On the Volume Chemistry of Solid Compounds: the Legacy of Wilhelm Biltz

For the calculation of the atomic or ionic volumes the Quantum Theory of Atoms In Molecules method was applied. The regions (basins) around the nuclei confined by the zero‐flux surfaces in the electron density gradient are called QTAIM atoms. They are non‐overlapping and completely fill the space. The volume of the basins gives volumes of atoms or ions. The integration of the electron density within the volumina yields effective charges, defining neutral or ionic character of the given QTAIM species. Present investigations refer to metal hydrides, metal nitrides and to intermetallic compounds of the system Al‐Pt. A linear relation between the ionic volumina of hydrogen or nitrogen established according to QTAIM and after Biltz has been found with (homodesmic) binary metal hydrides and binary metal nitrides, but has been observed merely as a trend with stronger deviations for heterodesmic compounds, such as ternary hydrido‐ and nitridometallates A_a[M_mX_x] (A – alkali or alkaline earth metal, M – transition metal and X – H or N). The deviation from linearity for heterodesmic compounds is caused by the different kinds of chemical bonds being present within the [M_mX_x] anions on the one hand and between the anions and the cations on the other hand reflected by the calculated volumes and the QTAIM charges of M and X components. Concerning the intermetallic compounds of the system Al‐Pt, the quantum chemical calculations reveal negative charges for the platinum atoms and positive ones for the aluminium atoms in accordance with their electronegativities. Introducing the variation of the atomic volume with the composition extends the Vegard's approach and gives a non‐linear slope for the concentration dependence of mean atomic volume which explains qualitatively the experimental results.     

A Bond Path and an Attractive Ehrenfest Force Do Not Necessarily Indicate Bonding Interactions: Case Study on M2X2 (M=Li,Na, K; X=H,OH, F,Cl)

Interactions in dimers of model alkali metal derivatives M₂X₂ (M=Li or Na or K; X=H or F, Cl, OH) are studied in the frame of the quantum theory of atoms in molecules (QTAIM) using the interacting quantum atoms approach (IQA). Contrary to opinion prevalent in QTAIM studies, the interaction between two anions linked by a bond path is demonstrated to be strongly repulsive. One may therefore say that a bond path does not necessarily indicate bonding interactions. The interactions between two anions or two cations that are not linked by a bond path are also strongly repulsive. The repulsive anion–anion and cation–cation interactions are outweighed by much stronger attractive anion–cation interactions, and the model molecules are therefore in a stable state. The attractive Ehrenfest forces (calculated in the frame of the QTAIM) acting across interatomic surfaces shared by anions in the dimers do not reflect the repulsive interactions between anions. Probable reasons of this disagreement are discussed. The force exerted on the nucleus and the electrons of a particular atom by the nucleus and the electrons of any another atom in question is proposed. It is assumed that this force unambiguously exposes whether basins of two atoms are attracted or repelled by each other in a polyatomic molecule.     

Identification of molecules in inorganic compounds from X-ray or neutron diffraction data and correction of their structures on the basis of vibrational spectroscopy data

A method of identification of molecules in inorganic crystals with asymmetric M-X...M bridges has been suggested on the basis of analysis of interatomic distances in the structure unit M (−X...M) _n , which includes the atoms of the first and second coordination spheres. This analysis makes it possible to discern molecules (complex anions or cations) as a groups of atoms linked with each other by short M-X bonds, whereas the atoms of neighboring groups are linked by long M...X bonds. The symmetry of such a group is often lower than it follows from X-ray or neutron diffraction data. Studying vibrational spectra affords information on the true symmetry of a molecule. The use of the method is exemplified by the rhombohedral BaTiO₃ phase.     

