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 sp3 hybridization of the O center e.g., C2v H2O y Using Cartesian coordinates of H2 as an example H1 H2 104 0.9 H 0.709 0.554 0.000 O x Syntax for the Cartesian coordinate format: Atomic label, x-coordinate, y-coordinate, z- coordinate The Cartesian coordinate style is not intuitive to give us bond lengths, bond angles, and dihedral angles of atoms of interest!

Molecular Structure Specification for Water e.g., C2v H2O y Here is the molecular structure of water that is given in Cartesian coordinates H1 H2 104 0.9 O x Spin multiplicity Total charge on this molecule 0 1 O 0.000 0.000 0.000 H -0.709 0.554 0.000 H 0.709 0.554 0.000 x-Coordinate y-Coordinate z-Coordinate Atomic symbol Unit used: angstrom for lengths

Parts II: Z-matrix (Internal Coordinates)

Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format Without Variables e.g., C2 H2O2 Using H4 internal coordinates as an example 3 H 2 0.9 1 105. 3 120. 2 1 4 Syntax for The Z-matrix format: Atomic label, Atom 2, Bond length, Atom 3, Bond angle, Atom 4, Dihedral angle 3 4 Atomic label: For current atom Atoms 1-3: Previously specified atoms, namely reference atoms Bond length: For the bond joining the current atom to atom 2 Bond angle: Formed by this bond and the bond joining atom 2, and atom 3 Dihedral 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 e.g., C2 H2O2 3 Here is the molecular structure of hydrogen peroxide in the Z-matrix format 2 3 4 1 (Positive dihedral angles correspond to clockwise rotation in Newman projections) 4 Total charge on the molecule Spin multiplicity 0 1 O O 1 1.4 H 1 0.9 2 105. H 2 0.9 1 105. 3 120. Oxygen atom #1 Oxygen atom #2: O2-O1 = 1.4 Ǻ Hydrogen #3: H3-O1 = 0.9 Ǻ; H3-O1-O2 = 105 Unit: Angstrom for lengths and degrees for angles Hydrogen #4: H4-O2 = 0.9 Ǻ; H4-O2-O1 = 105; H4-O2-O1-H3 = 120

Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format With Variables e.g., C2 H2O2 Here is another version of the hydrogen peroxide molecular specification 3 2 1 0 1 O O 1 R1 H 1 R2 2 A H 2 R2 1 A 3 D Variables: R1 1.4 R2 0.9 A 105. D 120. 4 Oxygen atom #1 Oxygen atom #2: O2-O1 = R1 = 1.4 Ǻ Hydrogen #1: H3-O1 = R2 = 0.9 Ǻ; H3-O1-O2 = A = 105 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 e.g., C2, H2O2 Here is the third version of the hydrogen peroxide molecular specification 3 1 2 Total charge on the molecule Spin multiplicity 4 0 1 O O 1 R1 H 1 R2 2 A H 2 R2 1 A 3 D Variables: R1 1.4 R2 0.9 Constants: A 105. D 120. Oxygen atom #1 Oxygen atom #2: O2-O1 = R1 = 1.4 Ǻ Hydrogen #1: H3-O1 = R2 = 0.9 Ǻ; H3-O1-O2 = A = 105 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 e.g., Cs, Propene (CH2CHCH3) 1.09 Step 1: Specify carbon atoms 120 1.34 The atoms inside the redline all lies in a plane 1.52 1.09 0 1 C C 1 C2C C 2 C3C 1 A3 Variables: C2C 1.34 C3C 1.52 A3 120. Charge and multiplicity C: C1 at the end of the double bond C: C2 on the other end of the double bond C: C3 Third carbon C2C: C-C double bond length C3C: C-C single bond length A3: C3-C2-C1 bond angle

Construct a Z-matrix for a More Complex Molecule e.g., Cs, Propene (CH2CHCH3) Step 2: Specify the hydrogens on C1 and C2 1.09 H 1 H4C 2 A4 3 D4 H 1 H5C 2 A5 3 D5 H 2 H6C 1 A6 3 D5 Variables: H4C 1.09 H5C 1.09 H6C 1.09 A4 120. A5 120. A6 120. Constants: D4 0. D5 180. H: H1 120 1.34 H: H2 1.52 H: H3 1.09 H4C: H1-C1 bond length H5C: H5-C1 bond length H6C: H6-C2 bond length A4: H1-C1-C2 bond angel A5: H2-C1-C2 bond angel A6: H3-C2-C1 bond angel D4: The H1-C1-C2-C3 dihedral D5: The H2(or H3)-C1-C2-C3 dihedral Note that the decimal points in D4 and D5 must be included !

Construct a Z-matrix for a More Complex Molecule e.g., Cs, Propene (CH2CHCH3) 1.09 Step 3: Specify the planar hydrogen on C3 120 1.34 1.52 1.09 H 3 H7C 2 A7 1 D5 Variables: H7C 1.09 A7 109.5 Constants: D5 180. H: H4 H7C: H4-C3 bond length A7: H4-C3-C2 bond angle D5: D9 = D5, H4-C3-C2-C1 dihedral Newman Projections are often used to visualize dihedral angles

Construct a Z-matrix for a More Complex Molecule e.g., Cs, Propene (CH2CHCH3) Step 4: Specify the non-planar hydrogens on C3 1.09 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 120 1.34 1.52 1.09 H 3 H8C 2 A8 1 D8 H 3 H9C 2 A9 1 –D8 Variables: H8C 1.09 H9C 1.09 A8 109.5 A9 109.5 D8 60. H: H5 H: H6 H8C: H5-C3 bond length H9C: H6-C3 bond length A8: H5-C3-C2 bond angle A9: H6-C3-C2 bond angle D8: D9 = -D8, the H5-C3-C2-C1 dihedral Newman Projections are often used to visualize dihedral angles

