aop-arp-bklet-for-flipbook

http://www.ugc-inno-nehu.com/events-2017.html#E09

CLARIFICATION ON PRE-CONCEIVED NOTIONS:

AS in the diagram above, When energy levels are indicated
one above the other it does not imply, that there is such a
distance measurable in units of length between the particles
having the higher enrgy. The energy level diagram is y-axis
scaled in energy units and not cm/km units. It is quite possible
that two particles are much closer (adjacent) to each other but
the energy of the two particles can be much different. Thus
energy level diagrams for our convenience of sketching on
paper drawn a few cms away from each other, in reality no
such line can be darwn for any given energy. The lines drawn
for representing energy by levels is all imaginary. Energy
level differences correspond to actual distances only
depending upon the nature of interactions how much they

depend on distances. Gravitational forces and potential energy
of body at a height is different from the potential energy of
object at lesser height from ground. The objects from a height
fall to the ground, hence the energy differences really
correspond to height from ground. Electrostatic interactions
depend on distance of separation between charges. But this
level may not be referred as high or low from ground level, in
which ever direction it may be it depends only on the distance
of separation; horizontal or vertical.
In view of the clarifications in the previous para, the diagram
below can be less confusing and more realistic.

Thus the situation of why, H2O + hole+ =H2O+ (unstable and
decomposes to products as radicals) occurs more readily, but

not H2O+e-=H2O- is not only to be answered redox potential
wise but also the source or dissipation of energy associated
with oxidation reduction has to be considered and what really
are the energy diffenernces of the positive water ion and
negative water ion has to be known.

To get a preliminary trends a semi empirical QM calculations
are carried out and the results are given numerically in Table,
and graphically as plots which should be aiding in the context
of such queries more convincingly and restore confidence in
students asserting the reasons.

The QM Calculation software ARGUS LAB can be
downloaded and installed from:
http://www.ugc-inno-nehu.com/arguslab/

Another convenient access is to http://www.webmo.net which
calculates at remote server and bring results to to display in
the browser window of the PC.

All QM Calculations are
by PM3 - UHF Method

PM3 is a semi empirical method. In this method as it is semi
empirical, certain integral values (as occurring in secular determinant
elements) are obtained not by evaluating mathematically performing
the integration, but by recognizing the integral as evaluating a
quantity which can be obtained experimentally. Then where ever
such integrals occur, the value obtained experimentally (and tested
well for the transferability of experimental values from one molecule
to another) is substituted for the integral value. In a ab initio
method, all integrals are explicitly evaluated at every stage. For the
details of the PM3 method, in the software ARGUSLAB, used for the
calculation, descriptions that is adequate.

These are all-valence electron calculations, by which it means that
the in each atom only the electron outer most orbit of quantum
number “n” (the primary quantum number) are included and in the
bonding sense, these are the electrons which participate in bonding
to form molecules. Other electrons in the inner orbits are called core
electrons, which has standard parameterized value for each atom.
Thus for C- atom, 1s2 is designated as the core of the atom and
2s2and 2p2 together constitute the valence electrons.

For Oxygen atom, electronic configuration is 1s2, 2s2, 2p4. The 6
electrons of outer most orbits with primary quantum number 2 are
the valence electrons. The core electrons are supposed to remain
unaffected.

