NO₂

Experimentelle Daten (NIST)

R_NO = 1.1934 A

Bindungswinkel: 134.1 °

Schwingungsfrequenzen: A₁: 1318.1, A₁: 750.0, B₂: 1618.0 cm^-1

Atomisierungsenergie: 0K: 927.4 kJ/mol, 298K: 936.8 kJ/mol

Elektronische Anregungsenergie: 15000 cm^-1

Ionisierungsenergie: 9.586 eV

Dipolmoment: 0.316 D

Input: STO-6G (no2_6g_zmt_opt)

! NO2-Molekuel

$CONTRL SCFTYP=UHF MULT=2 RUNTYP=OPTIMIZE COORD=ZMT $END

$SYSTEM TIMLIM=1000 MEMORY=5000000 $END

$BASIS GBASIS=STO NGAUSS=6 $END

$GUESS GUESS=HUCKEL $END

$DATA

NO2-Molekuel

CNV 2

O2 1 rno

O3 1 rno 2 ano

rno=1.300

ano=120.0

$END

Output: STO-6g (no2_6g_zmt_opt.out)

TOTAL NUMBER OF SHELLS = 6

TOTAL NUMBER OF BASIS FUNCTIONS = 15

NUMBER OF ELECTRONS = 23

CHARGE OF MOLECULE = 0

STATE MULTIPLICITY = 2

NUMBER OF OCCUPIED ORBITALS (ALPHA) = 12

NUMBER OF OCCUPIED ORBITALS (BETA ) = 11

TOTAL NUMBER OF ATOMS = 3

1 ***** EQUILIBRIUM GEOMETRY LOCATED *****

NO2-Molekuel

COORDINATES OF SYMMETRY UNIQUE ATOMS (ANGS)

ATOM CHARGE X Y Z

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

N1 7.0 0.0000000000 0.0000000000 -0.3716681692

O2 8.0 1.1316212335 0.0000000000 0.1576841684

COORDINATES OF ALL ATOMS ARE (ANGS)

ATOM CHARGE X Y Z

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

N1 7.0 0.0000000000 0.0000000000 -0.3716681692

O2 8.0 -1.1316212335 0.0000000000 0.1576841684

O2 8.0 1.1316212335 0.0000000000 0.1576841684

THE CURRENT FULLY SUBSTITUTED Z-MATRIX IS

O2 1 1.2493120

O2 1 1.2493120 2 129.8612819

TOTAL ENERGY = -203.2257103676

SPIN SZ =0.500

S-SQUARED =0.770

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

MOLECULAR ORBITALS

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

**** ALPHA SET ****

1 2 3 4 5

-20.6460 -20.6460 -15.8435 -1.5503 -1.3721

B1 A1 A1 A1 B1

1 N 1 S 0.000000 0.000458 0.996555 -0.154333 0.000000

2 N 1 S 0.000000 -0.005022 0.016093 0.495007 0.000000

3 N 1 X 0.004094 0.000000 0.000000 0.000000 -0.280686

4 N 1 Y 0.000000 0.000000 0.000000 0.000000 0.000000

5 N 1 Z 0.000000 -0.001887 0.002725 0.106838 0.000000

6 O 2 S 0.704848 0.704849 0.000231 -0.122483 -0.157818

7 O 2 S 0.010331 0.010271 -0.003249 0.431823 0.597928

8 O 2 X 0.002157 0.002220 -0.001902 0.110589 0.082337

9 O 2 Y 0.000000 0.000000 0.000000 0.000000 0.000000

10 O 2 Z -0.001130 -0.000869 0.000578 -0.048995 -0.053913

11 O 3 S -0.704848 0.704849 0.000231 -0.122483 0.157818

12 O 3 S -0.010331 0.010271 -0.003249 0.431823 -0.597928

13 O 3 X 0.002157 -0.002220 0.001902 -0.110589 0.082337

14 O 3 Y 0.000000 0.000000 0.000000 0.000000 0.000000

15 O 3 Z 0.001130 -0.000869 0.000578 -0.048995 0.053913

MO₁ MO₂ MO₃

Das ist etwas überraschend. Man hätte eigentlich erwartet (im Ein-Elektronenmodell), dass MO₁ aus einer Linearkombination der drei 1s-AO's gebildet wird. Letztere Linearkombination führt aber zu MO₄. Offensichtlich ist die Elektronenabstoßung im MO₄ größer.
MO₄ MO₅

