">O</i:mi><i:mn>2</i:mn></i:msub></i:math>. Variations in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>F</k:mi><k:mn>0</k:mn></k:msub><k:mo>,</k:mo><k:mspace width="0.16em"/><k:msub><k:mi>b</k:mi><k:mi>h</k:mi></k:msub></k:mrow></k:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>c</m:mi><m:mi>h</m:mi></m:msub></m:math> had profound impacts on the primary resonance features, with higher <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msub><n:mi>F</n:mi><n:mn>0</n:mn></n:msub></n:math> and lower <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:msub><o:mi>V</o:mi><o:mn>0</o:mn></o:msub></o:math> enhancing the response amplitude. Evidence for hysteresis in the frequency-response—a signature of multistability—is demonstrated. Superharmonic resonances are marked by increased amplitudes and significant hysteresis, especially for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:msub><p:mi mathvariant="normal">I</p:mi><p:mn>2</p:mn></p:msub></p:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:msub><r:mi>Cl</r:mi><r:mn>2</r:mn></r:msub></r:math>, driven by large <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:msub><s:mi>F</s:mi><s:mn>0</s:mn></s:msub></s:math> at low <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:msub><t:mi>V</t:mi><t:mn>0</t:mn></t:msub></t:math>. Bifurcation diagrams, maximal Lyapunov exponents, and Poincaré maps were used to unravel the transitions between periodic and chaotic states. Period-doubling bifurcations, sudden chaos, and an abundance of crisis events, viz boundary, interior, and attractor-merging crises, were identified as the routes to a range of different chaotic states. Symmetry-breaking, attractor-bubbling, and multistability were all found and are reported. Coexisting attractors and their basins of attraction showed striped, fractal, and Wada-like basin structures. The results highlight the complex dynamics stemming from the interaction between spectroscopic properties and external excitations of the sTW oscillator in diatomic molecules. They carry significant implications for experimental applications.