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Specifying Molecular Electronic and Geometrical Structures

Specifying Molecular Electronic and Geometrical Structures. Parts I: Cartesian Coordinates. How to Construct Cartesian coordinates of an Atom in a Molecule. e.g., C 2v H 2 O. sp 3 hybridization of the O center. y. H1. H2. 104 . 0.9. O. x.

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Specifying Molecular Electronic and Geometrical Structures

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  1. Specifying Molecular Electronic and Geometrical Structures

  2. Parts I: Cartesian Coordinates

  3. How to Construct Cartesian coordinates of an Atom in a Molecule e.g., C2v H2O sp3 hybridization of the O center y H1 H2 104 0.9 O x Using Cartesian coordinates of H2 as an example H 0.709 0.554 0.000 Syntax for the Cartesian coordinate format: Atomic label, x-coordinate, y-coordinate, z- coordinate

  4. 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 (Unit used : angstrom for lengths) Atomic symbol The Cartesian coordinate style is not intuitive to give us bond lengths, bond angles, and dihedral angles of atoms of interest!

  5. Parts II: Z-matrix (Internal Coordinates)

  6. 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 1, and atom 2 Dihedral angle: Formed by the plane containing atoms 2-4 with the plane containing the current atom, atom 2, and atom 1

  7. Molecular Structure Specification for Hydrogen Peroxide in Z-matrix Format Without Variables e.g., C2 H2O2 Here is the molecular structure of hydrogen peroxide in the Z-matrix format 3 2 3 4 1 (Positive dihedral angles correspond to clockwise rotation in Newman projections) 4 Spin multiplicity Total charge on the molecule 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

  8. 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

  9. 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 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. 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

  10. Construct a Z-matrix for a More Complex Molecule e.g., Cs, Propene (CH2CHCH3) Step 1: Specify carbon atoms 1.09 1.34 120 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

  11. 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 1.34 120 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 !

  12. Construct a Z-matrix for a More Complex Molecule e.g., Cs, Propene (CH2CHCH3) 1.09 Step 3: Specify the planar hydrogen on C3 1.34 120 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

  13. 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 1.34 120 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

  14. 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 1.34 120 1.52 1.09 Step 5: List all created internal coordinates in a Z-matrix

  15. Parts III: Mixed Internal and Cartesian Coordinates

  16. 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

  17. 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

  18. 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

  19. Parts IV: Using Dummy Atoms in Z-matrices

  20. Use of Dummy Atom X to Fix the Three-fold Axis in C3v Ammonia Cs: e.g., C3v, NH3 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 use of dummy atoms within Z-matrices, which are represented by the pseudo atomic symbol X, is to fix a symmetric axis

  21. Use of Dummy Atom X to Contact Nonbonding Molecular Fragments X J. Phys. Chem. B113 (2009) 5290 In the calculations, a dummy atom X is placed in the six-atom cycle

  22. Sources for Geometrical Structural Parameters • Periodic table of elements • Standard references like the CRC series • Published experiments and calculations • Hybridization of central ions or atoms

  23. Parts V: Summarize Geometry Specification

  24. 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

  25. Connectivity Specification H3 H5 C1 C2 H4 H6 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 Atom1 D2=0.0 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. • careful, though 2 5 1. 6 1. • assigning the same label to two or more geometric variables means they have to remain equal throughout entire calculation 3 Geometrical connectivity 4 5 6

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