Explanation The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero. The secular determinant for a system that is described in terms of n ideal wavefunctions is expressed as follows: | H 11 − E S 11 H 12 − E S 12 ... H 1 n − E S 1 n H 21 − E S 21 H 22 − E S 22 ... H 2 n − E S 2 n ... ... ... ... H n 1 − E S n 1 H n 2 − E S n 2 ... H n n − E S n n | = 0 Where, • H is the average energy integrals. • S is the overlap integrals. • E is the energy. The number of rows and columns of a secular determinant for a system depends on the number of wavefunctions. Thus, a system that is described in terms of four ideal wavefunctions contains 4 × 4 secular determinant Interpretation Introduction (b) Interpretation: The explanation of the complexity of a secular determinant as the number of ideal wavefunctions increases is to be stated. The number of H and S integrals that are needed to be evaluated is to be predicted. Concept introduction: The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

2nd Edition

ISBN: 9781133958437

Author: Ball, David W. (david Warren), BAER, Tomas

Publisher: Wadsworth Cengage Learning,

See similar textbooks

Concept explainers

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are im…

Question

Chapter 12, Problem 12.50E

Interpretation Introduction

(a)

Interpretation:

The secular determinant for a system that is described in terms of four ideal wavefunctions is to be stated.

Concept introduction:

Variation theory states that the average energy of any wavefunction for a given system is equal to or greater than its ground-state energy. It provides more accurate value of energy for a particular system. It is used to find the approximate solutions to the Schrödinger equation.

Interpretation Introduction

(b)

Interpretation:

The explanation of the complexity of a secular determinant as the number of ideal wavefunctions increases is to be stated. The number of H and S integrals that are needed to be evaluated is to be predicted.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Expert Solution & Answer

Chapter 12 Solutions

Physical Chemistry

Ch. 12 - In the Stern-Gerlach experiment, silver atoms were...Ch. 12 - Prob. 12.2E Ch. 12 - Prob. 12.3E Ch. 12 - Suppose s=12 for an electron. Into how many parts...Ch. 12 - Using and labels, write two possible...Ch. 12 - List all possible combinations of all four quantum...Ch. 12 - What are the degeneracies of the H atom...Ch. 12 - Prob. 12.8E Ch. 12 - a Differentiate between the quantum numbers s and...Ch. 12 - Is the spin orbital 1s for the H atom still...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.