molecular specification anan wu 2014-10-10. typical gaussian input molecular specification this...
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Molecular Specification
Anan Wu2014-10-10
Typical Gaussian Input
Molecular specification
This input section mainly specifies the nuclear positions. There are several ways In which the nuclear configuration can be specified: as a Z-matrix, as Cartesian Coordinates, or as a mixture of the two.
Gaussian Input file in Cartesian coordinates and in Z-matrix
Cartesian Z-matrix
Z-matrix: is a way to represent a system build of atoms. A Z-matrix is also known as internal coordinate representation. It provides a description of each molecule in terms of bond length, bond angle and dihedral angel, the so-called internal coordinates.
9 variables 3 variables (2 effective)
• What’s the difference between Cartesian coordinates and Z-matrix
• Why one needs to specify the nuclear configuration in Z-matrix? • How to?
Degrees of freedom A degree of freedom of a physical system refer to a real parameter that is
necessary to characterize the state of a physical system
In 3-D space, one can describe the n-particles system with 3N Cartesian coordinates. However, are all these Cartesian coordinates chemically relevant?
Degrees of freedom
𝑅=√ (𝑥1−𝑥2 )2+( 𝑦1− 𝑦 2 )2+ (𝑧 1− 𝑧 2 )2
Let’s say the C atom has coordinate (x1,y1,z1)and the O atom has coordinate (x2,y2,z2) with z2 unknown. Application of the formula for distance between two atoms results in one equation with one unknown, in which we can solve for z2.
R describes the internal motion between two atoms. Hence, it’s called internal coordinate.
Degrees of freedom
3N = 6 = 3 + 2 + 1
Translation Rotation Vibration
Degrees of freedom
Degrees of freedomMonatomic Linear Molecules Non-Linear Molecules
Translation (x, y and z)
3 3 3
Rotation(x, y and z)
0 2 3
Vibration 0 3N-5 3N-6
Total 3 3N 3N
chemically relevant
We generally use the bond length, bond angle and dihedral angle to describe the internal motions (vibrations) of the molecule. This representation is called Z-matrixrepresentation. A skillful choice of internal coordinates can make the interpretation of results straightforward.
• Why one needs to specify the nuclear configuration in Z-matrix?
Why Z-matrix?
In certain cases, Cartesian coordinates are inappropriate to describe internal motions.
How to construct Z-matrix?
Bond length:
2-1 2-1+1 N-1
Bond angle:
3-1 3-1+1 N-2
Dihedral angle:
4-1 4-1+1 N-3
3N - 6
Examples:
N2O CH3OH
Dummy atom
N2O N2O
Dummy atom
Tasks :
Group 1 : How to describe the puckering motion of cyclic molecules?
Group 2 : How to determine the symmetry of a molecule given the atomic coordinates?