# The Basic Theorem of Temperature-Dependent Processes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Discussion

**“if there exists a linear correlation for “structure–properties” at two temperatures, the point of their intersection will be a common point for the same correlation at other temperatures, until the Arrhenius law is violated”.**To prove the

**theorem**, we consider the right-hand side plot in Figure 1 separately, which is a typical case of an LFER $\sigma $-correlation plot in the Arrhenius equation approximation presented in Figure 2.

**“basic theorem of isokinetic relationships”**.

## 3. Some Consequences of the Theorem

#### 3.1. Interpretation of Known Empirical Regularity

**LFER (a linear free-energy relationship)**principle and their energy parameters, the

**isokinetic relationship**or

**compensation effect**. In addition, the consequences of the theorem enable us to understand the physical meaning of certain empirical regularities. Equally interesting and useful in a practical sense is considering the regions diagram shown in Figure 2. It is about the patterns of change in the same type of processes in which the operating temperature (T${}_{i}$) changes in regions before and after ${T}_{iso}$, or in which the parameter ${\sigma}_{i}$ changes in regions before and after ${\sigma}_{iso}$.

#### 3.2. The Effect of the Temperature on the Impact of Variable Parameter ${\sigma}_{i}$

**the order of the effect of the variable ${\sigma}_{i}$ in a series of reactions of the same type reverses during the transition of the operating temperatures through**

**T**

**${}_{\mathit{i}\mathit{s}\mathit{o}}$.**We want to emphasize that this conclusion arises from a mathematical analysis of the obtained dependencies, assuming that they are preserved when passing through a point T${}_{iso}$. To date, there is almost no experimental evidence for this [84,85,86,87], and more experimental evidence is clearly needed.

#### 3.3. The Effect of the Variable Parameter ${\sigma}_{i}$ on the Free Energy of Activation

#### 3.4. The Negative Activation Energies

## 4. Outlook and Possible Applications

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Temperature dependence of a well-behaved linear free-energy relationship (LFER).

**Left-hand side**: Arrhenius plot. Introduction of the isokinetic parameter $\sigma $(iso) would make the specific rate, k(iso), insensitive to temperature (upper broken line).

**Right-hand side**: $\sigma $-correlation plot. At the isokinetic temperature, ${T}_{iso}$, the specific rate, $k\left({T}_{iso}\right)$, is insensitive to parameter variation. Figure is adapted from R. Schmid et al. [79].

**Figure 2.**The LFER-correlation plots of f(T1) to f(T4) and f(T${}_{iso}$) of one series of conditional experiments with variable parameters ${\sigma}_{i}$ in the temperature range T${}_{1}$ to T${}_{4}$, including T${}_{iso}$, respectively. Groups of points A${}_{1}$, A${}_{2}$, and A${}_{3}$, A${}_{4}$ correspond to processes with parameters ${\sigma}_{1}$ and ${\sigma}_{2}$ at temperatures of T${}_{3}$ and T${}_{iso}$.

**Figure 3.**Resonance structure of the activated complex of a reaction of the radical PINO• and cumene.

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**MDPI and ACS Style**

Sapunov, V.N.; Saveljev, E.A.; Voronov, M.S.; Valtiner, M.; Linert, W.
The Basic Theorem of Temperature-Dependent Processes. *Thermo* **2021**, *1*, 45-60.
https://doi.org/10.3390/thermo1010004

**AMA Style**

Sapunov VN, Saveljev EA, Voronov MS, Valtiner M, Linert W.
The Basic Theorem of Temperature-Dependent Processes. *Thermo*. 2021; 1(1):45-60.
https://doi.org/10.3390/thermo1010004

**Chicago/Turabian Style**

Sapunov, Valentin N., Eugene A. Saveljev, Mikhail S. Voronov, Markus Valtiner, and Wolfgang Linert.
2021. "The Basic Theorem of Temperature-Dependent Processes" *Thermo* 1, no. 1: 45-60.
https://doi.org/10.3390/thermo1010004