Introduction

Anhydrous alkali metal oxalates M2C2O4 form an interesting group of compounds with very similar layered crystal structures and well-defined oxalate anions as an independent entity surrounded by metallic cation and decompose thermally via two step process with respective carbonate as an intermediate product [2–11]:

$$ {\text{M}}_{ 2} {\text{C}}_{ 2} {\text{O}}_{ 4} \to {\text{MCO}}_{ 3} + {\text{CO}} \to {\text{MO}} + {\text{CO}} + {\text{CO}}_{ 2} $$

which differ significantly from the thermal decomposition pathway characteristic for anhydrous transition metal oxalates (one-step process following either \( {\text{M}}_{ 2} {\text{C}}_{ 2} {\text{O}}_{ 4} \to {\text{MO}} + {\text{CO}} + {\text{CO}}_{ 2} \) or \( {\text{M}}_{ 2} {\text{C}}_{ 2} {\text{O}}_{ 4} \to {\text{M}} + 2 {\text{CO}}_{ 2} \) pathway).

There is still lack of consistent theoretical description and explanation of the pathways of thermal decomposition of anhydrous metal oxalate, despite many experimental results available, but it seems plausible that the electronic structure and chemical bonding properties decide which pathway during thermal decomposition process given compound will follow and thus theoretical studies of these properties should provide us with some important information about the relations between electronic and crystal structure and bonding properties and a pathway of thermal decomposition process and in principle allow us to predict (or at least explain) the pathway experimentally observed for given compound. Our theoretical approach based on the topological analysis of electron density (Bader’s Quantum Theory of Atoms in Molecules [12] formalism) obtained from first principles FP-LAPW calculations and structural and bonding properties—bonds valence, bond strength, and stresses associated with deviation of given structure from ideal one (Brown’s Bond Valence Method [13]) applied mostly for transition metal oxalates and presented recently in a series of papers [14–20] turned out to be very promising and not only gave us additional insight into the thermal decomposition process in those oxalates but also helped us to describe it as a series of consecutive bond breaking steps proceeding in theoretically predicted order.

The results of similar analysis, carried out for anhydrous alkali metal oxalates are presented in this paper, which due to the size is divided into two parts: first one was devoted to electronic structure and electron density topology analysis and this one deals with bonding properties and thermal decomposition process analyzed in the light of entirety of the obtained results.

Results

The use of empirical correlations between the bond length and strength (valence) of chemical bonds, have a long history in crystal chemistry, starting from Pauling [21]. The present state of the art and perspectives of Bond Valence Model in inorganic crystal chemistry has been reviewed by Urusov and Orlov [22] and recently more extensively by Brown [13].

The “experimental” values of valences s expij can be easily calculated from the XRD data and since the sum of such valences will not, in general, be exactly equal to the atomic valence V i (i.e., will not fulfill the valence sum rule), the measure of the difference between the \( \sum {s_{\text{ij}}^{\exp } } \) and the expected value V i, defined as

$$ d_{\text{i}} = V_{\text{i}} - \sum\limits_{\text{j}} {s_{\text{ij}}^{\prime } } $$

can be used for calculating the reliability factor of the crystal structure. A convenient measure of the agreement over the whole structure is given by the index, D, which is the root-mean-square average of the d i values

$$ D = \sqrt {\left\langle {d_{\text{i}}^{2} } \right\rangle } $$

Larger values of d i and D indicate the existence of strained bonds, which can lead to instabilities in the crystal and show most strained regions in the structure (which can simultaneously be the sites of the highest reactivity or liability).

The difference between the theoretically predicted and experimentally observed bond lengths can be used as another indicator of bond strain. In this case, the strain factor δ for a certain group of bonds or the structure as a whole, can be described by following formula:

$$ \delta = \sqrt {\frac{{\sum\limits_{{\text{i}} = 1}^{N} {\left( {s_{\text{i}}^{\text{theor}} - s_{\text{i}}^{ \exp } } \right)^{2} } }}{N}} $$

While d i indicates the magnitude of unbalanced charge for given atom in the structure, the strain factors δ provide us with an additional information about the differences in strains acting on single bonds or group of bonds.

