The first wave functions of helium hydride HeH++ molecular ion
EIGENVALUE 1 = -1.016
EIGENVECTOR1(X,0,0) along the X-axis
EIGENVALUE 1 = -1.016
EIGENVECTOR 1 in PLANES X=0 Y=0 and Z=0
EIGENVALUE 1 = -1.016
PROFILE X=EIGENVECTOR1(0,Y,Z)
The superposed white line joins (-d,0,0) and (d,0,0) on the X-axis
Two protons in (-d,0,0) and one proton in (d,0,0) with d=1/2
EIGENVALUE 1 = -1.016
PROFILE Y=EIGENVECTOR1(X,0,Z)
EIGENVALUE 1 = -1.016
PROFILE Z=EIGENVECTOR1(X,Y,0)
EIGENVALUE 1 = -1.016
SECTION COLOR=EIGENVECTOR1(0,Y,Z)
EIGENVALUE 1 = -1.016
SECTION COLOR=EIGENVECTOR1(X,0,Z)
EIGENVALUE 1 = -1.016
SECTION COLOR=EIGENVECTOR1(X,Y,0)
EIGENVALUE 1 = -1.016
ISOSURFACE 0.5 of EIGENVECTOR1(X,Y,Z)
EIGENVALUE 1 = -1.016
ISOSURFACES of EIGENVECTOR1(X,Y,Z)
EIGENVALUE 2 = 0.668
EIGENVECTOR2(X,0,0) along the X-axis
EIGENVALUE 2 = 0.668
PROFILE X=EIGENVECTOR2(0,Y,Z)
EIGENVALUE 2 = 0.668
PROFILE Y=EIGENVECTOR2(X,0,Z)
EIGENVALUE 2 = 0.668
PROFILE Z=EIGENVECTOR2(X,Y,0)
EIGENVALUE 2 = 0.668
SECTION COLOR=EIGENVECTOR2(0,Y,Z)
EIGENVALUE 2 = 0.668
SECTION COLOR=EIGENVECTOR2(X,0,Z)
EIGENVALUE 2 = 0.668
SECTION COLOR=EIGENVECTOR2(X,Y,0)
EIGENVALUE 2 = 0.668
ISOSURFACES -0.5, 0.5 of EIGENVECTOR2(X,Y,Z)
EIGENVALUE 2 = 0.668
ISOSURFACES of EIGENVECTOR2(X,Y,Z)
EIGENVALUE 3 = 0.973
EIGENVECTOR3(X,0,0) along the X-axis
EIGENVALUE 3 = 0.973
PROFILE X=EIGENVECTOR3(0,Y,Z)
EIGENVALUE 3 = 0.973
PROFILE Y=EIGENVECTOR3(X,0,Z)
EIGENVALUE 3 = 0.973
PROFILE Z=EIGENVECTOR3(X,Y,0)
EIGENVALUE 3 = 0.973
SECTION COLOR=EIGENVECTOR3(0,Y,Z)
EIGENVALUE 3 = 0.973
SECTION COLOR=EIGENVECTOR3(X,0,Z)
EIGENVALUE 3 = 0.973
SECTION COLOR=EIGENVECTOR3(X,Y,0)
EIGENVALUE 3 = 0.973
ISOSURFACES -0.2, 0.2 of EIGENVECTOR3(X,Y,Z)
EIGENVALUE 3 = 0.973
ISOSURFACES of EIGENVECTOR3(X,Y,Z)
EIGENVALUE 4 = 0.974
EIGENVECTOR4(X,0,0) along the X-axis
EIGENVALUE 4 = 0.974
PROFILE X=EIGENVECTOR4(0,Y,Z)
EIGENVALUE 4 = 0.974
PROFILE Y=EIGENVECTOR4(X,0,Z)
EIGENVALUE 4 = 0.974
PROFILE Z=EIGENVECTOR4(X,Y,0)
EIGENVALUE 4 = 0.974
SECTION COLOR=EIGENVECTOR4(0,Y,Z)
EIGENVALUE 4 = 0.974
SECTION COLOR=EIGENVECTOR4(X,0,Z)
EIGENVALUE 4 = 0.974
SECTION COLOR=EIGENVECTOR4(X,Y,0)
EIGENVALUE 4 = 0.974
ISOSURFACES -0.2, 0.2 of EIGENVECTOR4(X,Y,Z)
EIGENVALUE 4 = 0.974
ISOSURFACES of EIGENVECTOR4(X,Y,Z)
EIGENVALUE 5 = 1.095
EIGENVECTOR5(X,0,0) along the X-axis
EIGENVALUE 5 = 1.095
PROFILE X=EIGENVECTOR5(0,Y,Z)
EIGENVALUE 5 = 1.095
PROFILE Y=EIGENVECTOR5(X,0,Z)
EIGENVALUE 5 = 1.095
PROFILE Z=EIGENVECTOR5(X,Y,0)
EIGENVALUE 5 = 1.095
SECTION COLOR=EIGENVECTOR5(0,Y,Z)
EIGENVALUE 5 = 1.095
SECTION COLOR=EIGENVECTOR5(X,0,Z)
EIGENVALUE 5 = 1.095
SECTION COLOR=EIGENVECTOR5(X,Y,0)
EIGENVALUE 5 = 1.095
ISOSURFACE -0.2 of EIGENVECTOR5(X,Y,Z)
EIGENVALUE 5 = 1.095
ISOSURFACES of EIGENVECTOR5(X,Y,Z)
EIGENVALUE 6 = 1.453
EIGENVECTOR6(X,0,0) along the X-axis
EIGENVALUE 6 = 1.453
PROFILE X=EIGENVECTOR6(0,Y,Z)
EIGENVALUE 6 = 1.453
PROFILE Y=EIGENVECTOR6(X,0,Z)
EIGENVALUE 6 = 1.453