6 7 8 9 10

-0.8845 -0.7022 -0.6682 -0.6436 -0.4690

A1 A1 B1 B2 B1

1 N 1 S -0.164038 0.001832 0.000000 0.000000 0.000000

2 N 1 S 0.721148 -0.023918 0.000000 0.000000 0.000000

3 N 1 X 0.000000 0.000000 0.476273 0.000000 -0.183155

4 N 1 Y 0.000000 0.000000 0.000000 0.631216 0.000000

5 N 1 Z -0.199005 0.628479 0.000000 0.000000 0.000000

6 O 2 S 0.117650 0.043878 -0.071416 0.000000 0.018885

7 O 2 S -0.556647 -0.235573 0.386763 0.000000 -0.112229

8 O 2 X 0.169431 0.325247 -0.265563 0.000000 0.478919

9 O 2 Y 0.000000 0.000000 0.000000 0.451360 0.000000

10 O 2 Z -0.160351 0.284830 0.405277 0.000000 0.508203

11 O 3 S 0.117650 0.043878 0.071416 0.000000 -0.018885

12 O 3 S -0.556647 -0.235573 -0.386763 0.000000 0.112229

13 O 3 X -0.169431 -0.325247 -0.265563 0.000000 0.478919

14 O 3 Y 0.000000 0.000000 0.000000 0.451360 0.000000

15 O 3 Z -0.160351 0.284830 -0.405277 0.000000 -0.508203

11 12 13 14 15

-0.3951 -0.3912 0.1604 0.5680 0.7719

A1 A2 B2 A1 B1

1 N 1 S -0.060086 0.000000 0.000000 -0.137922 0.000000

2 N 1 S 0.359587 0.000000 0.000000 0.931058 0.000000

3 N 1 X 0.000000 0.000000 0.000000 0.000000 1.173865

4 N 1 Y 0.000000 0.000000 0.812888 0.000000 0.000000

5 N 1 Z -0.544288 0.000000 0.000000 0.678707 0.000000

6 O 2 S 0.001131 0.000000 0.000000 0.061949 -0.064508

7 O 2 S 0.000954 0.000000 0.000000 -0.423012 0.488921

8 O 2 X -0.018417 0.000000 0.000000 -0.715985 0.570974

9 O 2 Y 0.000000 0.709636 -0.567576 0.000000 0.000000

10 O 2 Z 0.633507 0.000000 0.000000 0.125370 -0.372020

11 O 3 S 0.001131 0.000000 0.000000 0.061949 0.064508

12 O 3 S 0.000954 0.000000 0.000000 -0.423012 -0.488921

13 O 3 X 0.018417 0.000000 0.000000 0.715985 0.570974

14 O 3 Y 0.000000 -0.709636 -0.567576 0.000000 0.000000

15 O 3 Z 0.633507 0.000000 0.000000 0.125370 0.372020

**** BETA SET ****

1 2 3 4 5

-20.6359 -20.6358 -15.8329 -1.5104 -1.3258

B1 A1 A1 A1 B1

1 N 1 S 0.000000 0.000438 0.996718 -0.155815 0.000000

2 N 1 S 0.000000 -0.004694 0.015353 0.504885 0.000000

3 N 1 X 0.003891 0.000000 0.000000 0.000000 -0.307839

4 N 1 Y 0.000000 0.000000 0.000000 0.000000 0.000000

5 N 1 Z 0.000000 -0.001845 0.002877 0.119602 0.000000

6 O 2 S 0.704977 0.704982 0.000195 -0.120026 -0.155201

7 O 2 S 0.009762 0.009681 -0.003084 0.420646 0.583725