A density functional theory study on boundary of “superreduced” transition metal carbonyl anions [M(CO)n](M=Cr, n=5, 4, 3, z=2, 4, 6; M=Mn, n=5, 4, 3, z=1, 3, 5; M=Fe, n=4, 3, 2, z=2, 4, 6; M=Co, n=4, 3, 2, z=1, 3, 5)

A nonlocal density functional theory (DFT) method has been applied to the calculations on optimized geometry, Mulliken atomic net charges and interatomic Mulliken bond orders as well as total bonding energies (E) in the binary transition metal carbonyl anions with different reduced states [M(CO)_n]^z− (M=Cr, n=5, 4, 3, z=2, 4, 6; M=Mn, n=5, 4, 3, z=1, 3, 5; M=Fe, n=4, 3, 2, z=2, 4, 6; M=Co, n=4, 3, 2, z=1, 3, 5). For comparison of relative stability, a relative stabilization energy D is defined as D=E([M(CO)_n]^z−)−nE(CO). The calculated C–O distances are lengthened monotonously with the increase of the anionic charge, but the M–C distances are significantly lengthened only in the higher reduced states. The relative stabilization energy calculated is a considerable negative value in the lower reduced states, but a larger positive value in the higher reduced states. The DFT calculations show that with the increase of the anionic charge, the Mulliken net charges on the M, C, and O atoms all increase, however, an excess of the anionic charge is mainly located at the central metal atom. The calculated C–O Mulliken bond orders decrease consistently with the increase of the anionic charge, but the M–C bond orders exhibit an irregular behavior. However, the total bond orders calculated clearly explain the higher reduced states to be considerably unstable. From analysis of the calculated results, it is deduced that the stability of the binary transition metal carbonyl anions [M(CO)_n]^z− studied are associated with the coordination number n and the anionic charge z, further, it is possible for the anions studied to be stable if n≥z, conversely, it is impossible when n<z.     

The Electrochemical Behavior of Complexes of Cobalt and Nickel with δ-Valerolactam at the Dropping Mercury Electrode

The kinetics of the polarographic reduction of Co(II) and Ni(II) has been investigated in the presence of an increasing concentration of the complex forming agent δ-valerolactam at pH 6.0 and at constant ionic strength (0.1 M KNO₃,). In both cases the waves were found to be diffusion controlled and irreversible. The values of the kinetic para-meters such as the forward rate constant K°_{f, k} and the charge transfer coefficient αn have been calculated as a function of ligand concentration. The diffusion current was precisely proportional to the concentration up to a metal ion concentration of 3.5 mM. Hence, a straight line is useful as a calibration curve in the quantitative analysis of these two metal ions. The method has also been applied to the determination of these metals in certain alloys.     

含苯并咪唑基配体Zn(Ⅱ)、Cd(Ⅱ)配位聚合物的合成、结构以及荧光性质研究(英文)

以3,5-二(苯并咪唑基)吡啶(L)、间苯二甲酸(m-H2BDC)、4-羧基肉桂酸(H2CCA)、ZnSO4·7H2O和Cd(NO3)2·4H2O为原料,使用溶剂热方法合成了两个配位聚合物[Zn(L)(m-BDC)](1)和[Cd(L)(CCA)]·2H2O(2),利用红外、元素分析、热重分析和X-射线粉末衍射对其进行了表征,利用X-射线单晶衍射对结构进行了测定,并研究了配合物的荧光性质。在配合物1中,L与金属离子连接形成了一维(1D)链结构,而间苯二甲酸根离子与金属离子构成了一个M2(m-BDC)2(M=金属离子)的单元。一维链之间通过M2(m-BDC)2单元连接形成二维网状(2D)结构。在配合物2中,和配合物1类似,L与金属离子连接形成一维链,但与1不同的是羧酸配体与金属离子配位也构成了一维链结构,两种一维链通过配位作用连接构成二维结构。     

catena‐Poly[[[(di‐2‐pyridylamine‐κ2N2,N2′)copper(II)]‐μ‐benzene‐1,3‐dicarboxylato‐κ3O1,O1′:O3] monohydrate], a zigzag coordination polymer with strong π–π interactions

The novel title coordination polymer, {[Cu(C₈H₄O₄)(C₁₀H₉N₃)]·H₂O}_n, synthesized by the slow‐diffusion method, takes the form of one‐dimensional zigzag chains built up of Cu^II cations linked by benzene‐1,3‐dicarboxylate (ipht) anions. An exceptional characteristic of this structure is that it belongs to a small group of metal–organic polymers where ipht is coordinated as a bridging tridentate ligand with monodentate and chelate coordination of individual carboxylate groups. The Cu^II cation has a highly distorted square‐pyramidal geometry formed by three O atoms from two ipht anions and two N atoms from a di‐2‐pyridylamine (dipya) ligand. The zigzag chains, which run along the b axis, further construct a three‐dimensional metal–organic framework via strong face‐to‐face π–π interactions and hydrogen bonds. A solvent water molecule is linked to the different carboxylate groups via hydrogen bonds. Thermogravimetric and differential scanning calorimetric analyses confirm the strong hydrogen bonding.     

