Specifying Molecular Electronic and Geometrical Structures

Specifying Molecular Electronic and Geometrical Structures

Overview of Gaussian Input File Sections

Parts I: Cartesian Coordinates

How to Construct Cartesian coordinates of an Atom in a Molecule

Using Cartesian coordinates of H2 as an example

Syntax for the Cartesian coordinate format:Atomic label, x-coordinate, y-coordinate, z- coordinate

OH1 H2

x

ye.g., C2v H2O

H 0.709 0.554 0.000

The Cartesian coordinate style is not intuitive to give us bond lengths, bond angles, and dihedral angles of atoms of interest!

0.9104

sp3 hybridization of the O center

Molecular Structure Specification for Water

OH1 H2

x

yHere is the molecular structure of water that is given in Cartesian coordinates

0 1O 0.000 0.000 0.000H -0.709 0.554 0.000H 0.709 0.554 0.000

Spin multiplicityTotal charge on this molecule

Atomic symbol

x-Coordinate y-Coordinate z-Coordinate

e.g., C2v H2O

Unit used: angstrom for lengths

0.9104

Parts II: Z-matrix (Internal Coordinates)

Using H4 internal coordinates as an example

H 2 0.9 1 105. 3 120.

e.g., C2 H2O2

1

23

4 Syntax for The Z-matrix format:Atomic label, Atom 2, Bond length, Atom 3, Bond angle, Atom 4, Dihedral angle

Atomic label: For current atomAtoms 1-3: Previously specified atoms, namely reference atomsBond length: For the bond joining the current atom to atom 2Bond angle: Formed by this bond and the bond joining atom 2, and atom 3Dihedral angle: The plane containing atoms 2-4 with the plane containing the current atom, atom 2, and atom 3

Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format Without Variables

43

Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format Without Variables

Here is the molecular structure of hydrogen peroxide in the Z-matrix format

0 1O O 1 1.4H 1 0.9 2 105.H 2 0.9 1 105. 3 120.

Spin multiplicityTotal charge on the molecule

Oxygen atom #2: O2-O1 = 1.4 Ǻ

Oxygen atom #1

e.g., C2 H2O2

Hydrogen #3: H3-O1 = 0.9 Ǻ; H3-O1-O2 = 105

1

23

4

Hydrogen #4: H4-O2 = 0.9 Ǻ; H4-O2-O1 = 105; H4-O2-O1-H3 = 120

(Positive dihedral angles correspond to clockwise rotation in Newman projections)

Unit: Angstrom for lengths and degrees for angles

43

Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format With Variables

Here is another version of the hydrogen peroxide molecular specification

0 1O O 1 R1H 1 R2 2 AH 2 R2 1 A 3 D Variables: R1 1.4 R2 0.9 A 105. D 120.

Oxygen atom #2: O2-O1 = R1 = 1.4 Ǻ

Oxygen atom #1

e.g., C2 H2O2

Hydrogen #1: H3-O1 = R2 = 0.9 Ǻ; H3-O1-O2 = A = 105

1

23

4

Hydrogen #2: H4-O2 = R2 = 0.9 Ǻ; H4-O2-O1 = A = 105; H4-O2-O1-H3 = D = 120

Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format With Variables and Constants

Here is the third version of the hydrogen peroxide molecular specification

0 1O O 1 R1H 1 R2 2 AH 2 R2 1 A 3 D Variables: R1 1.4 R2 0.9

Constants: A 105. D 120.

Spin multiplicityTotal charge on the molecule

Oxygen atom #2: O2-O1 = R1 = 1.4 Ǻ

Oxygen atom #1

e.g., C2, H2O2

Hydrogen #1: H3-O1 = R2 = 0.9 Ǻ; H3-O1-O2 = A = 105

1 2

3

4

Hydrogen #2: H4-O2 = R2 = 0.9 Ǻ; H4-O2-O1 = A = 105; H4-O2-O1-H3 = D = 120

Construct a Z-matrix for a More Complex Molecule

The atoms inside the redline all lies in a plane

e.g., Cs, Propene (CH2CHCH3)

Step 1: Specify carbon atoms

0 1C C 1 C2CC 2 C3C 1 A3 Variables: C2C 1.34 C3C 1.52 A3 120.

Charge and multiplicityC: C1 at the end of the double bondC: C2 on the other end of the double bond

C: C3 Third carbon

A3: C3-C2-C1 bond angleC3C: C-C single bond length

C2C: C-C double bond length

1.34

1.52120

1.09

1.09

e.g., Cs, Propene (CH2CHCH3)

Step 2: Specify the hydrogens on C1 and C2H 1 H4C 2 A4 3 D4 H 1 H5C 2 A5 3 D5H 2 H6C 1 A6 3 D5Variables:H4C 1.09H5C 1.09H6C 1.09A4 120.A5 120.A6 120.Constants:D4 0.D5 180.

H: H1

H: H2

H: H3

D4: The H1-C1-C2-C3 dihedral

H4C: H1-C1 bond length

H5C: H5-C1 bond length

H6C: H6-C2 bond length

D5: The H2(or H3)-C1-C2-C3 dihedral

Note that the decimal points in D4 and D5 must be included !

