Molecular Modeling for EducatorsÔ

Semi-Empirical Quantum Mechanics

Version 5.2

CNDO

MOPAC

 

Two well-known public domain semi-empirical quantum mechanics programs are bundled into Molecular Modeling for Educators. CNDO and MOPAC are accessed through the Tools menu. They use the molecules that you draw with MMEd as input.

CNDO

This program is accessed through the Tools menu. It is used primarily for the calculation of atomic partial charge, dipole moment, HOMO and LUMO values. There is also a method for calculating Log of the octanol water partition coefficient associated with this method.

CNDO stands for 'Complete neglect of differential overlap'. It is less rigorous then the routines found in MOPAC and does not do geometry optimizations. Both programs are known as semi-empirical because they are based on a mixture of first principles of chemistry and physics with experimental results that are used to determine the Hamiltonians. Programs doing quantum chemistry based only on first principles are known as 'ab-initio' calculations. CNDO uses two main approximations that deviate from ab-initio: a) a core approximation and b) the zero-differential overlap approximation. CNDO, INDO and MNDO are examples of "Self consistent field theory", which obtain the results by solving simultaneous non-linear equations iteratively until the results between two iterations are close. CNDO knows nothing of bonds and calculates pure wave functions based on atom location and atom type. MMEd uses a version of CNDO known as CNDO/2.

CNDO is primarily used for calculation of partial atomic charge and dipole moment, for which it is known to give fairly good answers. The "closed" shell method is faster than the "open" shell method for calculating CNDO results, but the mathematics is less rigorous. CNDO also reports the total energy and binding energy of a molecule. If the closed shell method is chosen it reports the eigenvalues from which HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy levels can be determined:

Eigenvalues (energy levels) for chloroethane:

-1.5104 -1.1402 -1.004 -.90667 -.8089 -.70532 -.63821 -.56419

1 2 3 4 5 6 7 8

 

-.51512 -.51362 .099803 .22428 .23891 .26694 .26879 .28066

9 10 11 12 13 14 15 16

 

.29986 .30499 .31842 .36986 .37868 .39477

17 18 19 20 21 22

 

The HOMO value in the above example is the last negative value

(-0.51362). There are 20 valence electrons in chloroethane, with two electrons/orbital. Thus the tenth eigenvalue is the HOMO (20 divided by 2 =10) and the eleventh eigenvalue is the LUMO value (.099803).

If open shell is chosen, the results of the matrices used in calculating the results are reported. Consult a specialist in quantum mechanics to interpret these results. If you have ionic species present then use the Open shell method. The partial charges and dipole moment are at the end of the file. The file is called "CNDO.TXT". It is an ASCII file that can be stored and read later. If you have not changed the name of your word processing application in the file "moldat.txt", MMEd will attempt to open a Microsoft Notepad file to read CNDO.TXT. If the file is greater than 64 kilobytes in size Notepad cannot read it and you must use a word processor capable of reading larger files to read the results (you will be prompted for WordPad for larger files). MMEd's CNDO can handle only molecules of 75 atoms or less and cannot handle any atoms with atomic numbers greater than 18. The modified DelRe method can handle larger molecules and some atoms with higher atomic numbers (Br, I), but cannot handle some of the metal atom types handled by CNDO.

You also have the option of using the INDO procedure instead of CNDO. INDO stands for "intermediate neglect of differential overlap".

INDO is only parameterized for atoms with atomic numbers less than 9, so cannot be used for molecules with P, S or Cl in them. If you want to obtain coupling constants for the atoms in a molecule, than INDO will list this result with the partial charges at the end of the file.

CNDO has been used to determine optimum bond lengths and angles. The conformation with the lowest total energy is the most stable. Manually changing bond angles or lengths with the Change Reference bond lengths and angles option in the Geometry menu, then running CNDO could be useful for this.

CNDO is very sensitive to geometry. It may not converge or it may give very large values for partial charges if the geometry of a molecule is far from ideal, especially if there is severe non-bonded overlap. If you have this problem, optimize the geometry before running CNDO. Even with nearly optimum geometry, you may occasionally run into a problem with non-convergence (with resulting unbelievably large partial charges and dipole moments). Try rotating a bond slightly and running the program again.