Evaluation of N—H…S and N—H…π interactions in O,O′‐diethyl N‐(2,4,6‐trimethylphenyl)thiophosphate: a combination of X‐ray crystallographic and theoretical studies

In the crystal structure of O,O′‐diethyl N‐(2,4,6‐trimethylphenyl)thiophosphate, C₁₃H₂₂NO₂PS, two symmetrically independent thiophosphoramide molecules are linked through N—H…S and N—H…π hydrogen bonds to form a noncentrosymmetric dimer, with Z′ = 2. The strengths of the hydrogen bonds were evaluated using density functional theory (DFT) at the M06‐2X level within the 6‐311++G(d,p) basis set, and by considering the quantum theory of atoms in molecules (QTAIM). It was found that the N—H…S hydrogen bond is slightly stronger than the N—H…π hydrogen bond. This is reflected in differences between the calculated N—H stretching frequencies of the isolated molecules and the frequencies of the same N—H units involved in the different hydrogen bonds of the hydrogen‐bonded dimer. For these hydrogen bonds, the corresponding charge transfers, i.e. lp (or π)→σ*, were studied, according to the second‐order perturbation theory in natural bond orbital (NBO) methodology. Hirshfeld surface analysis was applied for a detailed investigation of all the contacts participating in the crystal packing.     

Clusters of Ammonium Cation—Hydrogen Bond versus σ‐Hole Bond

MP2/6‐311++G(d,p) calculations were performed on the NH₄⁺ ??? (HCN)_n and NH₄⁺ ??? (N₂)_n clusters (n=1–8), and interactions within them were analyzed. It was found that for molecules of N₂ and HCN, the N centers play the role of the Lewis bases, whereas the ammonium cation acts as the Lewis acid, as it is characterized by sites of positive electrostatic potential, that is, H atoms and the sites located at the N atom in the extension of the H?N bonds. Hence, the coordination number for the ammonium cation is eight, and two types of interactions of this cation with the Lewis base centers are possible: N?H ??? N hydrogen bonds and H?N ??? N interactions that are classified as σ‐hole bonds. Redistribution of the electronic charge resulting from complexation of the ammonium cation was analyzed. On the one hand, the interactions are similar, as they lead to electronic charge transfer from the Lewis base (HCN or N₂ in this study) to NH₄⁺. On the other hand, the hydrogen bond results in the accumulation of electronic charge on the N atom of the NH₄⁺ ion, whereas the σ‐hole bond results in the depletion of the electronic charge on this atom. Quantum theory of “atoms in molecules” and the natural bond orbital method were applied to deepen the understanding of the nature of the interactions analyzed. Density functional theory/natural energy decomposition analysis was used to analyze the interactions of the ammonium ion with various types of Lewis bases. Different correlations between the geometrical, energetic, and topological parameters were found and discussed.     

含苯并咪唑基配体Zn(Ⅱ)、Cd(Ⅱ)配位聚合物的合成、结构以及荧光性质研究

以3,5-二(苯并咪唑基)吡啶(L)、间苯二甲酸(m-H₂BDC)、4-羧基肉桂酸(H₂CCA)、ZnSO₄·7H₂O和Cd(NO₃)₂·4H₂O为原料,使用溶剂热方法合成了两个配位聚合物[Zn(L)(m-BDC)] (1)和[Cd(L)(CCA)]·2H₂O (2),利用红外、元素分析、热重分析和X-射线粉末衍射对其进行了表征,利用X-射线单晶衍射对结构进行了测定,并研究了配合物的荧光性质。在配合物1中,L与金属离子连接形成了一维(1D)链结构,而间苯二甲根离子与金属离子构成了一个M₂(m-BDC)₂(M=金属离子)的单元。一维链之间通过M₂(m-BDC)₂单元连接形成二维网状(2D)结构。在配合物2中,和配合物1类似,L与金属离子连接形成一维链,但与1不同的是羧酸配体与金属离子配位也构成了一维链结构,两种一维链通过配位作用连接构成二维结构。     

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca₆H₉[N(SiMe₃)₂]₃(pmdta)₃ (pmdta=N,N,N′,N′′,N′′-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n−1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.     