There are options to be chosen, depending on the number of valence electrons
in the molecular system is even or odd. Atomic and molecular orbital hold
maximum of a pair of electrons and these electrons obey Hund’s rule and
remain paired in a given Eigen energy value. (If there are possibilities of
degenerate Eigen sates, then since the electrons can occupy one electron each
or together in one state which would be energetically equivalent. And hence
Hund’s rule would not be applicable as a criterion of electron occupancy). It is
this spin pairing designated by α and β states. The spin angular momentum
vectors are oriented opposite to each other and such a paired electron states
to prevail would require an even number of electrons and non degenerate
energy levels. When there is even number of electrons in the system, then all
the electrons all get paired and in remain paired is possible depending on
prevailing degeneracy of eigen states. If there is only odd number of electrons
in the system, then there must be at least one unpaired electron in the system.
Then the identity of which electron in which orbital should be the unpaired
electron? Most possibly it could be the Highest Occupied Molecular Orbital –
the HOMO level. When there is even number of electron, one may choose to
have different multiplicities to result. The final pair of electrons may be left for
unpaired occupation then there would be two unpaired electrons – this would
require system to be in Triplet state. Completely paired system would be
Singlet. Odd number electron systems would have invariably doublet state.
Even number of electrons can have a Singlet or Triplet states. Thus when spin
multiplicity is singlet, The Restricted Hartree Fock (RHF) method is set for
calculations. For such even number electron systems in singlet state,
Unrestricted Hartree Fock (UHF) method is chosen, the spin pairing may not be
conditionally binding, but one may find that energetic of the system during
calculation, results the same RHF type of result for UHF method also. If for odd
number of electrons in the system software would permit only UHF
calculation, and return an error message if RHF option, even by default, is set
for the calculation. Thus one may find for RHF calculation, there would be one
orbital Eigen state for each of the energy and spin paired occupation is
ensured. The paired electrons would occupy one and the same energy Eigen
state. For UHF calculation, corresponding to each one of the RHF Eigen state,
there would be two states one for the α-spin orientation, and another for β-
spin orientation. Thus the energy levels themselves would occur in pairs for the
two spin states. If UHF is set when RHF is a definite possibility, then also the
program would report pair of energy levels corresponding to RHF results, with
the pair of orbital each member having same energy as the other.

Hydrogen Molecule; neutral in charge; 2 electron system.

RHF result:

LUMO

HOMO <α|β>

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

UHF result

α β

LUMO There is one Unoccupied orbital “U”.

HOMO There is one Occupied orbital “O”.

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

Case of H2 Molecule (UHF)

α β HOMO LUMO

Hydrogen Molecule; neutral in charge; 2 electron system.

αβ

LUMO There is one Unoccupied orbital “U”.

HOMO There is one Occupied orbital “O”.

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

Hydrogen Molecule negatively charged ion; H2- ; 3 electron system

αβ

LUMO There is only β spin Unoccupied orbital “U”.

HOMO There is one Occupied orbital “O”.

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

Hydrogen Molecule positively charged ion; H2+ ; 1 electron system

αβ

LUMO There is one Unoccupied orbital “U”.

HOMO There is only α spin Occupied orbital

------------------------------“-O--”-.---------------------------------------

H2O neutral molecule: 8-electron system

UHF results RHF results

αβ αβ

H2O- negative ion: 9-electron system

αβ

H2O+ positive ion: 7-electron system

αβ

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

**

* ArgusLab (tm) *

**

* Version 4.0 *

**

* Copyright (c) 1996-2003 *

**

* Planaria Software LLC *

* ALL RIGHTS RESERVED *

**

* [email protected] *

* http://www.planaria-software.com *

**

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

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

WARNING -- ArgusLab may not be used in any manner that competes
with

the business of Planaria Software LLC or will provide assistance to
any competitor of Planaria Software LLC. The licensee of this
program
is prohibited from giving any competitor of Planaria Software LLC.
access to this program. By using this program, the user
acknowledges
that Planaria Software LLC. is engaged in the business of creating
and
licensing software in the field of computational chemistry and
represents and warrants to Planaria Software LLC that it is not a
competitor of Planaria Software LLC. and that it will not use this
program in any manner prohibited above.
*******************************************************************
****

********* Validated Experiment & Chemical System Settings **********
Calculation started: Tue Jan 16 17:27:47 2018
Title:

D:\h2o-pos-neg-chrg\h2o-go-sp.gouhf-sprhf

System Type Quantum Mechanical
Hamiltonian PM3 (NDDO)

SCF Type RHF
Run Type SCF
Atoms 3
Electrons 8
Water Model SPCE
Coordinates angstroms
Basis set Minimal Valence Basis as STO 6G
Max. SCF cycles 800
SCF convergence 1.5936e-013 au. for energy

PM3 param file C:\Program Files\ArgusLab\params\pm3.prm
SCF saved every 1000 cycles

Two-electron integrals 1000
buffer size random list in core
storage
one center
Property integrals length operator
Dipole integrals

