# COMPUTATIONAL CHEMISTRY

## Learning outcomes of the course unit

The educational objectives of the Computational Chemistry Course agree with those foreseen by the Degree Course Council:

Knowledge and ability to understand

The student has:

- knowledge and ability to understand knowledge of the structural characterization methods of organic and inorganic compounds and materials

- knowledge of the correlations between structure and properties of molecules and materials

- knowledges, also at practical and operational levels, of computational chemistry methods for the study and characterization of molecular properties

- knowledge on obtaining chemical information by consulting databases

Ability to apply knowledge and understanding

The student:

- is able to understand and predict the relationship between structure and properties of even complex systems;

- possesses advanced skills in the processing of scientific data;

-It has the ability to understand a problem related to his profession, to perform a critical evaluation and to propose specific solutions

- possesses the ability to use scientific instruments, to process data

experimental, to plan and execute the analysis and characterization of real samples;

- is able to make use of IT / computational methods for data processing.

Autonomy of judgment

The student:

- is able to critically evaluate his knowledge and skills and his results;

- possesses organizational skills at work and ability to organize group work;

- is able to evaluate the structure-property correlations using the most modern computational techniques;

- is able to find and analyze sources of information, databases, literature;

Communication skills

The student is able:

- to communicate in written and verbal form on chemical / scientific problems, also with the use of multimedia systems and also in English;

- to support a contradictory on the basis of a judgment developed autonomously on issues

inherent to their studies;

- to interact with other people and work in groups also on multidisciplinary projects, although it is

also able to work in full autonomy both from the point of view of temporal planning and the objectives and methods to achieve them;

- to carry out training and experimental training activities for undergraduate students.

Learning skills

The student:

- is able to easily retrieve information from literature, databases and the internet;

- possesses personal skills in logical reasoning and in the critical approach to new problems;

- is able to learn independently, addressing new scientific issues or professional problems;

- is able to continue to independently study solutions to complex problems also

interdisciplinary, finding the information useful to formulate answers and knowing how to defend their own

proposals in specialized and non-specialized contexts.

## Prerequisites

Basic elements of molecular quantum mechanics

## Course contents summary

Theory:

1) The surfaces of molecular potential energy

2) Concepts and methods of molecular electronic structure

3) The Hartree-Fock Method

4) Expansion basis sets for molecular orbitals

5) Post-SCF methods of electronic correlation

6) Density functional theory

7) Electronic properties from Hartree-Fock and DFT calculations

8) Study of potential energy surfaces (PES):

9) Vibrational frequencies from calculations of molecular electronic structure

10) Thermochemistry in gas phase from calculations of electronic structure

11) NMR shielding constants from calculations of molecular electronic structure

12) Reaction mechanisms and potential energy surfaces

13) Explicit and implicit models of solvation

Laboratory:

1) Calculation of Hartree-Fock and DFT equilibrium geometries

2) Electronic structure and molecular orbitals from Hartree-Fock and DFT calculations

3) Hartree-Fock and DFT calculations of the molecular electrostatic potential

4) Hartree-Fock / MP2 / DFT calculations of the dissociation enthalpy of chemical bonds

5) DFT calculation of chemical shifts in organic compounds

6) DFT / PCM calculation of the energy profile for a SN2 reaction in gas phase and in solution

## Course contents

1. The surfaces of molecular potential energy

a. Hamiltonian and molecular wave function

b. Born-Oppenheimer approximation

c. The electronic problem

d. The nuclear problem

e. Molecular energy surfaces (PES)

f. Minimum and saddle points of the PES

2) Concepts and methods of molecular electronic structure

b. Electronic wave functions

c. Methods of molecular electronic structure

3) Hartree-Fock method

a. The single-determinant wave function

b. The Hartree-Fock energy and its components

c. Fock equations

d. The algebraic approximation and the Roothan-Hall equations

e. Hartree-Fock Closed-Shell / Open-Shell wave functions

f. Structure of the software for the Hartree-Fock calculation

4) Basis sets for molecular calculations

a. Gaussian primitive functions

b. Minimal basis sets

c. Multiple-Zeta basis sets

d. Polarization functions

e. Diffuse functions

f. Effective core potentials

5) Post-SCF methods of electronic correlation

a. Limits of the Hartree-Fock method and correlation energy

b. Post-Hartree-Fock methods

c. Configuration interaction methods (CI)

d. Moeller-Plesset perturbation methods

is. Coupled-clusters methods

6) Density functional theory

a. The theorems of Hohemberg and Kohn

b. The Kohn-Sham method

c. Exchange and correlation energy

d. Kohn-Sham equations

e. The exchange and correlation functional s

7) Electronic properties from Hartree-Fock and DFT calculations

a. Software for Hartree-Fock and DFT calculations

b. Hartree-Fock and DFT electronic energy

c. Molecular orbitals and orbital energies

d. Electronic density and density matrix: atomic charges and bond-order indexes

e. Electronic density analysis according to Mulliken

f. Molecular electric dipole moment

g. Molecular electrostatic potential

8) Study of potential energy surfaces (PES):

a. Minimum points and saddle points of the PES

b. Geometry optimization: energy analytical gradients and optimization algorithms.

9) Vibrational frequencies from calculations of molecular electronic structure

a. The nuclear problem

b. The harmonic approximation and the calculation of the vibrational frequencies

c. The zero-point energy

d. Calculation of harmonic frequencies in Gaussian 16

10) Thermochemistry in gas phase from calculations of electronic structure

a. From the function of molecular partition to the thermodynamic functions of internal energy, enthalpy, entropy, Gibbs and Helmholtz energies

b. Contributions to the molecular partition function

c. Thermodynamic functions at 0K

d. Thermal contributions to thermodynamic functions

e. From the molecular partition function to the equilibrium constants

11) NMR shielding constants from calculations of molecular electronic structure

a. Molecular properties as derivatives of electronic energy

b. The NMR shielding constants according to the Ramsey theory

c. NMR calculations in Gaussian 16

12) Reaction mechanisms and potential energy surfaces

a. Minimum, saddle points of the PES, intrinsic co-ordinate of reaction

b. Transition states and potential energy barriers (activation energy)

c. Study of reaction mechanisms in Gaussian 16

d. From activation energy to constant kinetics: transition state theory.

13) Solvation models.

a. Explicit and implicit models of solvation

b. The Polarizable Continuum Model (PCM)

c. The PCM in Gaussian 16

## Recommended readings

I.N. Levin, "Quantum Chemistry", 6th Ed., Pearson, Pearson, 2009

J.B. Foresman and Ae. Frisch, “Exploring Chemistry with Electronic Structure Methods”, 3rd Ed., Pittsburg,2017

## Teaching methods

The teaching activities consist of Lectures (32h), laboratory exercises and practice (30h), and by tutoring seminars.

The slides used during the Lectures will be weekly uploaded on the Elly platform.

The slides will be part of the teaching material along with the reference text book.

## Assessment methods and criteria

The final verification will consist of an oral examination aimed to assess the degree of knowledge and understanding of the computational chemistry tools for the study and characterization of the properties of molecular systems of current chemistry interest.