1.34

1.52120

1.09

1.09

A4: H1-C1-C2 bond angelA5: H2-C1-C2 bond angelA6: H3-C2-C1 bond angel

Construct a Z-matrix for a More Complex Molecule

e.g., Cs, Propene (CH2CHCH3)

Step 3: Specify the planar hydrogen on C3

H 3 H7C 2 A7 1 D5 Variables:H7C 1.09A7 109.5Constants:D5 180.

1.34

1.52120

H: H4

H7C: H4-C3 bond length

A7: H4-C3-C2 bond angle

D5: D9 = D5, H4-C3-C2-C1 dihedral

1.09

Newman Projections are often used to visualize dihedral angles

1.09

Construct a Z-matrix for a More Complex Molecule

e.g., Cs, Propene (CH2CHCH3)

Step 4: Specify the non-planar hydrogens on C3

H 3 H8C 2 A8 1 D8 H 3 H9C 2 A9 1 –D8Variables:H8C 1.09H9C 1.09A8 109.5A9 109.5D8 60.

H: H5

H: H6

H8C: H5-C3 bond length

H9C: H6-C3 bond length

A8: H5-C3-C2 bond angle

D8: D9 = -D8, the H5-C3-C2-C1 dihedral

The geometry of C3 is tetrahedral, and thus the bond angle of each of the hydrogens with respect to the C3-C2 bond is 109.5

Newman Projections are often used to visualize dihedral angles

A9: H6-C3-C2 bond angle

1.34

1.52120

1.09

1.09

Construct a Z-matrix for a More Complex Molecule

e.g., Cs, Propene (CH2CHCH3)

Step 5: List all created internal coordinates in a Z-matrix

1.34

1.52120

1.09

1.09

0 1 C C 1 C2C C 2 C3C 1 A3 H 1 H4C 2 A4 3 D4 H 1 H5C 2 A5 3 D5 H 2 H6C 1 A6 3 D5 H 3 H7C 2 A7 1 D5 H 3 H8C 2 A8 1 D8 H 3 H9C 2 A9 1 -D8Variables: C2C 1.34 C3C 1.52 H4C 1.09 H5C 1.09 H6C 1.09 H7C 1.09 H8C 1.09 H9C 1.09 A3 120. A4 120. A5 120. A6 120. A7 109.5 A8 109.5 A9 109.5 D8 60. Constants: D4 0. D5 180.

Construct a Z-matrix for a More Complex Molecule

Parts III: Mixed Internal and Cartesian Coordinates

e.g., Oh, Cr(CO)6

Specify the complete molecular structure

0 1Cr 0. 0. 0. C 1.93 0. 0. O 3.07 0. 0.C -1.93 0. 0.O -3.07 0. 0.C 0. 1.93 0.O 0. 3.07 0.C 0. -1.93 0.O 0. -3.07 0.C 0. 0. 1.93O 0. 0. 3.07C 0. 0. -1.93O 0. 0. -3.07

Cartesian Coordinates for Cr(CO)6

1.93

1.14

Electron configuration: (Ar)3d54s1

Mixed Cartesian and Internal Coordinates for Cr(CO)5NH3

e.g., Cr(CO5)NH3

1.93

1.14

0 1Cr 0 0. 0. 0. C 0 1.93 0. 0. O 0 3.07 0. 0.C 0 -1.93 0. 0.O 0 -3.07 0. 0.C 0 0. 1.93 0.O 0 0. 3.07 0.C 0 0. -1.93 0.O 0 0. -3.07 0.C 0 0. 0. -1.93O 0 0. 0. -3.07N 0 0. 0. 2.27H 12 HN 1 HNCr 2 0.H 12 HN 1 HNCr 13 DH 12 HN 1 HNCr 13 –DVariablesHN 1.02HNCr 115.D 120.

1.02

2.27

Cartesian coordinates are included in a Z-matrix by specifying the bonded-to atom as 0

Mixed Cartesian and Internal Coordinates for Cr(CO)5NH3

e.g., Cs, Cr(CO5)NH3

1.93

1.14

0 1Cr 0 0. 0. 0. C 0 CCr 0. 0. O 0 3.07 0. 0.C 0 -CCr 0. 0.O 0 -3.07 0. 0.C 0 0. CCr 0.O 0 0. 3.07 0.C 0 0. -CCr 0.O 0 0. -3.07 0.C 0 0. 0. -CCrO 0 0. 0. -3.07N 0 0. 0. 2.27H 12 HN 1 HNCr 2 0.H 12 HN 1 HNCr 13 DH 12 HN 1 HNCr 13 –DVariablesCCr 1.93HN 1.02HNCr 115.D 120.