PROFILE Z=EIGENVECTOR6(X,Y,0)
EIGENVALUE 6 = 1.453
SECTION COLOR=EIGENVECTOR6(0,Y,Z)
EIGENVALUE 6 = 1.453
SECTION COLOR=EIGENVECTOR6(X,0,Z)
EIGENVALUE 6 = 1.453
SECTION COLOR=EIGENVECTOR6(X,Y,0)
EIGENVALUE 6 = 1.453
ISOSURFACES -0.2, 0.2 of EIGENVECTOR6(X,Y,Z)
EIGENVALUE 6 = 1.453
ISOSURFACES of EIGENVECTOR6(X,Y,Z)
EIGENVALUE 6 = 1.453
7 ISOSURFACES of EIGENVECTOR6(X,Y,Z)
EIGENVALUE 6 = 1.453
7 ISOSURFACES of EIGENVECTOR6(X,Y,Z)
EIGENVALUE 7 = 1.490
EIGENVECTOR7(X,0,0) along the X-axis
EIGENVALUE 7 = 1.490
PROFILE X=EIGENVECTOR7(0,Y,Z)
EIGENVALUE 7 = 1.490
PROFILE Y=EIGENVECTOR7(X,0,Z)
EIGENVALUE 7 = 1.490
PROFILE Z=EIGENVECTOR7(X,Y,0)
EIGENVALUE 7 = 1.490
SECTION COLOR=EIGENVECTOR7(0,Y,Z)
EIGENVALUE 7 = 1.490
SECTION COLOR=EIGENVECTOR7(X,0,Z)
EIGENVALUE 7 = 1.490
SECTION COLOR=EIGENVECTOR7(X,Y,0)
EIGENVALUE 7 = 1.490
COLOR=EIGENVECTOR7(X,0,Z) and (X,Y,0)
EIGENVALUE 7 = 1.490
ISOSURFACES of EIGENVECTOR7(X,Y,Z)
EIGENVALUE 7 = 1.490
ISOSURFACES of EIGENVECTOR7(X,Y,Z)
EIGENVALUE 8 = 1.498
EIGENVECTOR8(X,0,0) along the X-axis
EIGENVALUE 8 = 1.498
PROFILE X=EIGENVECTOR8(0,Y,Z)
EIGENVALUE 8 = 1.498
PROFILE Y=EIGENVECTOR8(X,0,Z)
EIGENVALUE 8 = 1.498
PROFILE Z=EIGENVECTOR8(X,Y,0)
EIGENVALUE 8 = 1.498
SECTION COLOR=EIGENVECTOR8(0,Y,Z)
EIGENVALUE 8 = 1.498
SECTION COLOR=EIGENVECTOR8(X,0,Z)
EIGENVALUE 8 = 1.498
SECTION COLOR=EIGENVECTOR8(X,Y,0)
EIGENVALUE 8 = 1.498
ISOSURFACES of EIGENVECTOR8(X,Y,Z)
EIGENVALUE 8 = 1.498
ISOSURFACES of EIGENVECTOR8(X,Y,Z)
EIGENVALUE 9 = 1.498
EIGENVECTOR9(X,0,0) along the X-axis
EIGENVALUE 9 = 1.498
PROFILE X=EIGENVECTOR9(0,Y,Z)
EIGENVALUE 9 = 1.498
PROFILE Y=EIGENVECTOR9(X,0,Z)
EIGENVALUE 9 = 1.498
PROFILE Z=EIGENVECTOR9(X,Y,0)
EIGENVALUE 9 = 1.498
PROFILE Z=EIGENVECTOR9(X,Y,0)
EIGENVALUE 9 = 1.498
SECTION COLOR=EIGENVECTOR9(0,Y,Z)
EIGENVALUE 9 = 1.498
SECTION COLOR=EIGENVECTOR9(X,0,Z)
EIGENVALUE 9 = 1.498
SECTION COLOR=EIGENVECTOR9(X,Y,0)
EIGENVALUE 9 = 1.498
ISOSURFACES of EIGENVECTOR9(X,Y,Z)
EIGENVALUE 9 = 1.498
ISOSURFACES of EIGENVECTOR9(X,Y,Z)
EIGENVALUE 10 = 1.515
EIGENVECTOR10(X,0,0) along the X-axis
EIGENVALUE 10 = 1.515
PROFILE X=EIGENVECTOR10(0,Y,Z)
EIGENVALUE 10 = 1.515
PROFILE Y=EIGENVECTOR10(X,0,Z)
EIGENVALUE 10 = 1.515
PROFILE Z=EIGENVECTOR10(X,Y,0)
EIGENVALUE 10 = 1.515
SECTION COLOR=EIGENVECTOR10(0,Y,Z)
EIGENVALUE 10 = 1.515
SECTION COLOR=EIGENVECTOR10(X,0,Z)
EIGENVALUE 10 = 1.515
SECTION COLOR=EIGENVECTOR10(X,Y,0)
EIGENVALUE 10 = 1.515
ISOSURFACES of EIGENVECTOR10(X,Y,Z)
EIGENVALUE 10 = 1.515
ISOSURFACES of EIGENVECTOR10(X,Y,Z)
EIGENVALUE 10 = 1.515
ISOSURFACES of EIGENVECTOR10(X,Y,Z)
It seems that the 3 last eigenvectors are obtained by rotations.
If the plan y=0 is chosen for the eigenvalue 8,
this is the plan z=0 for the eigenvalue 9 and
this is the plan x=0 for the eigenvalue 10.
In fact, the eigenvalues 8 (1.498), 9 (1.498) and 10 (1.515)
seems to be an eigenvalue of multiplicity 3.
Page written by Alain Perronnet
Last update November 27-th 2003