8 O 2 X 0.002110 0.002161 -0.001851 0.119262 0.091562

9 O 2 Y 0.000000 0.000000 0.000000 0.000000 0.000000

10 O 2 Z -0.001080 -0.000826 0.000539 -0.030689 -0.033020

11 O 3 S -0.704977 0.704982 0.000195 -0.120026 0.155201

12 O 3 S -0.009762 0.009681 -0.003084 0.420646 -0.583725

13 O 3 X 0.002110 -0.002161 0.001851 -0.119262 0.091562

14 O 3 Y 0.000000 0.000000 0.000000 0.000000 0.000000

15 O 3 Z 0.001080 -0.000826 0.000539 -0.030689 0.033020

6 7 8 9 10

-0.7997 -0.6268 -0.5982 -0.5977 -0.3774

A1 B2 B1 A1 A2

1 N 1 S -0.152830 0.000000 0.000000 0.058688 0.000000

2 N 1 S 0.669077 0.000000 0.000000 -0.284768 0.000000

3 N 1 X 0.000000 0.000000 0.542958 0.000000 0.000000

4 N 1 Y 0.000000 0.623752 0.000000 0.000000 0.000000

5 N 1 Z -0.001064 0.000000 0.000000 0.592327 0.000000

6 O 2 S 0.126346 0.000000 -0.078169 0.008417 0.000000

7 O 2 S -0.605685 0.000000 0.427856 -0.054124 0.000000

8 O 2 X 0.254799 0.000000 -0.402630 0.301673 0.000000

9 O 2 Y 0.000000 0.456534 0.000000 0.000000 0.709636

10 O 2 Z -0.085768 0.000000 0.176588 0.336006 0.000000

11 O 3 S 0.126346 0.000000 0.078169 0.008417 0.000000

12 O 3 S -0.605685 0.000000 -0.427856 -0.054124 0.000000

13 O 3 X -0.254799 0.000000 -0.402630 -0.301673 0.000000

14 O 3 Y 0.000000 0.456534 0.000000 0.000000 -0.709636

15 O 3 Z -0.085768 0.000000 -0.176588 0.336006 0.000000

11 12 13 14 15

-0.3470 0.1469 0.1830 0.5962 0.8378

B1 A1 B2 A1 B1

1 N 1 S 0.000000 -0.058389 0.000000 -0.136191 0.000000

2 N 1 S 0.000000 0.345273 0.000000 0.926811 0.000000

3 N 1 X 0.155463 0.000000 0.000000 0.000000 1.141661

4 N 1 Y 0.000000 0.000000 0.818629 0.000000 0.000000

5 N 1 Z 0.000000 -0.594660 0.000000 0.695786 0.000000

6 O 2 S -0.011935 0.003129 0.000000 0.063012 -0.063272

7 O 2 S 0.079812 -0.001406 0.000000 -0.429006 0.478109

8 O 2 X 0.414363 -0.001228 0.000000 -0.699673 0.538968

9 O 2 Y 0.000000 0.000000 -0.563423 0.000000 0.000000

10 O 2 Z 0.571697 0.614313 0.000000 0.166468 -0.452454

11 O 3 S 0.011935 0.003129 0.000000 0.063012 0.063272

12 O 3 S -0.079812 -0.001406 0.000000 -0.429006 -0.478109

13 O 3 X 0.414363 0.001228 0.000000 0.699673 0.538968

14 O 3 Y 0.000000 0.000000 -0.563423 0.000000 0.000000

15 O 3 Z -0.571697 0.614313 0.000000 0.166468 0.452454

ATOMIC SPIN POPULATION (ALPHA MINUS BETA)

ATOM MULL.POP. LOW.POP.