1.02

2.27

The variable names for Cartesian coordinates are given symbolically in the same manner as for internal coordinates

Parts IV: Using Dummy Atoms in Z-matrices

Use of Dummy Atom X to Fix the Three-fold Axis in C3v Ammonia

e.g., C3v, NH3 Cs

:

NX 1 1.H 1 nh 2 hnx H 1 nh 2 hnx 3 120.0 H 1 nh 2 hnx 3 -120.0Variablesnh 1.0hnx 110.0

H2

H3

H1N(X)

NH 1 nhH 1 nh 2 hnxH 1 nh 2 hnx 3 -120.0Variablesnh 1.0hnx 107.5

X

C3v:

The use of dummy atoms within Z-matrices, which are represented by the pseudo atomic symbol X, is to fix a symmetric axis

The value of a bond angle appearing in Z-matrices, 180 is not accepted in previous versions of Gassian, but in the latest version.

J. Phys. Chem. B 113 (2009) 5290

X

In the calculations, a dummy atom X is placed in the six-atom cycle

Use of Dummy Atom X to Contact Nonbonding Molecular Fragments

Sources for Geometrical Structural Parameters

Published literature and periodic table of elements Standard references like the CRC series Previous calculations

hybridization Bond angle Geometry Examplessp 180 Line CHCH, BeCl2, Hg(NH3)2+

sp2 120 Planar triangle CH2CH2, BF2, [CuCl3]2-

sp3 109.5 Tetrahedron CH4, BF2, [Ni(NH3)4]2+

dsp2 90 Square Ni(CN)42-

dsp3 90, 120 Trigonal bipyramid PCl5, Fe(CO)5

d2sp3 90 Octahedron SF6, Co(CN)6

Hybridization of central ions or atoms

Parts V: Summarize Geometry Specification

1. Cartesian coordinates:• atomic symbol, x, y, z coordinates of each nucleus• Gaussian expects values in Angstroms• convenient because most molecular building programs will

output Cartesian coordinates

2. Z-matrix coordinates:

• specify positions of atoms relative to one another using bond lengths, angles and dihedral angles (3N-6 variables)

• Gaussian expects values in Angstroms and degrees

• also called internal coordinates

• one section specifies connectivity, second section specifies values of variables corresponding to bond lengths, etc.

• convenient for PES scans because bonds and angles are defined explicitly

Cartesian & Z-matrix Styles

C1 C2

H3

H4 H6

H5

• 1st column specifies atom type

• 2nd column defines a bond, e.g. the ‘1’ in line 2 indicates that atom 2 is bonded to atom 1

• 3rd column gives the label of a variable corresponding to the bond length

• 4th column defines an angle, e.g. the ‘2’ in line 3 indicates that the 3rd atom forms a 3-1-2 (H3-C1-C2) angle

• 5th column gives the label of a variable containing the value of the bond angle

• 6th column defines a dihedral angle, e.g. the ‘3’ in line 4 indicates that the 4 th atom forms a dihedral 4-1-2-3 (H4-C1-C2-H3) dihedral angle

• 7th column gives the label of a variable containing the value of the dihedral angle

CC 1 B1H 1 B2 2 A1H 1 B3 2 A2 3 D1H 2 B4 1 A3 3 D2H 2 B5 1 A4 5 D3

Connectivity Specification

C1 C2

H3

H4 H6

H5

example:• line 5 means: a hydrogen atom is bonded atom 2 with a bond distance of B4,

forms an angle with atoms 2 and 1 with a value of A3, and forms a dihedral angle with atoms 2, 1, and 3 with a value of D2

B4A3

D2

CC 1 B1H 1 B2 2 A1H 1 B3 2 A2 3 D1H 2 B4 1 A3 3 D2H 2 B5 1 A4 5 D3

Connectivity Specification

C1 C2

H3

H4 H6

H5CC 1 B1H 1 B2 2 A1H 1 B3 2 A2 3 D1H 2 B4 1 A3 3 D2H 2 B5 1 A4 5 D3

B4A3

D2

variables:B1=1.5B2=1.1B3=1.1B4=1.1B5=1.1A1=120.0A2=120.0A3=120.0A4=120.0D1=0.0D2=0.0D3=180.0

• can simplify by taking advantage of symmetry• expect C-H bonds to be same lengths

use variable B2 for all C-H bonds

• expect H-C-C angles to be the same use variable A1 for all H-C-C angles

Connectivity Specification

C1 C2

H3

H4 H6

H5CC 1 B1H 1 B2 2 A1H 1 B2 2 A1 3 D1H 2 B2 1 A1 3 D2H 2 B2 1 A1 5 D3

B4A3

D2

variables:B1=1.5B2=1.1A1=120.0D1=0.0D2=0.0D3=180.0

• can simplify by taking advantage of symmetry• expect C-H bonds to be same lengths

use variable B2 for all C-H bonds

• expect H-C-C angles to be the same use variable A1 for all H-C-C angles

• careful, though• assigning the same label to two or more geometric

variables means they have to remain equal throughout entire calculation

1 2 2. 3 1. 4 1.2 5 1. 6 1. 3456

Geometrical connectivity

Atom1Atom2

Bond orders formed between Atoms 1, 2

Connectivity Specification

Problem

Try your hand at constructing a Z-matrix of the trans conformation of dichloroethane (trans-ClCH2CH2Cl)

1.531.76

1.09

Geometrical structural parameters given for trans-ClCH2CH2Cl