## 2 Methodology of the Analysis  
A common AHT cycle consists of two isobars and two isosteres in the Clausius-Clapeyron coordinates \(\ln(P)\) vs. \((-1/T)\) (Figure 1a). The temperatures of evaporator Tev, condenser \(T\)con, adsorption \(T\)ads, and regeneration \(T\)reg completely define this four temperature (4T) cycle. The efficiency of the adsorbent use in a particular AHT cycle is higher if the amount of adsorbate exchanged under the conditions of the cycle is larger [6]. To estimate the mass of adsorbate that the adsorbent will exchange in a specific cycle the following route is suggested: (1) measurement of adsorption isobar at the pressure \(P\)ev, and determination of the equilibrium adsorbate uptake \(w\)max at the temperature \(T\)ads, (2) measurement of the isobar at the pressure \(P\)con and determination of the equilibrium adsorbate uptake \(w\)min at the temperature \(T\)des as well as the amount of exchanged adsorbed \(\Delta w=w\)max \(-w\)min. This difference has to be maximized. Such measurements are time and labor consuming. On the other hand, for the same working pairs, the adsorption equilibrium data has already been reported in the literature, however, they were measured at temperatures and pressures different from those in the cycle studied. In this case, the equilibrium uptakes can be evaluated from the universal adsorption curve \"the adsorption capacity \(w\)--the adsorption potential \(\Delta F\)\" plotted on the basis of the already available experimental data. The Polanyi adsorption potential \(\Delta F=-RT\ln[P/P_{\rm o}(T)]\), where \(P_{\rm o}\) is the saturated vapor pressure at temperature \(T\), was introduced in 1914, considering the adsorption process similar to the compression of adsorbate vapor in a certain field of adsorption forces near the adsorbent surface [18]. Later, it was shown that the adsorption potential \(\Delta F\) can be used as a universal measure of the adsorbent affinity to the adsorptive [19]. It was found in [20] that for many adsorbents, both micro- and mesoporous, there is a one-to-one correspondence between the equilibrium uptake \(w\) and the \(\Delta F\)-value \(w=f(\Delta F)\) (Figure 1b). In other words, adsorption curves measured at different conditions coincide in the coordinates \"\(w\) vs. \(\Delta F\)\"(Figure 1b). The weak adsorption isostere (line 3-4 on Figure 1a) corresponds to the adsorption potential \(\Delta F_{1}\) at the end of desorption stage (point 3) and to the minimal uptake \(w\)min = \(w\) (\(\Delta F_{1}\)). The rich isostere (line 1-2) corresponds to the end of adsorption stage (point 1) and to the maximal uptake \(w\)max = \(w\) (\(\Delta F_{2}\)), where  
\[\Delta F_{1}=-{\rm RTregln}[P(T{\rm con})/P({\rm Treg})], \tag{1}\]  
\[\Delta F_{2}=-{\rm RTadsln}[P({\rm Tev})/P({\rm Tads})]. \tag{2}\]  
Therefore, the requirements for the adsorbent optimal for the specific AHT cycle can be formulated in terms of the boundary adsorption potentials \(\Delta F_{1}\) and \(\Delta F_{2}\): the adsorbent should exchange as much adsorbate as possible in the \(\Delta F\)-interval between \(\Delta F_{1}\) and \(\Delta F_{2}\). The boundary potentials are defined by the operating temperature \(T\)reg, \(T\)con, \(T\)ads, and \(T\)ev. These temperatures, in turn, depend on the climate of the place where the AHT unit is used, regeneration temperature, and temperature of the required useful heat/cold. In adsorption technologies, both traditional (activated carbons, zeolites, silica gels) and innovative materials (aluminophosphates, metal organic frameworks, composites \"salt in a porous matrix\"--CSPM) are used as sorbents. Pure (AIPO) and substituted aluminophosphates (MeAPO) are zeolite-like microporous structures [22; 23]. These systems are characterized by moderate hydrophilicity due to the electrically neutral network [24].