Brown and Shannon [23] pointed out, that bond valence not only measures the number of electrons associated with a bond, but also, in practice, the degree of covalency. Thus, Bond Valence Model can serve as additional (complementary to topological properties of bond critical point and bond order) tool for crystal bond properties analysis. For all structures studied in this paper, as a starting point in BVM analysis, the respective sets of equations (Table 1) consistent with topological properties of electron density (assumed one to one correspondence between bonds and BCPs) has been formulated and solved (assuming C–C bond valence equal to 1). Since the crystal structures of potassium and rubidium (β phase) and cesium and rubidium (α phase) anhydrous oxalates are identical, only the equations for potassium and cesium oxalates are presented here. The results of BVM calculations carried out for anhydrous alkali metal oxalates are presented in Tables 2, 4, 6, 8, 10 and 12 (calculated bond valences with residual strain factors d i and D) and Tables 3, 5, 7, 9, 11 and 13 (theoretical bond valences and bond lengths calculated according to valence sum rule equations and bonds strain factors δ for bond groups and the whole structure).

Table 1 Sets of Valence Sum Rule equations defined within Bond Valence Method formalism for structural and bonding properties analysis of anhydrous alkali metal oxalates
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Table 2 The results of BVM analysis carried out for anhydrous lithium oxalate: bond and atomic valences s ij and V ij, atomic residual strain factors d i and global structure instability index D
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Table 3 The results of BVM analysis carried out for anhydrous lithium oxalate: bond valences s calcij calculated for experimental bond lengths R exp, theoretical bond valences calculated from Valence Sum Rule equations s theorij , experimental and theoretical bond lengths R exp and R theor, relative bond differences ΔR/R and bond strain factors δ
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Table 4 The results of BVM analysis carried out for anhydrous sodium oxalate: bond and atomic valences s ij and V ij, atomic residual strain factors d i and global structure instability index D
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Table 5 The results of BVM analysis carried out for anhydrous sodium oxalate: “experimental” s calcij and theoretical s theorij bond valences, experimental and theoretical bond lengths R exp and R theor, relative bond differences ΔR/R and bond strain factors δ
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Table 6 The results of BVM analysis carried out for anhydrous potassium oxalate: bond and atomic valences s ij and V ij, atomic residual strain factors d i and global structure instability index D
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Table 7 The results of BVM analysis carried out for anhydrous potassium oxalate: “experimental” s calcij and theoretical s theorij bond valences, experimental and theoretical bond lengths R exp and R theor, relative bond differences ΔR/R and bond strain factors δ
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Table 8 The results of BVM analysis carried out for anhydrous rubidium oxalate (α phase): bond and atomic valences s ij and V ij, atomic residual strain factors d i and global structure instability index D
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Table 9 The results of BVM analysis carried out for anhydrous rubidium oxalate (α phase): “experimental” s calcij and theoretical s theorij bond valences, experimental and theoretical bond lengths R exp and R theor, relative bond differences ΔR/R and bond strain factors δ
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Table 10 The results of BVM analysis carried out for anhydrous rubidium oxalate (β phase): bond and atomic valences s ij and V ij, atomic residual strain factors d i and global structure instability index D
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Table 11 The results of BVM analysis carried out for anhydrous rubidium oxalate (β phase): “experimental” s calcij and theoretical s theorij bond valences, experimental and theoretical bond lengths R exp and R theor, relative bond differences ΔR/R and bond strain factors δ
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Table 12 The results of BVM analysis carried out for anhydrous cesium oxalate: bond and atomic valences s ij and V ij, atomic residual strain factors d i and global structure instability index D
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Table 13 The results of BVM analysis carried out for anhydrous cesium oxalate: “experimental” s calcij and theoretical s theorij bond valences, experimental and theoretical bond lengths R exp and R theor, relative bond differences ΔR/R and bond strain factors δ
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Anhydrous lithium oxalate

Data presented in Table 2 show that the crystal structure of anhydrous lithium oxalate is characterized by very small degree of deviation from ideal one (global instability index D equal to 0.11 valence units) and in the proximity of every atom in this structure all bonds are too long on average—evidently this is the results of necessary compromise between bond lengths inside oxalate anion constraining possible system geometry and minimization of electrostatic interactions between lithium cations and oxalate anions. The environments of carbon and oxygen O1 atoms are most deviated ones in the structure (d i ≅ 0.14 v.u.), while in case of lithium atoms this deviation is much smaller (d i  ≅ 0.07 v.u.) and for oxygen O2 it is practically negligible (d i below 0.03 v.u.).

