Understanding the Importance of Hessian in Computational Chemistry Simulations

In summary, the Hessian is needed to determine the saddle point of a reactants. If the Hessian (second derivative) switches sign it is a saddle point. If you didn't check the hessian one might not be sure that the point is a saddle point and not a min/max. The Hessian will tell you whether the energy for the calculated geometry is a local maxima or minima.
  • #1
greisen
76
0
Hi,

First I hope it is okay to post the problem here(?). I have some general questions regarding the use of software for chemistry simulations - my questions are more fundamental than software specific.

I would like to simulate a chemical reaction - so I should be searching for the saddle point of the reactants. In order to find this it is necessary with the Hessian - which is the second derivative of the energy. But why is it necessary to include this in order to compute the saddle point?

If one has problems getting the calculation of the Hessian to converge - what possible adjustments can one make - increasing numbers of iterations?

Thanks in advance
 
Physics news on Phys.org
  • #2
When a point has derivative zero it can be a min, max or a saddle point. The hessian is needed to determine which of those three types the point of interest is. If the hessian (second derivative) switches sign it is a saddle point. If you didn't check the hessian one might not be sure that the point is a saddle point and not a min/max.
 
  • #3
The Hessian will tell you whether the energy for the calculated geometry is a local maxima or minima. It will be positive for minima and negative for maxima. The first derivative or gradient (slope) only tells you where the change in energy is zero. The gradient = 0 only tells you that the geometry is at either a local minimum or maximum.

Sometimes the saddle point can be fairly steep (sharp?). To accurately converge to the optimal geometry, your program usually needs to approach the saddle point in very small increments (decrease the mesh size). This usually means that much more calculation is required (calculation = time). Some programs will decrease the mesh size when the change in the output between iterations becomes very small.

Small differences in the output can cause other problems as well. Often these calculations are handled as matrix calculations. Diagonalizing a matrix involves dividing by a difference. As the difference becomes small, the result is a large number. Large numbers and small numbers can cause significant errors in computation if they are not handled properly. I experienced a difficulty converging on an answer that was ultimately solved by declaring the matrix variables in double precision.
 

1. What is computational chemistry?

Computational chemistry is a branch of chemistry that uses computer simulations and mathematical models to study chemical systems and processes. It involves the use of algorithms, software, and high-performance computers to perform calculations and predict the behavior of atoms and molecules.

2. How is computational chemistry used in research?

Computational chemistry is used in research to design and optimize new chemical compounds, understand reaction mechanisms, and predict the properties and behavior of molecules. It is also used to study complex chemical systems such as biomolecules, materials, and environmental processes.

3. What are the benefits of using computational chemistry?

Using computational chemistry allows researchers to save time and resources by performing virtual experiments, which can reduce the need for costly and time-consuming laboratory experiments. It also provides a deeper understanding of chemical systems and can guide experimental design.

4. What types of calculations are performed in computational chemistry?

Computational chemistry uses a variety of methods and techniques, such as molecular mechanics, molecular dynamics, quantum mechanics, and density functional theory, to perform calculations on chemical systems. These calculations can range from simple energy calculations to complex simulations of chemical reactions.

5. Is computational chemistry accurate?

The accuracy of computational chemistry depends on the methods used and the complexity of the chemical system being studied. While it cannot replace experimental data, it can provide valuable insights and predictions that can guide experimental work. With advancements in technology and methods, computational chemistry continues to improve in accuracy and reliability.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
797
  • STEM Academic Advising
Replies
14
Views
969
  • Computing and Technology
Replies
32
Views
863
Replies
5
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
717
  • Quantum Interpretations and Foundations
6
Replies
204
Views
7K
  • Biology and Chemistry Homework Help
Replies
6
Views
2K
  • Quantum Physics
Replies
22
Views
411
  • Computing and Technology
Replies
20
Views
2K
Back
Top