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Four new Ni^II, Co^II, Zn^II, and Cu^II complexes with the promising anti-tuberculosis drug (<i>E/Z</i>)-N′-((5-Hydroxy-3,4-bis(hydroxymethyl)-6-methylpyridin-2-yl)methylene)-isonicotino-hydrazide (<b>L</b>H) were synthesized and characterized by structural methods: single-crystal X-ray diffraction, vibrational spectroscopy, and mass spectrometry. The Ni^II, Co^II, and Zn^II metal ions form only amorphous phases with various morphologies according to mass spectrometry and IR spectroscopy. The Cu^II forms a crystalline 1D coordination polymer with the relative formula <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mrow><mrow><mo>{</mo><mrow><mrow><mo>[</mo><mrow><mi>Cu</mi><mstyle mathvariant="bold" mathsize="normal"><mi>L</mi></mstyle><mi>Cl</mi></mrow><mo>]</mo></mrow><mi>·</mi><mn>0.5</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></mrow><mo>}</mo></mrow></mrow><mo>∞</mo><mn>1</mn></mmultiscripts></mrow></semantics></math></inline-formula>. Even though the <b>L</b>H ligand in the crystalline state includes a mixture of <i>E</i>-/<i>Z</i>-isomers, only the tautomeric iminol <i>E</i>-/<i>Z</i>-form is coordinated by Cu^II in the crystal. The copper(II) complex crystallizes in the monoclinic <i>P</i>2₁/<i>n</i> space group with the corresponding cell parameters a = 16.3539(11) Å, b = 12.2647(6) Å, and c = 17.4916(10) Å; α = 90°, β = 108.431(7)°, and γ = 90°. DFT calculations showed that the <i>Z</i>-isomer of the <b>L</b>H ligand in solution has the lowest formation energy due to intramolecular hydrogen bonds. According to the quantum chemical calculations, the coordination environment of the Cu^II atom during the transfer of the molecule into the solution remains the same as in the crystal, except for the polymeric bond, namely, distorted trigonal bipyramidal. Some of the complexes investigated can be used as effective sensors in biosystems.