The results presented in Table 3 complement the above analysis: three Li–O bonds (r2–r4) are too long and one (r1) is too short. Oxygen atom O1 forms three bonds: two of them—with carbon and lithium, (r4 and r6, respectively)—much too long and most strongly stretched and the third (r2) close to ideal one. This results in average length of the bonds created by O1 atom significantly longer than in ideal structure. Similarly, all bonds formed by carbon atom are too long leading to the highest deviation of its environment in comparison to ideal structure. O2 atom forms two bonds with lithium (r1 is too short and r3 too long, similarly deviated from ideal ones), and one slightly too long, with carbon (r5), which results in almost total stress cancellation.

Presented results, together with electronic structure and topological properties presented in Part I of this paper [1] show that in anhydrous lithium oxalate structure C–C bond is the weakest one and one can safely assume that during thermal decomposition process this bond should break as a first one. Since the strains in this structure are relatively small, one can expect their moderate relaxation and charge transfer to remaining bonds regions. The prediction of the next step in this structure is difficult, since naïve analysis based on bond orders would suggest wrongly thermal decomposition to metal and carbon dioxide (similar to e.g., anhydrous cadmium or silver oxalate [14, 15]). But it is well-known from the experiment [24, 25] that anhydrous lithium oxalate decompose thermally to lithium carbonate and then—in much higher temperature—to lithium oxide. What is more, such process of formation of metallic lithium would necessitate quite big charge transfer from oxygen atoms in COO− anions to lithium cations, which taking into account their calculated net charge equal to +0.85e and the difference in electronegativity between oxygen and lithium and strongly ionic character of Li–O bonds is not plausible and one can safely assume that much more probable is the process of breaking of these bonds, without charge transfer between lithium and oxygen and setting COO− anions free inside the gaps within cationic sub-lattice.

Therefore, in our opinion, the pathway of thermal decomposition of anhydrous lithium oxalate is as follow: first C–C bond breaks, which leads to freeing of COO− anions (connected with cationic sub-lattice via non-directional ionic bonds) and to breaking of these ionic bonds in the next step, which allow these anions to change the position and spatial orientation within coordination polyhedron built from twelve lithium cations quite easily and leads to the formation of intermediate [OCOCO2]2− anions, which afterward decompose to CO 2−3 anions and carbon oxide(II) molecules, according to the following reaction [4, 26]:

$$ {\text{C}}_{ 2} {\text{O}}_{4}^{2 - } \Leftrightarrow 2 {\text{COO}}^{ - } \to \left[ {{\text{OCOCO}}_{ 2} } \right]^{2 - } \to {\text{CO}}_{3}^{2 - } + {\text{CO}} $$

The final step in thermal decomposition process consists of the structural alteration, which—due to very high similarity of anhydrous lithium oxalate and lithium carbonate structures [27]—is relatively small (Fig. 1) and leads to lithium carbonate as a final product, in agreement with the experimental findings [24, 25].

Fig. 1
figure 1

Comparison of anhydrous lithium oxalate (a) and lithium carbonate (b) crystal structure. To emphasize structure similarities, C2O 2−4 and CO 2−3 anions have been replaced by balls (bigger and lighter), placed in the centers of mass of respective anions

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Anhydrous sodium oxalate

Similar analysis can be carried out for the rest of the structures and thus, due to some space limitations, we will focus in the rest of our paper on most important results only and present a concise analysis done on their basis. The results presented in Table 4 show that the crystal structure of anhydrous sodium oxalate is only slightly deviated from ideal one (D ≅ 0.15 v.u.) and for all atoms the bonds they are creating are too long, a compromise between bonds lengths within oxalate anion and Na–O bonds—similarly as in lithium oxalate. The environments of carbon atoms are most strongly deviated (d i ≅ 0.22 v.u.) while for the other atoms such deviation is significantly smaller (d i ≅ 0.1–0.13 v.u.).

