%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % GENIUSH-predicted 0/1 splittings, up to J=10, for H2O-16 and H2O-18 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file contains the computed 0/1 splittings {defined as E_(v1,v2,v3)[J,J,0]-E_(v1,v2,v3)[J,J,1]} % of H2O-18 and H2O-16 for different J values in the vibrational ground state and in the vibrational % bands of the P=4 polyad. The first-principles nuclear-motion computations have been performed using the latest, % symmetry-adapted version (J. Chem. Phys., 2017, 147, 134101.) of the GENIUSH program system % (J. Chem. Phys., 2009, 130, 134112. and J. Chem. Phys., 2011, 134, 074105.), which was specially extended % for J>0 for water. Eight computations were done for each splitting, combining four PESs with two basis sets. % The average of the eight results is given as the final splitting value, % and twice the standard deviation of the eight results is the uncertainty. % % The PESs used in the GENIUSH computations: % -CVRQD, including and excluding the diagonal Born-Oppenheimer correction (DBOC), developed for H2O-16 % (Science, 2003, 299, 539–542. and J. Chem. Phys., 2006, 125, 204307.) % -POKAZATEL, developed for H2O-16 (Mon. Not. R. Astron. Soc., 2018, 480, 2597–2608.) % -FIS3, developed for H2O-18 (J. Mol. Spectrosc., 2006, 236, 216–223.) % % Specification of the basis sets used in the GENIUSH computations: % Vibratinal basis: Laguerre-PO DVR functions on the [0.5,2.0] Angstrom interval for the O--H bond length % coordinates and Legendre DVR functions on the (0,180) degree interval for the H--O--H bond angle. % The rotational basis was 2J+1 Wang-functions. % (See Supplementary Note 4. of Nat. Commun., 2020, 11, 1708. for further details and references). % % The mass values employed in the computations: % m(H): 1.00727647 u % m(16O): 15.9905260 u % m(18O): 17.9947714 u % % The tables below show the results of the eight computation for the (120)[8,8,0/1] and (000)[8,8,0/1] H2O-18 % 0/1 splitting that are used for the determination of the lowest ortho energy. For the other 0/1 % splittings of H2O-16 and H2O-18 only the recommended value and uncertainty is given. % % Notation of the table: % -small basis : 20-20 basis functions for the bond length and 50 for the bond angle coordinate % -large basis : 30-30 basis functions for the bond length and 80 for the bond angle coordinate % -s : Recommended value of the 0/1 splitting in cm-1 % -u : Recommended uncertainty of the 0/1 splitting in cm-1 % -minus sign : Cases when the energy of (v1,v2,v3)[J,J,1] is larger than the energy of (v1,v2,v3)[J,J,0] % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % GENIUSH results (in cm-1) for 0/1 splittings used for the determination of the lowest ortho energy of H2O-18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | (120)[8,8,0/1] | (000)[8,8,0/1] | small basis large basis | small basis large basis ------------------------------------------------------------------------------------------------------------- CVRQD (with DBOC) | 4.655E-06 4.651E-06 | 7.092E-06 7.105E-06 CVRQD (without DBOC) | 4.730E-06 4.718E-06 | 7.159E-06 7.159E-06 POKAZATEL | 4.602E-06 4.615E-06 | 7.103E-06 7.096E-06 FIS3 | 4.552E-06 4.542E-06 | 7.094E-06 7.089E-06 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 0/1 SPLITTINGS OF H2O-16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vib. | (000) | (040) | (120) | (021) J |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 ----------------------------------------------------------------------------------------------------------------- 1 |5.2356E+00 2.9E-03 |6.2815E+00 5.6E-03 |5.8082E+00 4.4E-03 |5.9048E+00 4.4E-03 2 |1.2630E+00 2.2E-03 |7.353E-01 2.7E-03 |1.0714E+00 2.4E-03 |1.2003E+00 3.1E-03 3 |1.9943E-01 5.9E-04 |5.962E-02 3.7E-04 |2.67E-02 5.9E-03 |1.6005E-01 7.1E-04 4 |2.651E-02 1.1E-04 |4.298E-03 3.1E-05 |1.232E-02 1.1E-04 |1.830E-02 1.0E-04 5 |3.274E-03 1.7E-05 |5.80E-03 2.7E-04 |3.62E-03 1.1E-04 |2.7E-02 1.2E-02 6 |3.933E-04 2.5E-06 |1.54E-04 1.3E-05 |1.115E-04 3.3E-06 |1.05E-04 7.1E-05 7 |4.719E-05 3.5E-07 |4.14E-06 1.7E-07 |5.2E-04 7.3E-04 |3.100E-05 3.0E-07 8 |5.749E-06 4.9E-08 |3.08E-06 2.7E-07 |5.31E-06 1.7E-07 |1.06E-06 2.5E-07 9 |7.24E-07 1.5E-08 |1.536E-06 2.2E-08 |3.92E-07 2.2E-08 |-1.66E-06 1.1E-07 10 |8.3E-08 2.9E-08 |1.16E-07 6.2E-08 |2.75E-07 7.3E-08 |-7.2E-06 2.1E-06 vib. | (200) | (101) | (002) J |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 ----------------------------------------------------------------------------------------------------------------- 1 |5.1876E+00 3.2E-03 |5.2392E+00 2.9E-03 |5.3020E+00 3.0E-03 2 |2.191E+00 3.0E-02 |1.3981E+00 2.3E-03 |1.4723E+00 2.4E-03 3 |1.108E-01 4.8E-03 |2.4674E-01 7.0E-04 |2.7028E-01 7.5E-04 4 |3.648E-02 4.5E-04 |7.72E-02 4.0E-03 |4.159E-02 1.6E-04 5 |2.508E-02 4.0E-04 |1.448E-03 6.4E-05 |5.922E-03 2.9E-05 6 |2.829E-03 2.9E-05 |-6.97E-04 3.5E-05 |8.166E-04 4.9E-06 7 |1.397E-04 1.2E-06 |-8.80E-04 3.5E-05 |1.1182E-04 7.8E-07 8 |1.2735E-05 6.4E-08 |-4.045E-04 8.1E-06 |1.541E-05 1.3E-07 9 |4.94E-07 2.8E-08 |-1.097E-04 2.2E-06 |2.170E-06 4.0E-08 10 |1.28E-07 2.8E-08 |-3.014E-06 9.8E-08 |3.05E-07 3.4E-08 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 0/1 SPLITTINGS OF H2O-18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vib. | (000) | (040) | (120) | (021) J |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 ----------------------------------------------------------------------------------------------------------------- 1 |5.2757E+00 3.0E-03 |6.3063E+00 5.6E-03 |5.8451E+00 4.4E-03 |5.9307E+00 4.4E-03 2 |1.3080E+00 2.2E-03 |7.565E-01 2.8E-03 |1.0986E+00 2.1E-03 |1.2323E+00 3.2E-03 3 |2.1272E-01 6.3E-04 |6.275E-02 3.9E-04 |9.85E-02 2.5E-03 |1.6815E-01 7.5E-04 4 |2.912E-02 1.2E-04 |4.696E-03 3.6E-05 |1.435E-02 1.1E-04 |2.005E-02 2.2E-04 5 |3.703E-03 2.0E-05 |3.77E-03 1.4E-04 |2.877E-03 6.7E-05 |5.97E-03 6.0E-04 6 |4.582E-04 2.9E-06 |1.856E-04 4.5E-06 |1.393E-04 9.3E-06 |-2.21E-03* 1.8E-04* 7 |5.663E-05 4.3E-07 |4.58E-06 2.9E-07 |7.3E-05 2.2E-05 |3.566E-05 4.1E-07 8 |7.112E-06 5.9E-08 |5.6E-06 1.2E-06 |4.63E-06 1.4E-07 |3.08E-06 4.8E-07 9 |9.16E-07 1.2E-08 |7.58E-07 2.3E-08 |3.70E-07 2.2E-08 |-2.69E-06 1.8E-07 10 |1.19E-07 2.5E-08 |1.12E-07 4.3E-08 |1.3E-06 1.3E-06 |1.66E-06 3.5E-07 vib. | (200) | (101) | (002) J |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 |s/cm-1 u/cm-1 ----------------------------------------------------------------------------------------------------------------- 1 |5.2333E+00 3.2E-03 |5.2759E+00 2.8E-03 |5.3350E+00 3.0E-03 2 |2.0544E+00 6.8E-03 |1.4460E+00 2.4E-03 |1.5178E+00 2.5E-03 3 |1.641E-01 3.3E-03 |2.6257E-01 7.4E-04 |2.8612E-01 7.9E-04 4 |3.389E-02 2.9E-04 |8.27E-02 5.2E-03 |4.521E-02 1.8E-04 5 |3.453E-02 7.7E-04 |2.393E-03 6.8E-05 |6.609E-03 3.3E-05 6 |2.319E-03 2.6E-05 |-5.27E-04 3.7E-05 |9.358E-04 5.6E-06 7 |1.467E-04 1.4E-06 |-8.59E-04 3.9E-05 |1.3164E-04 9.1E-07 8 |1.5192E-05 9.6E-08 |-5.24E-04 1.5E-05 |1.868E-05 1.5E-07 9 |1.682E-06 3.9E-08 |-9.93E-05 2.8E-06 |2.702E-06 4.0E-08 10 |1.69E-07 8.7E-08 |-3.366E-06 9.9E-08 |3.88E-07 2.8E-08 * Results from the CVRQD PESs (including and excluding the diagonal Born-Oppenheimer correction) were excluded because the (021)[6,6,0/1] states could not be safely assigned.