After running CNDO, MMEd will keep track of the partial charges and dipole moment. The option to color the molecule by partial charges will result in the CNDO charges being displayed, instead of the modified DelRe charges.

Charge can also be used to calculate the log octanol water partition coefficient (log P, Log Kow) . A method was recently published by K.F. Moschner and A. Cece (1995) that used Gasteiger-Huckel charges and other atomic properties to calculate Log Kow. We have modified this method to work with CNDO (the regression coefficients were changed somewhat, and terms were added for aliphatic F, aliphatic Cl, and charge on sulfur). The r squared for our model was 0.90 and the model standard deviation was 0.54. The closed method of CNDO was used.

Calculating dipole moments from the Calculate menu uses the modified DelRe method and the Gasteiger method, not CNDO.

CNDO is often used instead of MOPAC for calculation of partial charges and dipole moments and some think gives a more reliable answer. The creators of CNDO found it less useful for geometry optimization and calculation of Heat of Formation and abandoned it for this reason in favor of ab-initio calculations (ab-initio is calculation from the first principles of chemistry).

 

For more on CNDO:

J. Pople and D. Beveridge, Approximate Molecular Orbital Theory, Mc Graw-Hill, 1970.

J. Pople and G.A. Segal, J. Chem. Phys., 43: 8136 (1965)

J. Pople and G.A. Segal, J. Chem. Phys., 44: 3289 (1966)

D.P. Santry and G.A. Segal, J. Chem. Phys., 47:158 (1967)

Raymond Daudel, Georges Leroy, Daniel Peeters and Michel Sana, Quantum Chemistry, John Wiley and Sons, New York, 1983.

The log P method referred to is in Environmental Toxicology and Risk Assessment - Third Volume, ASTM STP 1218, J.S. Hughes, G.R. Biddinger and E. Mones eds., Amercian Society for Testing and Materials, Philadelphia, 1995.

 MOPAC (version 6)

The semi-empirical quantum mechanics program MOPAC is accessed through the Tools menu. It has many uses including geometry optimization, calculation of some molecular properties such as heat of formation and ionization potential, and calculates partial atomic charge and dipole moments. It is capable of calculating of transition states of reactions and some thermodynamic properties. Some additional uses are described below.

This public domain version of MOPAC version 6 is included with MMEd. The program was written by J. Stewart and F. Seiler at the Air Force Academy and compiled for 32 bit WINDOWS by Victor Lobanov at the University of Florida. Since this program is public domain you may copy and distrisbute the file mopac.exe freely.

MOPAC should interact with MMEd without having to set up links to it (MMEd takes care of this). If this is not the case, do the following: Open MMEd. On the Files menu select Initialize Links. Set the three MOPAC links to:

Executable File = "c:\ your MMEd path\mopac.exe"

Input File Name = "c:\your MMEd path\for005."

Output File Name ="c:\your MMEd path\for005.mno"

After MOPAC is selected from the Tools menu the MOPAC Options window appears with a number of check boxes for you to select from. When the MOPAC job is finished, MMEd will, at the user's request, read in the geometry changes and charges.

There are three different basis sets used by MOPAC. The default method is MNDO (minimal neglect of differential overlap). AM1 (from Dewar's group at the University of Texas, Austin) and PM3 are more recent basis sets and PM3 supports quite a number of atom types in addition to those supported by MNDO. Like other semi-empirical methods the MOPAC methods use the theory of quantum mechanics (with simplifications) with basis set created in such a way to predict some molecular property. With MOPAC the experimental properties most likely to be used in creating the basis sets are Heat of formation and molecular geometry. For this reason, these two properties of molecules are often more accurately calculated than dipole moments by MOPAC.