Zweidimensionale Polymere mit hydrophober Umhüllung: Kristallstrukturen der isostrukturellen Metallkomplexe [M{C6H4(SO2)2N}(H2O)] (M = K,Rb) und des strukturverwandten Ammoniumsalzes [(NH4){C6H4(SO2)2N}(H2O)]

Metal Salts of Benzene‐1,2‐di(sulfonyl)amine. 4. Hydrophobically Wrapped Two‐Dimensional Polymers: Crystal Structures of the Isostructural Metal Complexes [M{C₆H₄(SO₂)₂N}(H₂O)] (M = K, Rb) and of the Structurally Related Ammonium Salt [(NH₄){C₆H₄(SO₂)₂N}(H₂O)] The previously unreported compounds KZ · H₂O ( 1 ), RbZ · H₂O ( 2 ) and NH₄Z · H₂O ( 3 ), where Z^– is Ndeprotonated ortho‐benzenedisulfonimide, are examples of layered inorgano‐organic solids, in which the inorganic component is comprised of metal or ammonium cations, N(SO₂)₂ groups and water molecules and the outer regions are formed by the planar benzo rings of the anions. The metal complexes 1 and 2 were found to be strictly isostructural, whereas 3 is structurally related to them by a non‐crystallographic mirror plane ( 1 – 3 : monoclinic, space group P2₁/c, Z = 4; single crystal X‐ray diffraction at low temperatures). In each structure, the five‐membered 1,3,2‐dithiazolide heterocycle possesses an envelope conformation, the N atom lying about 40 pm outside the mean plane of the S–C–C–S moiety. The metal complexes feature two‐dimensional coordination networks interwoven with O–H…O hydrogen bonds originating from the water molecules. The metal centres adopt an irregular nonacoordination formed by five sulfonyl O atoms, two N atoms and two μ₂‐bridging water molecules; each M⁺ is connected to four different anions. When NH₄⁺ is substituted for M⁺, the metal–ligand bonds are replaced by N⁺–H…O hydrogen bonds, but the general topology of the lamella is not affected. In the three structures, the lipophilic benzo groups protrude obliquely from the surfaces of the polar lamellae and display marked interlocking between adjacent layers.     

The Zintl Phase Cs7NaSi8 – From NMR Signal Line Shape Analysis and Quantum Mechanical Calculations to Chemical Bonding

Powder samples as well as red and transparent single crystals of the Zintl phase Cs₇NaSi₈ were synthesized and characterized by means of X‐ray diffraction and differential thermal analysis. Cs₇NaSi₈ was found to be isotypic to the recently reported phase Rb₇NaSi₈. It crystallizes in the Rb₇NaGe₈ structure type forming trigonal pyramidal Si₄^4– anions. Two unique environments of the cations are observed, a linear arrangement [Na(Si₄)₂]^7– with short Na–Si distances of 3.0 Å and a Cs2 atom coordinated by six Si₄^4– anions with long Cs–Si distances of 4.2 Å. The bonding situation was investigated by a combined application of ²⁹Si, ²³Na, and ¹³³Cs solid‐state NMR spectroscopy and quantum mechanical calculations of the NMR coupling parameters. In addition the electronic density of states (DOS), the electron localizability indicator (ELI) and the atomic charges using the QTAIM approach were studied. Good agreement of the calculated and experimental values of the NMR coupling parameters was obtained. An anisotropic bonding situation of the silicon atoms is indicated by the chemical shift anisotropy being similar to Rb₇NaSi₈. Confirmation is given by the observation of one lone‐pair‐like feature for each silicon atom and two types of two‐center Si–Si bonds using the ELI. Calculation and NMR spectroscopic determination of the ²³Na and ¹³³Cs electric field gradients prove anisotropies of the charge distribution around the cations. Due to the similar values for the Na atoms in M₇NaSi₈ (M = Rb, Cs) equal bonding situations can be concluded. The much larger anisotropy of the charge distribution of the Cs atoms can be addressed as the main difference to Rb₇NaSi₈.     