1 N1 0.317377 0.333924

2 O2 0.341312 0.333038

3 O2 0.341312 0.333038

********* ALL ELECTRONS ********

----- POPULATIONS IN EACH AO -----

MULLIKEN LOWDIN

1 N 1 S 1.99828 1.99484

2 N 1 S 1.56768 1.50104

3 N 1 X 0.99219 1.02542

4 N 1 Y 0.97867 0.97885

5 N 1 Z 1.26734 1.28723

6 O 2 S 1.99921 1.99835

7 O 2 S 1.89865 1.83929

8 O 2 X 1.20109 1.25532

9 O 2 Y 1.51067 1.51058

10 O 2 Z 1.48830 1.50277

11 O 3 S 1.99921 1.99835

12 O 3 S 1.89865 1.83929

13 O 3 X 1.20109 1.25532

14 O 3 Y 1.51067 1.51058

15 O 3 Z 1.48830 1.50277

TOTAL MULLIKEN AND LOWDIN ATOMIC POPULATIONS

ATOM MULL.POP. CHARGE LOW.POP. CHARGE

1 N1 6.804160 0.195840 6.787371 0.212629

2 O2 8.097920 -0.097920 8.106315 -0.106315

3 O2 8.097920 -0.097920 8.106315 -0.106315

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

BOND ORDER AND VALENCE ANALYSIS BOND ORDER THRESHOLD=0.050

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

BOND BOND BOND

ATOM PAIR DIST ORDER ATOM PAIR DIST ORDER ATOM PAIR DIST ORDER

1 2 1.249 1.660 1 3 1.249 1.660 2 3 2.263 0.441

TOTAL BONDED FREE

ATOM VALENCE VALENCE VALENCE

1 N1 3.459 3.320 0.139

2 O2 2.255 2.101 0.154

3 O2 2.255 2.101 0.154

ATOMIC SPIN DENSITY AT THE NUCLEUS (A.U.)

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

1 N1 7.0 0.2446451

2 O2 8.0 -0.0044587

3 O2 8.0 -0.0044587

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

ELECTROSTATIC MOMENTS

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

POINT 1 X Y Z (BOHR) CHARGE

0.000000 0.000000 -0.006582 0.00 (A.U.)

DX DY DZ /D/ (DEBYE)

0.000000 0.000000 -0.246211 0.246211

...... END OF PROPERTY EVALUATION ......

DZV

TOTAL NUMBER OF SHELLS = 15

TOTAL NUMBER OF BASIS FUNCTIONS = 27

NUMBER OF ELECTRONS = 23

CHARGE OF MOLECULE = 0

STATE MULTIPLICITY = 2

NUMBER OF OCCUPIED ORBITALS (ALPHA) = 12

NUMBER OF OCCUPIED ORBITALS (BETA ) = 11

TOTAL NUMBER OF ATOMS = 3

TOTAL ENERGY = -203.9462664347

ATOMIC SPIN POPULATION (ALPHA MINUS BETA)

ATOM MULL.POP. LOW.POP.

