# Exercise I: Structure and Electronic Energy of a Small Molecule


## Introduction

In this exercise the equilibrium structure and the electronic energy of a small molecule (or molecules) are calculated using various ab initio methods. This exercise has seven basic goals:

• to get to know the computing environment used in ab initio calculations
• to learn how to connect to a remote computer from the computers at the university and how to use the unix environment.
• to learn how to construct a simple z-matrix.
• to obtain basic knowledge of the Molpro program, so that you can use it to perform your ab initio calculations.
• to familiarize yourself with various ab initio methods encountered in the lectures such as HF, MP2, QCISD, CCSD(T) and B3LYP, and to let you understand their accuracy and capabilities with respect to experimental data.
• to familiarize yourself with some of the common ab initio basis set acronyms, to give you some hints on the methods which are used to obtain them, and to give you an idea of the computational efforts to obtain accurate results.
• to apply these methods and basis sets for the calculation of the equilibrium structures and electronic energies for H2, CO, H2, H2O2 and NH3.

## 2 A Quick Theoretical Overview

### 2.1 Ab initio methods

The term ab initio means from first principles. This does not mean we are solving the Schr¨odinger equation exactly. Rather, we are selecting a method that, in principle, can lead to a reasonable approximation to the solution of the Schr¨odinger equation, and then selecting a basis set that will implement that method in a reasonable way. By reasonable, we mean that the results are adequate for the application at hand. A method and basis set that is adequate for one application may be inadequate for another. We also have to take into 1 account the cost of doing calculations and the total amount of time required. A wide range of methods have been employed, but in this exercise we will restrict ourselves to one density funtional method and some commonly used methods that use molecular orbital theory (i.e. Hartree-Fock). The methods used in this exercise are the following:

• HF
• MP2
• QCISD
• CCSD(T)

### 3.5 Molden

We will use the Molden program to visualize our results. To use molden you must first type the command module load molden followed by molden work.molden to open the program.

### 3.6 Using Molpro

• All the computations will be performed in the work directory accessible via the command cd \$WRKDIR.
• Before you perform any calculations you must call molpro with the command module load molpro
• The file work.com will tell the program what to calculate.
• You can start the work by typing molpro work.com. The command molpro work.com & & will perform the calculation on the background. You can view ongoing computations with the command ps You can stop any ongoing process by pressing CTRL and C. (This is useful if you spot an error in your work file.)
• Molpro automatically makes the files work.out and work.xml
• After the calculation you should visualize your results with Molden

### 3.7 A Sample work.com File

With this sample file the geometry optimization of the H2 molecule can be performed. The texts after # are comments and can be left out of your file. ***, H2, #THIS IS HOW THE WORK NAME IS GIVEN ang #THE BOND LENGTHS WILL BE GIVEN IN Å geometry={ H1; H2,H1,r12} #THIS Z-MATRIX IDENTIFIES THE MOLECULE UNDER INVESTIGATION r12=0.74144 #HERE ARE THE STARTING VALUES FOR THE VARIABLES WITHIN THE Z-MATRIX basis=STO-3G #THE BASIS SET IS GIVEN HERE hf ccsd(t) #THIS IS THE COMPUTATIONAL METHOD USED. ALL METHODS EMPLOYING THE HF DETERMINANT AS A STARTING POINT SHOULD DO A HF CALCULATION FIRST optg #THE COMMAND TO OPTIMIZE GEOMETRY. IF THIS IS MISSING, ELECTRONIC ENERGY WILL BE COMPUTED ONLY WITH THE GIVEN GEOMETRY put,molden,h2.molden #MAKES AN INPUT FILE FOR MOLDEN 8

### 3.8 The Structure of the Z-Matrix

In general the z-matrix has the following structure

geometry={

Atom1;

Atom2,Atom1,r12;

Atom3,Atom1,r13,Atom2,a312;

Atom4,Atom3,r43,Atom1,a431,Atom2,t4312;

Atom5,Atom3,r53,Atom1,a531,Atom4,t5314}

Where Atomx should be replaced by the chemical symbol for the atom in question (O for oxygen etc.). To differentiate between atoms of the same kind, a serial number can be inserted behind the symbol (such as H1 and H2 in the sample work.com file). The letters r stand for bond lengths, a stand for bond angles and t for dihedral angles. For example r12 is the bond length between atoms 1 and 2, a312 is the bond angle between atoms 3, 1 and 2 (with atom 1 in the middle) and t4312 is the dihedral angle between atoms 4,3,1 and 2.

### 3.9 The Results

You can collect some of your results to the table below. Feel free to extend the table for the other calculations you perform. If you have time you may try other methods besides those described in this exercise, such as the explicitly correlated CCSD(T)-F12a-method (or if you are looking for a real challenge the local DFSCS-LMP2 method). In these cases you should consult the Molpro manual at http://www.molpro.net/info/current/doc/manual.pdf

 Molecule HF/STO-3G MP2/6-31G(d) CCSD(T)/AVTZ Experimental Coord1 Coord2 Energy time

## 4 Experimental structures of some molecules:

• $$\ce{H2}$$: r=0.74144 Å
• $$\ce{CO}$$: r=1.12832 Å
• $$\ce{H2O}$$: r=0.9578 Å and a=104.48°
• $$\ce{H2O2}$$: r(O-H)=0.967 Å, r(O-O)=1.4556 Å, a(O-O-H)=102.32°, and a(dihedral)=113.70°
• $$\ce{NH3}$$: r(N-H)=1.016, and a(H-N-H)=106.7 °

Exercise I: Structure and Electronic Energy of a Small Molecule is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.