Charge‐Scaling Effect in Ionic Liquids from the Charge‐Density Analysis of N,N′‐Dimethylimidazolium Methylsulfate

The charge scaling effect in ionic liquids was explored on the basis of experimental and theoretical charge‐density analyses of [C₁MIM][C₁SO₄] employing the quantum theory of atoms in molecules (QTAIM) approach. Integrated QTAIM charges of the experimental (calculated) charge density of the cation and anion resulted in non‐integer values of ±0.90 (±0.87) e. Efficient charge transfer along the bond paths of the hydrogen bonds between the imidazolium ring and the anion was considered as the origin of these reduced charges. In addition, a detailed QTAIM analysis of the bonding situation in the [C₁SO₄]^? anion revealed the presence of negative π_O→σ*_S‐O hyperconjugation.     

Experimental and theoretical studies of anions of transition-metal chelate complexes in alkylation reactions at a metal atom

Electrochemical reduction of a number of chelate complexes of transition metals (Chel)₂M or (Chel)₂MXY (M=Co, Rh, Ir, or Ni; Chel are anions of dmgH (dmg is dimethylglyoxime), (3,5-di-tert-butyl-4-hydroxyphenyl)mgH (mg is methylglyoxime),N-aryl-3-methoxysalicylaldoxime,N-aryl-3-methyl-2-thiocarboxamidopyridine, or 2-acetylindan-1,3-dione; X=Y=py, Ph₃P, or H₂O or X=Cl and Y=Ph₃P) in MeCN or DMF was studied using the cyclic voltammetry and rotating disk electrode techniques. Under the action of BuⁿBr, some electrochemically generated anions [(Chel)₂M]⁻ enter into the rather fast alkylation reactions (apparently, at the metal atom) to form (Chel)₂M—Alk. The geometries of four model neutral and anionic cobalt complexes were calculated using the semiempirical ZINDO/1 method. According to calculations, the transformation of the neutral complex (Chel)₂M into the anion [(Chel)₂M]⁻ leads to a change in the configuration from square-planar to square-pyramidal or from tetrahedral to disphenoid. The effects of steric hindrances, the HOMO energies, and the charge of the metal atom in the anionic complexes on the alkylation reactions at the metal atom are discussed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 71–77, January, 1999.     

Alkali‐Metal meta‐Hydroxyphenolates: Syntheses and Crystal Structures from Powder X‐Ray Diffraction

M[m‐C₆H₄O(OH)] (M = Li—Cs) have been obtained as highly air‐ and moisture‐sensitive powders from reaction mixtures of the appropriate alkali metals and resorcinol in thf. Both the potassium and rubidium compounds were structurally characterized by means of powder X‐ray diffraction using the Simulated Annealing method and the Rietveld profile refinement technique including C—C/C—O bond distance and C—C—C angle restraints. K[m‐C₆H₄O(OH)] (orthorhombic P2₁2₁2₁) forms infinite alternating chains of meta‐hydroxyphenolate anions connected by K—O bonds and short charge‐assisted hydrogen bonds, thereby generating a three‐dimensional network of corrugated layers similar to the structure of pure resorcinol. The potassium cations are surrounded by a triangle of oxygen and, moreover, coordinated by six adjacent phenylene rings to form a distorted octahedron. The complex crystal structure of Rb[m‐C₆H₄O(OH)] (monoclinic Pa) is characterized by layers of hydrogen‐bonded meta‐hydroxyphenolate triple units separated by corrugated rubidium layers. The three crystallographically different Rb atoms are coordinated by three, four, and five oxygens with irregular polyhedra, and the rubidiums are also involved in further electrostatic interactions by up to eight phenylene rings.     

