Early speculations about the existence of heavy hadron molecules were grounded on the idea that light-meson exchange forces could lead to binding. In analogy to the deuteron, the light mesons usually considered include the pion, sigma, rho and omega, but not the axial meson <math display="inline"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1260</mn><mo stretchy="false">)</mo></math>. Though it has been argued in the past that the coupling of the axial meson to the nucleons is indeed strong, its mass is considerably heavier than that of the vector mesons and thus its exchange ends up being suppressed. Yet, this is not necessarily the case in heavy hadrons molecules; we find that even though the contribution to binding from the axial meson is modest, it cannot be neglected in the isovector sector where vector meson exchange cancels out. This might provide a natural binding mechanism for molecular candidates such as the <math display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, <math display="inline"><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>4020</mn><mo stretchy="false">)</mo></mrow></math>, or the more recently observed <math display="inline"><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>3985</mn><mo stretchy="false">)</mo></math>. However, the <math display="inline"><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>3985</mn><mo stretchy="false">)</mo></mrow></math> is more dependent on a mixture of different factors, which (besides axial meson exchange) include <math display="inline"><mi>η</mi></math> exchange and the nature of scalar meson exchange. Together they point towards the existence of two <math display="inline"><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>3985</mn><mo stretchy="false">)</mo></math>-like resonances instead of one, while the observations about the role of scalar meson exchange in the <math display="inline"><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>3985</mn><mo stretchy="false">)</mo></math> might be relevant for the <math display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math>. Finally, the combination of axial meson exchange and flavor-symmetry breaking effects indicates that the isovector <math display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> <math display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> and the strange <math display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>2</mn><mo>+</mo></msup></math> <math display="inline"><msup><mi>D</mi><mo>*</mo></msup><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup></math> molecules are the most attractive configurations and thus the most likely molecular partners of the <math display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, <math display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4020</mn><mo stretchy="false">)</mo></math>, and <math display="inline"><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>3985</mn><mo stretchy="false">)</mo></math>.Read less <