| Summary: | It is shown that the electric dipole- and electric quadrupole–anapole polarizabilities, denoted respectively by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>f</mi><mrow><mi>α</mi><mi>β</mi></mrow><mo>′</mo></msubsup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>g</mi><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mi>γ</mi></mrow><mo>′</mo></msubsup></semantics></math></inline-formula>, and the anapole magnetizability <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mrow><mi>α</mi><mi>β</mi></mrow></msub></semantics></math></inline-formula>, are intrinsic properties of the electron cloud of molecules responding to optical fields. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>f</mi><mrow><mi>α</mi><mi>β</mi></mrow><mo>′</mo></msubsup></semantics></math></inline-formula> is a nonvanishing property of chiral and achiral compounds, whereas <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mrow><mi>α</mi><mi>β</mi></mrow></msub></semantics></math></inline-formula> is suitable for enantiomer discrimination of chiral species. They can conveniently be evaluated by numerical integration, employing a formulation complementary to that provided by perturbation theory and relying on the preliminary computation of electronic current density tensors all over the molecular domain. The origin dependence of the dynamic anapolar response is rationalized via related computational techniques employing numerical integration, as well as definitions of molecular property tensors, for example, electric dipole and electric quadrupole polarizabilties and magnetizability. A preliminary application of the theory is reported for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>a</mi></msub></semantics></math></inline-formula> enantiomer of the hydrogen peroxide molecule, evaluating tensor components of electric dipole-anapole polarizability and anapole magnetizability as functions of the dihedral angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>ϕ</mo><mo>≡</mo><mo>∠</mo></mrow></semantics></math></inline-formula> H-O-O-H in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>0</mn><mo>∘</mo></msup><mo>≤</mo><mo>ϕ</mo><mo>≤</mo><msup><mn>180</mn><mo>∘</mo></msup></mrow></semantics></math></inline-formula>.
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