Input Atomic Information
************************

1 O -0.020530 -0.006928 0.000000
2 H -0.020530 -0.569806 0.768970
3 H -0.020530 -0.569806 -0.768970

Cite ArgusLab as:
*****************
ArgusLab 4.0
Mark A. Thompson
Planaria Software LLC, Seattle, WA.
http://www.arguslab.com

Journal Citations for this Calculation
**************************************
Thompson, M. A., Zerner M. C.
J. Am. Chem. Soc., 113, 8210, (1991)

Mark A. Thompson, Eric D. Glendening,
and David Feller J. Phys. Chem. 98,
10465-10476, (1994)

Mark A. Thompson, and Gregory K. Schenter
J. Phys. Chem. 99, 6374-6386, (1995)

Mark A. Thompson, J. Phys. Chem. 100,
14492-14507, (1996)

PM3 references:
***************

James J. P. Stewart, J. Comp. Chem., 10,
209-220 (1989)

James J. P. Stewart, J. Comp. Chem., 10,
221-264, (1989)

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

Constructing Chemical System(s)

Basis Set
***********

basis functions : 6

shells :4

primitives : 24

AtNum Atom Type Nzeta STO coeff STO exp. Contraction

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

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

1HS 1 1.0000 0.9678

7.150641 C(1) = 0.009164 Exp(1) = 21.639463 Norm(1) =
2.003566 C(2) = 0.049361 Exp(2) = 3.967572 Norm(2) =
0.770722 C(3) = 0.168538 Exp(3) = 1.109984 Norm(3) =
0.345834 C(4) = 0.370563 Exp(4) = 0.381309 Norm(4) =
0.170125 C(5) = 0.416492 Exp(5) = 0.148074 Norm(5) =
0.087463 C(6) = 0.130334 Exp(6) = 0.060985 Norm(6) =

8O S 1 1.0000 3.7965
C(1) = -0.004151 Exp(1) = 399.044026 Norm(1) =
63.632019 C(2) = -0.020670 Exp(2) = 73.180617 Norm(2) =
17.832291 C(3) = -0.051503 Exp(3) = 20.565332 Norm(3) =
6.882748 C(4) = 0.334627 Exp(4) = 2.940888 Norm(4) =
1.600549 C(5) = 0.562106 Exp(5) = 1.334756 Norm(5) =
0.885037 C(6) = 0.171299 Exp(6) = 0.636538 Norm(6) =
0.507900

8OP 1 1.0000 2.3894

114.895290 C(1) = 0.007924 Exp(1) = 33.503464 Norm(1) =
21.411366 C(2) = 0.051441 Exp(2) = 8.737022 Norm(2) =
5.925285 C(3) = 0.189840 Exp(3) = 3.126190 Norm(3) =
1.991611 C(4) = 0.404986 Exp(4) = 1.306807 Norm(4) =
0.748890 C(5) = 0.401236 Exp(5) = 0.597561 Norm(5) =
0.293579 C(6) = 0.105186 Exp(6) = 0.282506 Norm(6) =

Memory for Main Chemical System
Max. number 2-ele. ints. = 39

Memory Requirements (bytes)
*****************************

Core 32928
Scratch 1344

Contents Of Parameter Database For Relevant Atoms
*************************************************

energy in EV. others in AU.

** WARNING ** PrintParams: under construction for this HamType

System charge 0.000000

***** Integrals *****

PM3 two-center two-electron integrals
MNDO-type Two-electron integrals: elapsed time 0 sec.

elapsed time 0 sec.

Coulomb integrals for semi-empirical
elapsed time 0 sec.

One-center exchange integrals for semi-empirical
elapsed time 0 sec.

Total number of 2-ele integrals 33
Dipole length integrals
elapsed time 0 sec.

Overlap integrals
elapsed time 0 sec.

Transformation Matrix
elapsed time 0 sec.

Integrals elapsed time 0 sec.