1 N1 0.462314 0.461698

2 O2 0.268843 0.269151

3 O2 0.268843 0.269151

********* ALL ELECTRONS ********

----- POPULATIONS IN EACH AO -----

MULLIKEN LOWDIN

1 N 1 S 1.99987 1.99139

2 N 1 S 0.98659 0.80383

3 N 1 S 0.55199 0.51795

4 N 1 X 0.95372 0.86873

5 N 1 Y 0.67347 0.59490

6 N 1 Z 1.00128 0.93245

7 N 1 X -0.00182 0.29671

8 N 1 Y 0.21617 0.29280

9 N 1 Z 0.17586 0.32284

10 O 2 S 2.00007 1.99480

11 O 2 S 0.98802 0.94536

12 O 2 S 0.93517 0.76727

13 O 2 X 0.99078 0.94621

14 O 2 Y 1.10797 1.04631

15 O 2 Z 1.14955 1.09321

16 O 2 X 0.22661 0.40934

17 O 2 Y 0.44721 0.50984

18 O 2 Z 0.37605 0.47686

19 O 3 S 2.00007 1.99480

20 O 3 S 0.98802 0.94536

21 O 3 S 0.93517 0.76727

22 O 3 X 0.99078 0.94621

23 O 3 Y 1.10797 1.04631

24 O 3 Z 1.14955 1.09321

25 O 3 X 0.22661 0.40934

26 O 3 Y 0.44721 0.50984

27 O 3 Z 0.37605 0.47686

----- MULLIKEN ATOMIC OVERLAP POPULATIONS -----

(OFF-DIAGONAL ELEMENTS NEED TO BE MULTIPLIED BY 2)

1 2 3

1 6.1121648

2 0.2224760 8.1003445

3 0.2224760 -0.1013788 8.1003445

TOTAL MULLIKEN AND LOWDIN ATOMIC POPULATIONS

ATOM MULL.POP. CHARGE LOW.POP. CHARGE

1 N1 6.557117 0.442883 6.621598 0.378402

2 O2 8.221442 -0.221442 8.189201 -0.189201

3 O2 8.221442 -0.221442 8.189201 -0.189201

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

BOND ORDER AND VALENCE ANALYSIS BOND ORDER THRESHOLD=0.050

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

BOND BOND BOND

ATOM PAIR DIST ORDER ATOM PAIR DIST ORDER ATOM PAIR DIST ORDER

1 2 1.250 1.587 1 3 1.250 1.587 2 3 2.256 0.250

TOTAL BONDED FREE

ATOM VALENCE VALENCE VALENCE

1 N1 3.434 3.174 0.260

2 O2 1.954 1.837 0.117

3 O2 1.954 1.837 0.117

ATOMIC SPIN DENSITY AT THE NUCLEUS (A.U.)

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

1 N1 7.0 0.3651130

2 O2 8.0 0.0768151

3 O2 8.0 0.0768151

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

ELECTROSTATIC MOMENTS

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

POINT 1 X Y Z (BOHR) CHARGE

0.000000 0.000000 0.000000 0.00 (A.U.)

DX DY DZ /D/ (DEBYE)

0.000000 0.000000 -0.778203 0.778203

...... END OF PROPERTY EVALUATION ......

TZV

TZV NDFUNC=1

TOTAL NUMBER OF SHELLS = 27

TOTAL NUMBER OF BASIS FUNCTIONS = 60

NUMBER OF ELECTRONS = 23

CHARGE OF MOLECULE = 0

STATE MULTIPLICITY = 2

NUMBER OF OCCUPIED ORBITALS (ALPHA) = 12

NUMBER OF OCCUPIED ORBITALS (BETA ) = 11

TOTAL NUMBER OF ATOMS = 3

THE CURRENT FULLY SUBSTITUTED Z-MATRIX IS

O2 1 1.1557744

O2 1 1.1557744 2 136.2005227

TOTAL ENERGY = -204.1029221986

SPIN SZ =0.500

S-SQUARED =0.766

TZV NDFUNC=1 DIFFSP=.TRUE.

TOTAL NUMBER OF SHELLS = 30

TOTAL NUMBER OF BASIS FUNCTIONS = 72

NUMBER OF ELECTRONS = 23

CHARGE OF MOLECULE = 0

STATE MULTIPLICITY = 2

NUMBER OF OCCUPIED ORBITALS (ALPHA) = 12

NUMBER OF OCCUPIED ORBITALS (BETA ) = 11

TOTAL NUMBER OF ATOMS = 3

THE CURRENT FULLY SUBSTITUTED Z-MATRIX IS

O2 1 1.1553657

O2 1 1.1553657 2 136.3050883

TOTAL ENERGY = -204.1048267747

SPIN SZ =0.500

S-SQUARED =0.766

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

ELECTROSTATIC MOMENTS

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

POINT 1 X Y Z (BOHR) CHARGE

0.000000 0.000000 -0.005903 0.00 (A.U.)