Construct a Z-matrix for a More Complex Molecule 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 -D8 Variables: 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. e.g., Cs, Propene (CH2CHCH3) 1.09 120 1.34 1.52 1.09 Step 5: List all created internal coordinates in a Z-matrix

Parts III: Mixed Internal and Cartesian Coordinates

Cartesian Coordinates for Cr(CO)6 e.g., Oh, Cr(CO)6 0 1 Cr 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. 1.93 O 0. 0. 3.07 C 0. 0. -1.93 O 0. 0. -3.07 1.93 1.14 Electron configuration: (Ar)3d54s1 Specify the complete molecular structure

Mixed Cartesian and Internal Coordinates for Cr(CO)5NH3 0 1 Cr 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. -1.93 O 0 0. 0. -3.07 N 0 0. 0. 2.27 H 12 HN 1 HNCr 2 0. H 12 HN 1 HNCr 13 D H 12 HN 1 HNCr 13 –D Variables HN 1.02 HNCr 115. D 120. e.g., Cr(CO5)NH3 1.02 2.27 1.93 1.14 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 0 1 Cr 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. -CCr O 0 0. 0. -3.07 N 0 0. 0. 2.27 H 12 HN 1 HNCr 2 0. H 12 HN 1 HNCr 13 D H 12 HN 1 HNCr 13 –D Variables CCr 1.93 HN 1.02 HNCr 115. D 120. e.g., Cs, Cr(CO5)NH3 1.02 2.27 1.93 1.14 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: N H 1 nh H 1 nh 2 hnx H 1 nh 2 hnx 3 -120.0 Variables nh 1.0 hnx 107.5 X H3 N(X) H1 H2 C3v: N X 1 1. H 1 nh 2 hnx H 1 nh 2 hnx 3 120.0 H 1 nh 2 hnx 3 -120.0 Variables nh 1.0 hnx 110.0 The value of a bond angle appearing in Z-matrices, 180 is not accepted in previous versions of Gassian, but in the latest version. The use of dummy atoms within Z-matrices, which are represented by the pseudo atomic symbol X, is to fix a symmetric axis

In the calculations, a dummy atom X is placed in the six-atom cycle Use of Dummy Atom X to Contact Nonbonding Molecular Fragments X J. Phys. Chem. B 113 (2009) 5290 In the calculations, a dummy atom X is placed in the six-atom cycle

Sources for Geometrical Structural Parameters Published literature and periodic table of elements Standard references like the CRC series Previous calculations Hybridization of central ions or atoms hybridization Bond angle Geometry Examples sp 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 Octahedron SF6, Co(CN)6

Parts V: Summarize Geometry Specification

Cartesian & Z-matrix Styles 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: also called internal coordinates specify positions of atoms relative to one another using bond lengths, angles and dihedral angles (3N-6 variables) one section specifies connectivity, second section specifies values of variables corresponding to bond lengths, etc. Gaussian expects values in Angstroms and degrees convenient for PES scans because bonds and angles are defined explicitly

Connectivity Specification H3 H4 H6 H5 C C 1 B1 H 1 B2 2 A1 H 1 B3 2 A2 3 D1 H 2 B4 1 A3 3 D2 H 2 B5 1 A4 5 D3 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 4th 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

Connectivity Specification H3 H4 H6 H5 C C 1 B1 H 1 B2 2 A1 A3 H 1 B3 2 A2 3 D1 B4 H 2 B4 1 A3 3 D2 H 2 B5 1 A4 5 D3 D2 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

Connectivity Specification H3 H4 H6 H5 C C 1 B1 H 1 B2 2 A1 A3 H 1 B3 2 A2 3 D1 B4 H 2 B4 1 A3 3 D2 H 2 B5 1 A4 5 D3 D2 variables: B1=1.5 B2=1.1 can simplify by taking advantage of symmetry B3=1.1 expect C-H bonds to be same lengths B4=1.1 use variable B2 for all C-H bonds B5=1.1 A1=120.0 expect H-C-C angles to be the same A2=120.0 use variable A1 for all H-C-C angles A3=120.0 A4=120.0 D1=0.0 D2=0.0 D3=180.0

Connectivity Specification H3 H4 H6 H5 C C 1 B1 H 1 B2 2 A1 A3 H 1 B2 2 A1 3 D1 B4 H 2 B2 1 A1 3 D2 H 2 B2 1 A1 5 D3 D2 variables: B1=1.5 B2=1.1 can simplify by taking advantage of symmetry A1=120.0 expect C-H bonds to be same lengths D1=0.0 use variable B2 for all C-H bonds D2=0.0 Atom1 Atom2 D3=180.0 expect H-C-C angles to be the same Bond orders formed between Atoms 1, 2 use variable A1 for all H-C-C angles 1 2 2. 3 1. 4 1. 2 5 1. 6 1. careful, though 3 assigning the same label to two or more geometric variables means they have to remain equal throughout entire calculation 4 Geometrical connectivity 5 6

Geometrical structural parameters given for trans-ClCH2CH2Cl Problem Try your hand at constructing a Z-matrix of the trans conformation of dichloroethane (trans-ClCH2CH2Cl) 1.76 1.09 1.53 Geometrical structural parameters given for trans-ClCH2CH2Cl