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