DX DY DZ /D/ (DEBYE)

0.000000 0.000000 -0.679536 0.679536

ROHF, CI, TRUDGE

Input

!
! NO2-Molekuel
!
$CONTRL SCFTYP=ROHF MULT=2 RUNTYP=TRUDGE COORD=HINT CITYP=GUGA $END
$SYSTEM TIMLIM=1000 MEMORY=5000000 $END
$TRUDGE OPTMIZ=GEOMETRY NPAR=2 IEX(1)=21,22 $END
$BASIS GBASIS=STO NGAUSS=6 $END
$GUGDM2 WSTATE(1)=1.0,0.0 $END
$CIDRT GROUP=C2V IEXCIT=2 NFZC=3 NDOC=8 NALP=1 NVAL=3 $END
$GUGDIA NSTATE=4 ITERMX=200 $END
$GUGDM IROOT=1 NFLGDM(1)=1 $END
$GUESS GUESS=MOREAD NORB=15 $END
$DATA
NO2-Molekuel
CNV 2

N 7.0 LC 0.00 0.0 0.0 - O
O 8.0 PCC 1.20 56.0 0.0 + O K
$END

--- ROHF ORBITALS --- GENERATED AT 16:05:11 LT 21-NOV-2002
NO2-Molekuel
E(ROHF)= -203.2195979212, E(NUC)= 62.4508128926, 2 ITERS
$VEC
1 1 0.00000000E+00 0.00000000E+00 0.00000000E+00 4.06863259E-03 0.00000000E+00
1 2 7.05018278E-01 9.63194509E-03 0.00000000E+00 2.23260752E-03-1.14647654E-03
1 3-7.05018278E-01-9.63194509E-03 0.00000000E+00 2.23260752E-03 1.14647654E-03
2 1 4.50907799E-04-4.74594282E-03 0.00000000E+00 0.00000000E+00-1.90810897E-03

Output

TRUDGE ENERGY VALUE AT NSTEP= 45 IS -203.4538325356

-----------------------------------------------------------
INTERNAL COORDINATES (ANGSTROMS/DEGREE)
I      BOND      ALPHA     BETA    SIGN ICONX IATCON INATOM
1   0.0000000   0.00000   0.00000 -1.0   1501502503    1
2   1.2992830 63.05514   0.00000   1.0   2501504503    3
-----------------------------------------------------------

              COORDINATES OF ALL ATOMS ARE (ANGS)
ATOM CHARGE       X             Y              Z
------------------------------------------------------------
N    7.0   0.0000000000   0.0000000000   0.0000000000
O    8.0   0.0000000000 -1.1582367653   0.5887477884
O    8.0   0.0000000000   1.1582367653   0.5887477884

INTERNUCLEAR DISTANCES (ANGS.)
------------------------------

             N            O             O

1 N   0.0000000    1.2992830 *    1.2992830 *
2 O   1.2992830 * 0.0000000      2.3164735 *
3 O   1.2992830 * 2.3164735 *    0.0000000

* ... LESS THAN 3.000

...... END OF NON-GRADIENT ENERGY MINIMIZATION ......

31G

TRUDGE ENERGY VALUE AT NSTEP= 19 IS -204.2519340858

NON-GRADIENT ENERGY MINIMIZATION ... CONVERGED

-----------------------------------------------------------
INTERNAL COORDINATES (ANGSTROMS/DEGREE)
I      BOND       ALPHA      BETA    SIGN ICONX IATCON INATOM
1   0.0000000    0.00000   0.00000   -1.0   1501502503 1
2   1.2290353   67.11032   0.00000    1.0   2501504503 3
-----------------------------------------------------------

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