***** SCF *****

Core repulsion 5.48205 au

Calculating one electron matrix
Diagonalizing starting one-ele. matrix
Performing SCF

Cycle Energy (au) Difference

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

1 -11.804580 -0.0158553
2 -11.820435218 -0.0975803
3 -11.918015512
4 -11.935564538 -0.017549
5 -11.938926856 -0.00336232
6 -11.939562475 -0.000635619
7 -11.939683675
8 -11.939707228 -0.0001212
9 -11.939711915 -2.35527e-005
10 -11.939712872 -4.68749e-006
11 -11.939713073 -9.57012e-007
12 -11.939713115 -2.00312e-007
13 -11.939713125 -4.28914e-008
14 -11.939713127 -9.36675e-009
15 -11.939713127 -2.07924e-009
16 -11.939713128
17 -11.939713128 -4.6764e-010
-1.06251e-010

-2.4329e-011

18 -11.939713128 -5.60618e-012
19 -11.939713128 -1.29319e-012
20 -11.939713128 -3.01981e-013
21 -11.939713128 -6.75016e-014

SCF converged

Writing final SCF to disk

Final SCF Energy = -11.9397131275 au

Final SCF Energy = -7492.2899 kcal/mol

Saving the final SCF to the restart file D:\h2o-pos-neg-chrg\h2o-
go-sp.gouhf-sprhf.restartscf

SCF elapsed time 0 sec.

***** Properties *****

Ground state properties
*****************************

***** Heat of Formation *****
-53.3387 kcal/mol

ZDO Atomic Charges
*******************

1 O -0.3583
2 H 0.1792
3 H 0.1792

Wiberg Atom-Atom Bond Orders
*****************************

1 2 3
0.000000
1 0.000000 0.000000
2 0.967905 0.000001
3 0.967905

Ground State Dipole (debye) length
1.74037840
XYZ
-0.00000000 -1.74037840 -0.00000000

Mulliken Atomic Charges
************************

1 O -0.3742
2 H 0.1871
3 H 0.1871

SCF eigenvalues (au) eigenvectors
**********************************

MO number -> 1234 5

Eigenvalues -> -1.351840 -0.645407 -0.533857 -0.452589
0.148595

1 O 2S 0.878297 0.000000 -0.333034 0.000000 -
0.343048 0.000000 0.000000 0.000000 1.000000 -
-0.104822 0.000000 -0.834172 0.000000
1 O 2Px 0.000000 -0.768115 0.000000 0.000000
0.000000 0.329853 -0.452769 0.310842 0.000000
0.329853 0.452769 0.310842 -0.000000
1 O 2Py
0.541451

1 O 2Pz
0.000000

2 H 1S
0.542747

3 H 1S
0.542747

MO number -> 6

Eigenvalues -> 0.195282

1 O 2S 0.000000
1 O 2Px -0.000000
1 O 2Py -0.000000
1 O 2Pz -0.640312
2 H 1S
3 H 1S 0.543139
-0.543139

Properties elapsed time 0 sec.

Total Elapsed Time 0 sec.

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

**

* ArgusLab (tm) *

**

* Version 4.0 *

**

* Copyright (c) 1996-2003 *

**

* Planaria Software LLC *

* ALL RIGHTS RESERVED *

**

* [email protected] *

* http://www.planaria-software.com *

**

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

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

WARNING -- ArgusLab may not be used in any manner that competes
with

the business of Planaria Software LLC or will provide assistance to
any competitor of Planaria Software LLC. The licensee of this
program
is prohibited from giving any competitor of Planaria Software LLC.
access to this program. By using this program, the user
acknowledges
that Planaria Software LLC. is engaged in the business of creating
and
licensing software in the field of computational chemistry and
represents and warrants to Planaria Software LLC that it is not a
competitor of Planaria Software LLC. and that it will not use this
program in any manner prohibited above.
*******************************************************************
****

********* Validated Experiment & Chemical System Settings **********
Calculation started: Tue Jan 16 19:21:39 2018
Title:

D:\h2o-pos-neg-chrg\h2o-go-sp.gouhf-spuhf

System Type Quantum Mechanical
Hamiltonian PM3 (NDDO)

SCF Type UHF
Run Type SCF
Atoms 3
Electrons 8
4
Alpha 4
Beta
1
Multiplicity SPCE
Water Model angstroms
Coordinates Minimal Valence Basis as STO 6G
Basis set 800
Max. SCF cycles 1.5936e-015 au. for energy
SCF convergence
C:\Program Files\ArgusLab\params\pm3.prm
PM3 param file 1000 cycles
SCF saved every
1000
Two-electron integrals random list in core
buffer size
storage one center
length operator
Property integrals
Dipole integrals