The data presented in Table 5 shed some additional light on the structural properties of sodium oxalate: all Na–O bonds (r1–r4) are too long and r4 is most strongly stretched. O1 atom forms three too long bonds: Na–O (r2, r3) and C–O (r6) and this last one is most strongly strained one in the entire structure (δC–O1 = 0.1). Among three bonds formed by O2 atoms (r1, r4, and r5) most strongly stretched is the longest one Na–O2 (r4) and slightly weaker C–O2 (r5) while the second Na–O2 bond (r1) is practically relaxed. Carbon atom forms three, strongly strained bonds (δ ≅ 0.05, 0.1 and 0.07, for r5, r6, and r7 respectively).

Since the results of calculations of electronic structure and topological properties of electron density and BVM analysis carried out for anhydrous sodium oxalate are very similar to these obtained for lithium oxalate, one can expect to find analogous to the described above series of consecutive steps of bonds breaking/forming during thermal decomposition process and decomposition of anhydrous sodium oxalate to sodium carbonate [28, 29] (since both oxalate and carbonate structures are very similar—such structural alteration can go very easily [30] (Fig. 2).

K2C2O4

Fig. 2
figure 2

Anhydrous sodium oxalate (a) and sodium carbonate (b) crystal structures. To emphasize the similarities of these structures, C2O 2−4 and CO 2−3 anions have been replaced by balls placed in the centers of mass of respective anions (bigger ones)

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From Table 6 follows that the crystal structure of anhydrous potassium oxalate deviates quite strongly from the ideal one (D ≅ 0.29) and all bonds are too long on average (again as a result of a compromise between lengths of relatively rigid mostly covalent bonds inside oxalate anions and lengths of ionic K–O bonds and repulsion forces between potassium cations). In this case most deviated ones are potassium atoms environments (d i ≅ 0.42 v.u.)—despite as much as eight K–O bonds, since they are significantly too long and their valences too small to fully compensate potassium cation formal valence (+1). For the rest of atoms these deviations are much smaller, but still significant (d i ≅ 0.2–0.26 v.u.).

Data presented in Table 7 confirm the above conclusions: all bonds in the structure are subjected to tension and C–C bonds are most strongly stretched. K–O bonds (r1–r4) are definitely too long (with strains similar to those acting on C–C bonds) and potassium atom environment is most deviated from ideal structure. O1 atom forms two strongly stretched bonds with potassium (r3, r4) and one much weaker strained with carbon (r6). Analogously O2 creates two shorter and thus slightly less stretched bonds with potassium (r1, r2) and much less strained bond with carbon (r5). Among three bonds created by carbon, the two with oxygen (r5, r6) are relatively not much elongated, while C–C bond (r6) is under strongest strains in the structure.

Presented results show that despite the different crystal structure than in case of lithium and sodium oxalates, the properties of electronic structure, electron density topology and the results of BVM analysis are very similar to those obtained for previous two cases, which allow us to assume the same pathway of thermal decomposition process of anhydrous potassium oxalate as earlier: first C–C bond breaks, which due to excessive thermal energy leads to breaking free of remaining COO− anions and next, as a result of their translational and rotational movements leads to the formation of unstable [OCOCO2]2− anions, which afterward decompose to CO 2−3 anions and carbon oxide(II) molecules [31–33]. The final step of this process consists of the structural alteration, which—due to very high similarity of anhydrous potassium oxalate and potassium carbonate structures—should undergo very easily, resulting in the formation of potassium carbonate as a final product of thermal decomposition process (topochemical reaction [26]).

