# Calculate reaction heat from quantum mechanics

• zhouhao
In summary, the conversation discusses doubts about the method for constructing the chemical reaction process of quantum mechanics in the reference document provided. The method uses the time-independent Schrodinger equation to construct the reaction process for the example of H2O molecular dissociation to H+ and OH- ions. The reaction heat is defined as the difference in energy between the final and initial states of the system. However, the method relies on a hypothesis called A, which may not be certain. The conversation also raises questions about the interference from foreign particles and the completeness of the quantum mechanics model for reaction processes.
zhouhao

## Homework Statement

I have some doubts about the method constructing chemical reaction process of quantum mechanics in the referencehttp://www.southampton.ac.uk/assets/centresresearch/documents/compchem/DFT_L2.pdf, for the example of ##H_2O## molecular dissociation to ##H^+## and ##OH^-## ions, time-independent Schrodinger equation was used to construct the reaction process:
##{\hat{H}}_{H_2O}{\psi}_{H_2O}(\vec r_e^i)=E_{H_2O}{\psi}_{H_2O}(\vec r_e^i)##
##{\hat{H}}_{H^++OH^-}{\psi}_{H^++OH^-}(\vec r_e^i)=E_{H^++OH^-}{\psi}_{H^++OH^-}(\vec r_e^i)##
Reaction heat was defined as ##\Delta{H}=E_{H^++OH^-}-E_{H_2O}##
This method fixed the position of nuclears.
If I want to derive the same reaction heat as the method, but through the wavefunction of a system consist of two hydron,one oxygen and ten electrons,the initial and end wavefunction should rely on a hypothesis,which is called A:

##{\psi}_{H,O,e}^1(\vec r_e^i,\vec r_H^1{(H,O,e),\vec r_H^2{(H,O,e))},\vec r_O{(H,O,e)}={\psi}_{H_2O}(\vec r_e^i)\delta^{\frac{3}{2}}({\vec r_H^1{(H,O,e)}-\vec r_H^1{(H_2O)}})\delta^{\frac{3}{2}}({\vec r_H^2{(H,O,e)}}-\vec r_H^2{(H_2O)}})\delta^{\frac{3}{2}}({\vec r_O{(H,O,e)}-\vec r_O{(H_2O)}})##

##{\psi}_{H,O,e}^2(\vec r_e^i,\vec r_H^1{(H,O,e),\vec r_H^2{(H,O,e)},\vec r_O{(H,O,e))}={\psi}_{H^++OH^-}(\vec r_e^i)\delta^{\frac{3}{2}}({\vec r_H^1{(H,O,e)}-\vec r_H^1{(H^++OH^-)}})\delta^{\frac{3}{2}}({\vec r_H^2{(H,O,e)}}-\vec r_H^2{(H^++OH^-)}})\delta^{\frac{3}{2}}({\vec r_O{(H,O,e)}-\vec r_O{(H^++OH^-)}})##

Then there is:
##{\hat{H}}_{H,O,e}{\psi}_{H,O,e}^1=E_{H_2O}{\psi}_{H,O,e}^1##
##{\hat{H}}_{H,O,e}{\psi}_{H,O,e}^2=E_{H^++OH^-}{\psi}_{H,O,e}^2##

When the hydron oxide electronic system interfered by foreign particles and the foreign particles run away,wavefunction of the system would be changed from ##{\psi}_{H,O,e}^1## to ##{\psi}_{H,O,e}^2##,and release reaction heat ##\Delta{H}=E_{H^++OH^-}-E_{H_2O}##.
Problem are:
The way of constructing reaction process in reference document depend on hypothesis A,why condition A established for sure?
What kind of interference from foreign particles could cause the reaction?I mean the wavefunction depend on hypothesis A.