Input Atomic Information
************************

1 O -0.020530 -0.006928 0.000000
2 H -0.020530 -0.569806 0.768970
3 H -0.020530 -0.569806 -0.768970

Cite ArgusLab as:
*****************
ArgusLab 4.0
Mark A. Thompson
Planaria Software LLC, Seattle, WA.
http://www.arguslab.com

Journal Citations for this Calculation
**************************************
Thompson, M. A., Zerner M. C.
J. Am. Chem. Soc., 113, 8210, (1991)

Mark A. Thompson, Eric D. Glendening,
and David Feller J. Phys. Chem. 98,
10465-10476, (1994)

Mark A. Thompson, and Gregory K. Schenter
J. Phys. Chem. 99, 6374-6386, (1995)

Mark A. Thompson, J. Phys. Chem. 100,
14492-14507, (1996)

PM3 references:
***************

James J. P. Stewart, J. Comp. Chem., 10,
209-220 (1989)

James J. P. Stewart, J. Comp. Chem., 10,
221-264, (1989)

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

Constructing Chemical System(s)

Basis Set
***********

basis functions : 6

shells :4

primitives : 24

AtNum Atom Type Nzeta STO coeff STO exp. Contraction

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

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

1HS 1 1.0000 0.9678

7.150641 C(1) = 0.009164 Exp(1) = 21.639463 Norm(1) =
2.003566 C(2) = 0.049361 Exp(2) = 3.967572 Norm(2) =
0.770722 C(3) = 0.168538 Exp(3) = 1.109984 Norm(3) =
0.345834 C(4) = 0.370563 Exp(4) = 0.381309 Norm(4) =
0.170125 C(5) = 0.416492 Exp(5) = 0.148074 Norm(5) =
0.087463 C(6) = 0.130334 Exp(6) = 0.060985 Norm(6) =

8O S 1 1.0000 3.7965
C(1) = -0.004151 Exp(1) = 399.044026 Norm(1) =
63.632019 C(2) = -0.020670 Exp(2) = 73.180617 Norm(2) =
17.832291 C(3) = -0.051503 Exp(3) = 20.565332 Norm(3) =
6.882748 C(4) = 0.334627 Exp(4) = 2.940888 Norm(4) =
1.600549 C(5) = 0.562106 Exp(5) = 1.334756 Norm(5) =
0.885037

C(6) = 0.171299 Exp(6) = 0.636538 Norm(6) =

0.507900

8OP 1 1.0000 2.3894

114.895290 C(1) = 0.007924 Exp(1) = 33.503464 Norm(1) =
21.411366 C(2) = 0.051441 Exp(2) = 8.737022 Norm(2) =
5.925285 C(3) = 0.189840 Exp(3) = 3.126190 Norm(3) =
1.991611 C(4) = 0.404986 Exp(4) = 1.306807 Norm(4) =
0.748890 C(5) = 0.401236 Exp(5) = 0.597561 Norm(5) =
0.293579 C(6) = 0.105186 Exp(6) = 0.282506 Norm(6) =

Memory for Main Chemical System
Max. number 2-ele. ints. = 39

Memory Requirements (bytes)
*****************************

Core 33672
Scratch 1344

Contents Of Parameter Database For Relevant Atoms
*************************************************

energy in EV. others in AU.

** WARNING ** PrintParams: under construction for this HamType

System charge 0.000000

***** Integrals *****
PM3 two-center two-electron integrals
MNDO-type Two-electron integrals: elapsed time 0 sec.
elapsed time 0 sec.
Coulomb integrals for semi-empirical

elapsed time 0 sec.

One-center exchange integrals for semi-empirical
elapsed time 0 sec.

Total number of 2-ele integrals 33
Dipole length integrals
elapsed time 0 sec.

Overlap integrals
elapsed time 0 sec.

Transformation Matrix
elapsed time 0 sec.

Integrals elapsed time 0 sec.

