We want to obtain mass-weighted coordinate by Z-matrix coordinate.We want to calculate the tunneling probability by mass-weighted coordinate. Then, how to calculate it?

We want to obtain mass-weighted coordinate by Z-matrix coordinate.We want to calculate the tunneling probability by mass-weighted coordinate. Then, how to calculate it?

These should be Cartesian displacements from the initial structure (x_i - x_i^0, for i=1,…,3*NAtoms), then weighted by the sqrt(mass) as you’ve indicated: q_i = sqrt(m_i) * (x_i - x_i^0).

Original X0 Y0 Z0 is as follows:

O 1.20343100 1.30607900 0.00833300

O -1.21511700 1.24204400 -0.02704000

O -1.95089800 -1.22184500 0.00615000

O 1.91598000 -1.25136200 0.03130500

H -0.08762100 1.29622200 -0.02556400

H 1.64046500 1.88221900 -0.63702500

H -1.53414700 0.27408800 -0.03448400

H -1.59329300 1.69512400 0.74534600

H 2.38504100 -1.54071800 0.82842900

H -1.30706000 -1.94327300 0.04953500

H 1.59616600 0.38981500 -0.04370300

H 2.36437800 -1.68795900 -0.70808600

H -2.72430500 -1.55448800 -0.47198800

The last X Y Z is as follows:

O 1.18427700 1.19135800 -0.10932000

O -1.20616000 1.17407100 0.11612200

O -2.31061600 -1.16967000 -0.10920400

O 2.33275000 -1.13370100 0.10267000

H -0.01225500 1.15167500 0.00192900

H 1.48597100 1.69400100 -0.88221400

H -1.66233200 0.27473600 0.08243700

H -1.51092900 1.66503700 0.89525700

H 3.03110800 -1.25409000 0.76202100

H -2.51819100 -1.77541000 0.61631300

H 1.65623400 0.30021100 -0.08005000

H 2.52526700 -1.74629400 -0.62096300

H -2.99886900 -1.29477800 -0.77896900

Each atomic masses are as follows:

Atom 1 has atomic number 8 and mass 15.99491

Atom 2 has atomic number 8 and mass 15.99491

Atom 3 has atomic number 8 and mass 15.99491

Atom 4 has atomic number 8 and mass 15.99491

Atom 5 has atomic number 1 and mass 1.00783

Atom 6 has atomic number 1 and mass 1.00783

Atom 7 has atomic number 1 and mass 1.00783

Atom 8 has atomic number 1 and mass 1.00783

Atom 9 has atomic number 1 and mass 1.00783

Atom 10 has atomic number 1 and mass 1.00783

Atom 11 has atomic number 1 and mass 1.00783

Atom 12 has atomic number 1 and mass 1.00783

Atom 13 has atomic number 1 and mass 1.00783

mass-weighted coordinate should be 10.44145.

But how to obtain this value?

First,

Second,

Then,

Last,

But, this value is not correct.Waiting for your help.