Key words accessed through the Check Boxes

 

Example - file created with SYMMETRY key word for fomaldehyde

SYMMETRY T=3600

molecule 1

MOPAC calculations:

O

C 001.1062 1

H 001.1062 1 123.5152 1

XX 001.6090 1 109.4712 1 180.0000 1 3 2 1

H 001.1062 1 112.9740 1 000.0000 1 2 3 4

XX 002.0920 1 123.4915 1 180.0000 1 2 3 4

0 0.00 0 0.00 0 0.00 0 0 0 0

3 1 5

3 2 5

C1 CI CS 1 D2 D2D D2H 4 C(INF)V 1

C2 C2V C2H 2 D3 D3D D3H 6 D(INF)H 2

C3 C3V C3H 3 D4 D4D D4H 8 T TD 12

C4 C4V C4H 4 D6 D6D D6H 12 OH 24

C6 C6V C6H 6 S6 3

 

ROT is a necessary key word for thermodynamics calculations (see THERMO above)

 

Some other MOPAC key words

Many of the MOPAC key words are handled checking boxes within the MMEd MOPAC options window. However, additional key words can be typed in by the user in the window that appears after you select MOPAC from the Tools menu. If you wish to type more than one key word, simply leave a space between the words. Here is a description of some of the key words.

 

Using MOPAC with charged species: MMEd will make an automatic assignment for the keywords CHARGE and BIRADICAL. You can change these assignments in the MOPAC set up window that appears after selecting MOPAC from the Tools menu. We recommend running an MM2 minimization before running MOPAC if the molecule contains typical organic atoms (H,C,N,O,F,S,Cl,Br). Do not run MM2 on a biradical molecule with a halogen counterion as MM2 is unable to handle these molecules (minimize before adding the counterion).

Atom types supported by MOPAC v. 6 methods:

MNDO: H, Li, Be, B, C, N, O, F, Na, Al, Si, P, S, Cl, K, Cr, Zn, Ge, Br, Sn, I, Hg, Pb

MINDO: H, C, N, O, F, P, S, Cl

AM1: H, B, C, N, O, F, Na, Al, Si, P, S, Cl, K, Zn, Ge, Br, I, Hg

PM3: H, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Zn, Ga, Ge, As, Se, Br, Cd, In, Sn, Sb, Te, I, Hg, Tl, Pb, Bi

Note: The MOPAC version 6 manual can be found on-line. The location changes, so find it by searching for "MOPAC" & "Manual" with Google or some other search engine.

For a historical overview of the development of self consistent field theory, MNDO and AM1 see M.J.S. Dewar, J. Mol. Structure, 100:41 (1983). Other references are given in the MOPAC output.

 

EXAMPLE of Output of the MOPAC Program: Methanol - PM3 method & defaults otherwise used...

PM3 CALCULATION RESULTS

******************************************************************************

* MOPAC: VERSION 6.00 CALC'D.

* T= - A TIME OF 3600.0 SECONDS REQUESTED

* DUMP=N - RESTART FILE WRITTEN EVERY 3600.0 SECONDS

* PM3 - THE PM3 HAMILTONIAN TO BE USED

***********************************************************************050BY100

PM3 T=3600

methanol

MOPAC calculations:

ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE

NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)

(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC

 

1 H

2 C 1.42600 * 1

3 O 1.42600 * 109.59820 * 2 1

4 H 1.03800 * 108.90000 * 180.00000 * 3 2 1

5 H 1.09100 * 109.43950 * 59.98036 * 2 3 4

6 H 1.09100 * 109.39720 * -60.05830 * 2 3 4

 

CARTESIAN COORDINATES

NO. ATOM X Y Z

1 H .0000 .0000 .0000

2 C 1.4260 .0000 .0000

3 O 1.9043 1.3434 .0000

4 H 2.9422 1.3307 .0000

5 H 1.7891 -.5147 .8908

6 H 1.7883 -.5136 -.8917

H: (PM3): J. J. P. STEWART, J. COMP. CHEM. 10, 209 (1989).

C: (PM3): J. J. P. STEWART, J. COMP. CHEM. 10, 209 (1989).

O: (PM3): J. J. P. STEWART, J. COMP. CHEM. 10, 209 (1989).

RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS = 7

INTERATOMIC DISTANCES

0

H 1 C 2 O 3 H 4 H 5 H 6

------------------------------------------------------------------------------

H 1 .000000

C 2 1.426001 .000000

O 3 2.330473 1.426001 .000000

H 4 3.229183 2.017385 1.038000 .000000

H 5 2.063812 1.091000 2.063810 2.351365 .000000

H 6 2.063286 1.091000 2.063286 2.351246 1.782523 .000000

CYCLE: 1 TIME: .01 TIME LEFT: 3599.7 GRAD.: 94.806 HEAT:-38.74331

CYCLE: 2 TIME: .00 TIME LEFT: 3599.7 GRAD.: 18.081 HEAT:-51.50708

TEST ON GRADIENT SATISFIED

HOWEVER, A COMPONENT OF GRADIENT IS LARGER THAN 1.00

 

CYCLE: 3 TIME: .01 TIME LEFT: 3599.7 GRAD.: 2.659 HEAT:-51.84609

TEST ON GRADIENT SATISFIED. HOWEVER, A COMPONENT OF GRADIENT IS LARGER THAN 1.00

CYCLE: 4 TIME: .00 TIME LEFT: 3599.7 GRAD.: 2.034 HEAT:-51.87029

TEST ON GRADIENT SATISFIED

PETERS TEST SATISFIED

-------------------------------------------------------------------------------

PM3 T=3600

molecule 1

MOPAC calculations:

PETERS TEST WAS SATISFIED IN BFGS OPTIMIZATION

SCF FIELD WAS ACHIEVED

PM3 CALCULATION VERSION 6.00

FINAL HEAT OF FORMATION = -51.87547 KCAL

TOTAL ENERGY = -474.14516 EV

ELECTRONIC ENERGY = -1047.61447 EV

CORE-CORE REPULSION = 573.46931 EV

IONIZATION POTENTIAL = 11.13903

NO. OF FILLED LEVELS = 7

MOLECULAR WEIGHT = 32.042

SCF CALCULATIONS = 13

COMPUTATION TIME = .300 SECONDS

 

ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE

NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)

(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC

1 H

2 C 1.09367 * 1

3 O 1.39488 * 104.52341 * 2 1

4 H .94876 * 107.49679 * 178.53101 * 3 2 1

5 H 1.09714 * 112.26971 * 60.14746 * 2 3 4

6 H 1.09705 * 111.99391 * -63.10691 * 2 3 4

 

INTERATOMIC DISTANCES

0

H 1 C 2 O 3 H 4 H 5 H 6

------------------------------------------------------------------------------

H 1 .000000

C 2 1.093666 .000000

O 3 1.976596 1.394880 .000000

H 4 2.770322 1.908301 .948761 .000000

H 5 1.787102 1.097142 2.075895 2.308212 .000000

H 6 1.788137 1.097047 2.072531 2.322287 1.788364 .000000

 

EIGENVALUES

-38.18050 -26.49485 -18.00090 -15.52497 -15.51916 -12.45782 -11.13903 3.50743

3.89100 4.22903 4.39032 5.64745

 

NET ATOMIC CHARGES AND DIPOLE CONTRIBUTIONS

ATOM NO. TYPE CHARGE ATOM ELECTRON DENSITY

1 H .0408 .9592

2 C .0698 3.9302

3 O -.3089 6.3089

4 H .1810 .8190

5 H .0086 .9914

6 H .0087 .9913

DIPOLE X Y Z TOTAL

POINT-CHG. .424 -.830 .019 .932

HYBRID .548 -.296 .016 .623

SUM .972 -1.126 .035 1.488

 

CARTESIAN COORDINATES

NO. ATOM X Y Z

1 H .0000 .0000 .0000

2 C 1.0937 .0000 .0000

3 O 1.4435 1.3503 .0000

4 H 2.3907 1.3996 .0232

5 H 1.4566 -.5235 .8933

6 H 1.4584 -.5189 -.8951

 

 

ATOMIC ORBITAL ELECTRON POPULATIONS

.95922 1.12406 .99024 .84783 .96803 1.80687 1.28257 1.24108

1.97838 .81901 .99145 .99127

.ARC FILE OPENED

 

TOTAL CPU TIME: .30 SECONDS

== MOPAC DONE ==

 

NOTICE of the Public Domain nature of MOPAC version 6:

the MOPAC computer program is a work of the United States Government

and as such is not subject to protection by copyright. You may freely

distribute the MOPAC.EXE file packaged with this program.

 

 

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