***** SCF *****

Core repulsion 5.48205 au

Calculating one electron matrix
Diagonalizing starting one-ele. matrix
Performing SCF

Cycle Energy (au) Difference

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

1 -11.804580 -0.107359
2 -11.911938843 -0.022431
3 -11.934369829 -0.00432905
4 -11.938698883 -0.000820006
5 -11.939518889 -0.000156319
6 -11.939675208 -3.03375e-005
7 -11.939705546 -6.027e-006
8 -11.939711573 -1.22811e-006
9 -11.939712801 -2.56574e-007
10 -11.939713057 -5.48458e-008
11 -11.939713112 -1.19602e-008
12 -11.939713124 -2.6518e-009
13 -11.939713127

14 -11.939713127 -5.95858e-010
15 -11.939713127 -1.35284e-010
16 -11.939713128
17 -11.939713128 -3.0969e-011
18 -11.939713128 -7.1374e-012
19 -11.939713128 -1.6378e-012
20 -11.939713128 -3.83693e-013
21 -11.939713128 -8.88178e-014
22 -11.939713128 -1.77636e-014
23 -11.939713128 -7.10543e-015
24 -11.939713128 -3.55271e-015

SCF converged 0

Writing final SCF to disk

Final SCF Energy = -11.9397131275 au

Final SCF Energy = -7492.2899 kcal/mol

Saving the final SCF to the restart file D:\h2o-pos-neg-chrg\h2o-
go-sp.gouhf-spuhf.restartscf

SCF elapsed time 0 sec.

***** Properties *****

Ground state properties
*****************************

***** Heat of Formation *****
-53.3387 kcal/mol

ZDO Atomic Charges
*******************

1 O -0.3583
2 H 0.1792
3 H 0.1792

Wiberg Atom-Atom Bond Orders
*****************************

123

1 0.000000 0.000000 0.000000
2 0.967905 0.000001
3 0.967905

Atomic spin densities
**********************

1 O 0.0000
2 H 0.0000
3 H 0.0000

S2 operator 0.000000
*********** 0.000000

exact
calculated

Ground State Dipole (debye) length
1.74037824
XYZ
-0.00000000 -1.74037824 -0.00000000

Mulliken Atomic Charges
************************

1 O -0.3742
2 H 0.1871
3 H 0.1871

SCF alpha eigenvalues (au) & eigenvectors
*****************************************

MO number -> 1234 5

Eigenvalues -> -1.351840 -0.645407 -0.533857 -0.452589
0.148595

1 O 2S 0.878297 -0.000000 -0.333034 0.000000
0.343048 0.000000 -0.000000 0.000000 1.000000 -
-0.104822 -0.000000 -0.834172 -0.000000 -
1 O 2Px
0.000000

1 O 2Py
0.541451

1 O 2Pz 0.000000 0.768115 -0.000000 0.000000
0.000000
0.329853 0.452769 0.310842 -0.000000 -
2 H 1S
0.542747 0.329853 -0.452769 0.310842 0.000000 -

3 H 1S 6
0.542747
0.195282
MO number ->
0.000000
Eigenvalues -> 0.000000
-0.000000
1 O 2S -0.640312
1 O 2Px 0.543139
1 O 2Py -0.543139
1 O 2Pz
2 H 1S
3 H 1S

SCF beta eigenvalues (au) & eigenvectors
****************************************

MO number -> 1234 5

Eigenvalues -> -1.351840 -0.645407 -0.533857 -0.452589
0.148595

1 O 2S 0.878297 -0.000000 -0.333034 0.000000
0.343048 0.000000 -0.000000 0.000000 1.000000 -
-0.104822 -0.000000 -0.834172 -0.000000 -
1 O 2Px 0.000000 0.768115 -0.000000 0.000000
0.000000 0.329853 0.452769 0.310842 -0.000000 -
0.329853 -0.452769 0.310842 0.000000 -
1 O 2Py
0.541451

1 O 2Pz
0.000000

2 H 1S
0.542747

3 H 1S
0.542747

MO number -> 6

Eigenvalues -> 0.195282

1 O 2S 0.000000
1 O 2Px 0.000000
1 O 2Py -0.000000
1 O 2Pz -0.640312
2 H 1S 0.543139
3 H 1S -0.543139

Properties elapsed time 0 sec.
Total Elapsed Time 0 sec.















http://www.ugc-inno-nehu.com/events-2017.html#E07