## Homework Equations

##{\hat{H}}_{H_2O}=
\sum\limits_{i=1}^{10}-\frac{{\hbar}^2}{2m_e}{\nabla}_e^i-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_H^1{(H_2O)}|}-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_H^2{(H_2O)}|}-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_O{(H_2O)}|}+\sum\limits_{i=1}^{10}\sum\limits_{j=i+1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_e^j|}+\frac{e^2}{|\vec r_H^1{(H_2O)}-\vec r_H^2{(H_2O)}|}+\frac{8e^2}{|\vec r_H^1{(H_2O)}-\vec r_O{(H_2O)}|}+\frac{8e^2}{|\vec r_H^2{(H_2O)}-\vec r_O{(H_2O)}|}##
##{\hat{H}}_{H^++OH^-}=
\sum\limits_{i=1}^{10}-\frac{{\hbar}^2}{2m_e}{\nabla}_e^i-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_H^1{(H^++OH^-)}|}-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_H^2{(H^++OH^-)}|}-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_O{(H^++OH^-)}|}+\sum\limits_{i=1}^{10}\sum\limits_{j=i+1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_e^j|}+\frac{e^2}{|\vec r_H^1{(H^++OH^-)}-\vec r_H^2{(H^++OH^-)}|}+\frac{8e^2}{|\vec r_H^1{(H^++OH^-)}-\vec r_O{(H^++OH^-)}|}+\frac{8e^2}{|\vec r_H^2{(H^++OH^-)}-\vec r_O{(H^++OH^-)}|}##
The Hamilton for {H,O,electrons} system:
##{\hat{H}}_{H,O,e}=
-\frac{{\hbar}^2}{2m_H}{\nabla}_{H}^1-\frac{{\hbar}^2}{2m_H}{\nabla}_{H}^2-\frac{{\hbar}^2}{2m_O}{\nabla}_{O}-\sum\limits_{i=1}^{10}-\frac{{\hbar}^2}{2m_e}{\nabla}_e^i-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_H^1{(H,O,e)}|}-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_H^2{(H,O,e)}|}-\sum\limits_{i=1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_O{(H,O,e)}|}+\sum\limits_{i=1}^{10}\sum\limits_{j=i+1}^{10}\frac{e^2}{|\vec r_e^i-\vec r_e^j|}+\frac{e^2}{|\vec r_H^1{(H,O,e)}-\vec r_H^2{(H,O,e)}|}+\frac{8e^2}{|\vec r_H^1{(H,O,e)}-\vec r_O{(H,O,e)}|}+\frac{8e^2}{|\vec r_H^2{(H,O,e)}-\vec r_O{(H,O,e)}|}##

## The Attempt at a Solution

So,I am confused with the model of calculating reaction heat if hypothesis A is not sure.

Last edited:
The quantum mechanics model of reaction process is not complete or there are some fundamental mistake?I am guessing that according to the law of conservation of energy,the reaction heat of dissociation of ##H_2O## should be equal to the reaction heat of formation of ##H_2O##.

## 1. How is reaction heat calculated using quantum mechanics?

Reaction heat is calculated using the principles of quantum mechanics, which is the study of the behavior of matter and energy at a subatomic level. This involves using mathematical equations and models to determine the energy changes that occur during a chemical reaction.

## 2. What is the significance of calculating reaction heat from quantum mechanics?

Calculating reaction heat from quantum mechanics allows scientists to gain a deeper understanding of the fundamental principles behind chemical reactions. This information can then be used to predict and control the outcomes of reactions, as well as develop new and more efficient chemical processes.

## 3. What factors influence the calculation of reaction heat using quantum mechanics?

The calculation of reaction heat using quantum mechanics takes into account various factors such as the molecular geometry, bond strengths, and electronic structures of the reactants and products. Other environmental factors such as temperature and pressure may also play a role.

## 4. How accurate are the results obtained from calculating reaction heat using quantum mechanics?

The accuracy of the results obtained from calculating reaction heat using quantum mechanics depends on the complexity of the reaction and the level of approximation used in the calculations. However, quantum mechanics has been shown to provide highly accurate predictions for many chemical reactions.

## 5. Are there any limitations to calculating reaction heat using quantum mechanics?

One limitation of calculating reaction heat using quantum mechanics is that it can be computationally intensive, especially for larger and more complex molecules. Additionally, some chemical reactions may involve processes that cannot be accurately described by current quantum mechanical models.

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