Polar-Covalent Bonding Beyond the Zintl Picture in Intermetallic Rare-Earth Germanides

A comparative chemical bonding analysis for the germanides La₂MGe₆ (M=Li, Mg, Al, Zn, Cu, Ag, Pd) and Y₂PdGe₆ is presented, together with the crystal structure determination for M=Li, Mg, Cu, Ag. The studied compounds adopt the two closely related structure types oS72-Ce₂(Ga_0.1Ge_0.9)₇ and mS36-La₂AlGe₆, containing zigzag chains and corrugated layers of Ge atoms bridged by M species, with La/Y atoms located in the biggest cavities. Chemical bonding was studied by means of the quantum chemical position-space techniques QTAIM (quantum theory of atoms in molecules), ELI-D (electron localizability indicator), and their basin intersections. The new penultimate shell correction (PSC0) method was introduced to adapt the ELI-D valence electron count to that expected from the periodic table of the elements. It plays a decisive role to balance the Ge−La polar-covalent interactions against the Ge−M ones. In spite of covalently bonded Ge partial structures formally obeying the Zintl electron count for M=Mg²⁺, Zn²⁺, all the compounds reveal noticeable deviations from the conceptual 8−N picture due to significant polar-covalent interactions of Ge with La and M ≠ Li, Mg atoms. For M=Li, Mg a formulation as a germanolanthanate M[La₂Ge₆] is appropriate. Moreover, the relative Laplacian of ELI-D was discovered to reveal a chemically useful fine structure of the ELI-D distribution being related to polyatomic bonding features. With the aid of this new tool, a consistent picture of La/Y−M interactions for the title compounds was extracted.     

Bis‐Triiodide von 1,2‐Ethandiaminkomplexen am Beispiel des Metalls Kupfer

In bis­(1,2‐ethanedi­amine‐N,N′)­bis­[tri­iodo(1?)‐I]copper, [Cu(I₃)₂­(C₂H₈N₂)₂], the triiodide anions form chains parallel to [001]. The central metal ion (site symmetry 2/m) of the complex cation is coordinated to four N atoms and to two I atoms. The geometry of the square‐bipyramidal complex is as expected, with d(Cu—N) = 2.006 (5) and d(Cu—I) = 3.3600 (9) Å.     

catena‐Poly[[[aqua[3‐(2‐pyridylsulfanyl)propionato N‐oxide‐κO1]copper(II)]‐μ‐[3‐(2‐pyridylsulfanyl)propionato N‐oxide‐κ3O3:O1,O1′] dihydrate]

In the title complex, {[Cu(C₈H₈NO₃S)₂(H₂O)]·2H₂O}_n, the Cu^II cation has a distorted square‐pyramidal coordination environment consisting of five O atoms, one from a water molecule, one from an N—O group and the other three from the carboxylate groups of two 3‐(2‐pyridylsulfanyl)propionate N‐oxide anions. The aqua[3‐(2‐pyridylsulfanyl)propionato N‐oxide]copper(II) moieties are bridged by 3‐(2‐pyridylsulfanyl)propionate N‐oxide anions to form an infinite three‐dimensional coordination polymer with a zigzag chain structure. The crystal structure is stabilized by hydrogen bonds.     

Isomerism and Vibrational Spectra of Alkali Metal Perrhenates: Ab Initio CISD+Q Calculations

The equilibrium geometric parameters, isomerization energies, force fields, vibrational frequencies and intensities in the IR spectra of MReO₄ molecules (M = Li, Na, K) are calculated by the configuration interaction method including all singly and doubly excited configurations with Davidson's correction for quartic excitations in expanded basis sets using effective relativistic core potentials. The calculations indicate that the chemical bonds between the metal atoms and the ReO₄ anion group are highly polar. It is found that the MReO₄ molecule has two isomers. The basic isomer with C_2v symmetry has bidentate b coordination of the M⁺ cation to the ReO ₄ ^- anion. The excited isomer is of C_3v symmetry and corresponds to monodentate m coordination of M⁺. The low relative energies of the m isomers (17-29 kJ/mole) and the low energy barriers to the intramolecular mb rearrangements (5-11 kJ/mole) indicate that MReO₄ molecules are structurally nonrigid systems where the M–XO₄ chemical bonds are polytopic. The results of calculations are compared with the available literature data on the structure and vibrational spectra of MReO₄ molecules.