α-Rb2C2O4

From data in Table 8 follow that crystal structure of anhydrous rubidium oxalate (α phase) deviates quite much from the ideal one (D ≅ 0.22) and the strongest deviation characterizes the environment of two symmetrically non-equivalent rubidium atoms (d i ≅ 0.35 v.u.), which despite different coordination numbers and thus different number of bonds (4 and 5), form bonds which are too long and are subjected to strong tensile strains. Much less deviated are the environments of carbon (d i ≅ −0.22 v.u.; on average bonds too short, thus subjected to compressive strains) and O1 oxygen (d i ≅ +0.24 v.u.; bonds on average too long and under tensile strains), while the environments of the remaining oxygen atoms (O2–O4) are almost not deviated from ideal ones.

Additional information about the amount of strains acting locally on atoms and thus about decomposition process provide data presented in Table 9. The strongest compressive strains act on two C–O bonds C–O (r11 and r13; δ above 0.2), while two remaining C–O bonds (r10 and r12) are almost unaltered. Analogously strong strains as on bonds (r11 and r13), but tensile this time, act on Rb2–O2 bond (r 9 , δ ≅ 0.19), much weaker on three Rb–O bonds (r1–r4 and r6, δ = 0.07–0.12) and very weak ones on Rb1–O4 bond (r5, δ = 0.03). Rb2–O4 and C–C (r7, r8, and r14, respectively) are almost relaxed. Rubidium atoms Rb1 and Rb2 form respectively four (r2–r5) and five (r1, r6–r9) significantly too long bonds, resulting in high deviations of their environments from ideal ones. One can see here easily the results of very difficult-to-reach compromise between bond lengths in rigid structure of oxalate anions with directional ionic-covalent and covalent bonds and optimal length for purely electrostatic non-directional ionic Rb–O bonds. Oxygen O1 forms two, too long bonds with rubidium (r4, r6) and slightly too long with carbon (r12), resulting in high strains in its environment. In case of C1 and C2 carbon atoms, high deviation of their environments results from strong asymmetry of strains acting on C–O bonds: one of them is much too short (r11 and r13) while the second one (r10 and r12) slightly too long, which—with almost relaxed C–C bond –leads to resultant compressive strains acting in the environments of carbon atoms. Two oxygen atoms (O2 and O4) form two, too short bonds with rubidium (O4 creates yet two additional, practically relaxed Rb–O4) and in the same time one too short bond with carbon, resulting in almost zero resultant deviation of their environments from ideal one. The last oxygen atom O3 forms one, slightly too long bond with Rb (r1) and one almost relaxed with carbon (r10) resulting in a very small deviation of its environment (d i ≅ 0.03).

The results obtained for anhydrous α-rubidium oxalate (presented in Part I of this paper [1]) show that the features of electronic structure and topological properties of chemical bonds are very similar to those found for all above analyzed alkali metal oxalate. Also valences and strains acting on bonds and atomic environments, calculated according to BVM formalism are qualitatively very similar to the above ones. Therefore one can expect to find similar mechanism of thermal decomposition process with similar pathway in this case as well, leading to identical final results. This supposition is confirmed by experimental findings—α-Rb2C2O4 decomposes thermally to rubidium carbonate and carbon oxide(II) [31, 34, 35].

Detailed analysis of the obtained results allows us to propose the following pathway of thermal decomposition process of anhydrous α-rubidium oxalate: first C–C bond—the weakest one in the structure—breaks, which is followed by breaking free of remaining COO− anions (breaking Rb–O bonds) and then due to their thermally activated translational and rotational movements leads to the formation of unstable [OCOCO2]2− anions, subsequently decomposed to CO 2−3 anions and carbon oxide(II) molecules. The final step of this process consists of the structure alteration due to the strains relaxation and minimization of the interactions of carbonate anions with cationic sublattice resulting in α-rubidium carbonate crystal structure formation, which due to high similarity of oxalate and carbonate structures (see Fig. 3) should undergo very easily.

β-Rb2C2O4

Fig. 3
figure 3

The comparison of the crystal structures of anhydrous rubidium oxalate (α phase; left column) and rubidium carbonate (α phase; right column). To emphasize the similarities of both structures, C2O 2−4 and CO 2−3 anions have been replaced by balls (bigger ones in the figure) placed in the center of mass of respective anions

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Since the crystal structures of anhydrous β-rubidium and potassium oxalates are very similar to each other (isostructural compounds), one can expect that despite minor differences in electronic structure and bonding properties and strain distribution, in both cases the thermal decomposition process will follow identical pathway. The detailed analysis of the results of electronic structure, electron density topology, and BVM analysis carried out for anhydrous β-rubidium oxalate confirm strongly this supposition (due to some space limitations we have omitted the details of this analysis here and let interested readers to do it by themselves) and allow us to state that also in this case the final products of thermal decomposition process are respective carbonate (β-rubidium carbonate) and carbon oxide(II).

Cs2C2O4

Analogously to the last example, the crystal structure of anhydrous cesium oxalate is isostructural with α-rubidium oxalate structure and the results obtained for the former are very similar to the ones obtained for the latter. Thus again, due to the lack of space we have omitted the details of this analysis here and let interested readers to do it by themselves.

The conclusions one can draw from the mentioned analysis are as follow: first C–C bonds break and this is followed by Rb–O bonds breaking and freeing COO− anions, which due to spatial reorientation and position changing, form a bond between oxygen atom from one anion and carbon atom from the other one, creating unstable intermediate [OCOCO2]2− anions, decomposed afterward to carbonate anions CO 2−3 and carbon oxide(II) molecules. The whole process is ended by structure alteration to minimize the interactions between carbonate anion and cationic sublattice (process energetically not very demanding, since both oxalate and carbonate structures are very similar, therefore it should undergo very easily), resulting in a formation of potassium carbonate as a final product of thermal decomposition process.

Conclusions

Theoretical analysis of the results of FP-LAPW ab initio calculations of electronic structure, total electron density topology (within Bader’s QTAIM formalism), and bond valence (Brown’s BVM approach) carried out for anhydrous alkali metal oxalates presented in this paper allows us to formulate the following conclusions. The proposed-by-us approach to the problem of thermal decomposition process in oxalates, namely using theoretical methods for the analysis of electronic structure and bonding properties to be able to predict (or at least to explain) the most probable pathway of thermal decomposition process in given oxalate, has been very useful when applied for transition metal anhydrous oxalates [14–20], but in case of alkali metal oxalates has faced some difficulties. These difficulties follow mostly the constraints of the methods used in our approach, which despite the complex treatment of the problem of bonding properties in crystal structure (global: from a point of view of band structure and densities of states, total and projected onto particular atoms and atomic orbitals and local: from a point of view of topological properties of bond critical points and local strains acting on particular bonds) allow analyzing properties permitting to propose the most probable sequence of structure decomposition (bonds breaking and related relaxation and structure alteration processes), but does not allow in a simple way taking into account the bond formation processes, which takes place during thermal decomposition of anhydrous alkali metal oxalates. Therefore this approach, when applied without due consideration, suggests the thermal decomposition to metal and carbon dioxide, in contradiction with the experimentally observed decomposition to metal carbonate and carbon oxide(II). Only more thorough analysis, taking into account not only topological properties of bonds and strains acting on them but also the properties of particular atoms in given structure (especially cations) and their influence on the character and properties of bonds (particularly metal–oxygen bonds, which in our opinion play a key role in thermal decomposition process, determining the decomposition pathway to carbonate, metal or metal oxide) allow explaining dissimilarity of decomposition pathway in case of ionic anhydrous oxalates.

While the topological analysis alone does not show so distinctly the differences of the properties of metal–oxygen bonds between d-electron metal and alkali metal anhydrous oxalates, the results of electronic structure calculations allow distinguishing of such properties very easily, since they show clearly not only how big are the differences resulting from different occupations of electronic shells in particular cations, but also how similar are the partial densities of states distribution projected onto particular atomic orbitals of carbon and oxygen, confirming the conclusions following from structural analysis about comparatively weak influence of the oxalate anion environment (cation type) on the behavior and properties of carbon and oxygen electrons, filling in qualitatively very similar way the same bands with like energies in different oxalate. It is, however, necessary to underline that as it follows from standard quantum mechanical simulation, the isolated oxalate anion tend to assume energetically most stable conformation in which COO− groups in oxalate anion are rotated against each other by 90° (symmetry D2d), while in most oxalates these anions have planar symmetry (D2h) with only two exceptions known to us (isostructural anhydrous α-rubidium and cesium oxalates), which shows that one cannot completely exclude the interactions between oxalate anions and cationic sub-lattice from theoretical analysis.

The topological analysis of electron density and properties of bond critical points shows that in all analyzed alkali metal anhydrous oxalates C–C bonds are the weakest ones, metal–oxygen bonds are slightly stronger, and carbon–oxygen bonds are the strongest (but the latter differ from the remaining ones in much smaller degree than in case of transition metal oxalates [14–20]). This allows us to formulate a thesis, that in every case of alkali metal oxalate, carbon–carbon bond will break as the first one during thermal decomposition process, resulting in partial structure alteration and strain relaxation. The most probable next step is breaking of Me–O bonds and setting free COO− anions inside the gaps within cationic sub-lattice, which can either give an electron to nearest cation (highly improbable thermodynamically) or due to thermally activated translational and rotational vibrations form a bond between oxygen atom from one anion and carbon atom from the other creating intermediate thermodynamically unstable [OCOCO2]2− anions, each of which decomposes shortly afterward to energetically stable CO 2−3 anion and electrically neutral carbon oxide(II) molecule. As we have shown in Figs. 1, 2, and 3 (due to space limitations we did it only for three oxalates, but this is true for all cases) respective oxalate and carbonate structures are very similar (decomposition process of anhydrous alkali metal oxalate is an example of topochemical reaction), thus the process of structure alteration from transitional structure (a result of creating carbonate anion in cationic sub-lattice of anhydrous oxalate) to respective carbonate can undergo relatively easy.

Summing up, the results presented in this paper allow us to state, that despite the fact that our theoretical approach faced some problems related to the process of bond forming during thermal decomposition of anhydrous alkali metal oxalates (C–O bonds), taking into account in our analysis also, apart from direct properties of chemical bond, factors related to the properties of particular atoms, shed some light on the bonding properties and their relation to particular thermal decomposition pathway and allowed us to formulate consistent picture of thermal decomposition of these compounds and to propose the most probable sequence of elementary bond breaking/creating steps taking place during this process, resulting in respective carbonate and carbon oxide(II) as a final products.

Finally, we would like to add one comment of a general nature considering the set of theoretical methods we used in presented analysis. The limitations of quantum mechanical methods applied to periodic solids are well-known and besides them one have to be also aware of the fact that electronic structure calculations within DFT formalism (the same applies to HF method) are done for stationary state which means that we can get the information (quite precise we may add) only for the initial state. The rest is of more or less hypothetical nature, but on a basis of additional data (from BVM analysis) providing us with some information about strains acting on particular bonds, local atomic environments, and overall structural deviation from ideal one, one can infer (even if mostly qualitatively) the most probable behavior of the structure in one or two next steps of thermal decomposition process, namely how the electron charge should flow and bond lengths change, both resulting in strain relaxation and thus bonds strength change, which usually is sufficient to allow one to propose the most probable sequence of consecutive steps leading to a final structure. In case of two step decomposition process this is even more difficult due to the necessity of taking into account the additional processes of bond formation, but even in this case, as we tried to show in this paper, it is possible to get some important insight into the thermal decomposition process and find the highly probable source of its different pathway in comparison with transition metal oxalates. One could try to use alternative approaches to get more quantitative results, e.g., molecular dynamics simulations or separate calculations for all possible consecutive transition states starting from initial structure up to the final one, but first of all this is not possible with the proposed approach based on this particular type of quantum mechanical calculations and it would require a choice of different methods, second it would be very tedious and time and resources consuming process and third, we are quite convinced that at the end, one would not get considerably more valuable information about thermal decomposition process in oxalates, resulting in an overall picture of thermal decomposition process, which would be significantly different than the one we propose.