Variable Ionic Masses

Author:

Harry Brough, University of Manchester

Introduction

ONETEP [Skylaris2005] assigns every ionic species a default mass, taken from an internal table and determined by the element. The species_mass block, introduced in v8.2, overrides these defaults on a per-species basis, allowing isotopic substitution without altering the electronic structure of the calculation.

This is of use for:

• Molecular dynamics — isotope effects on diffusion and rates of barrier crossing.

• Vibrational and phonon calculations — isotopic shifts of harmonic frequencies, zero-point energies, thermochemical corrections, and hence kinetic isotope effects.

Because the Born-Oppenheimer potential energy surface does not depend on the ionic masses, no aspect of the electronic structure calculation is changed: total energies, forces, NGWFs, the density kernel and the locations of stationary points are all identical to those obtained with the default masses. Only mass-dependent nuclear properties are affected.

Keywords

The atomic masses can be specified with the species_mass block keyword, as shown:

%block species_mass
H    2.014102
C    13.00335
O    17.99916
%endblock species_mass

This requests a calculation with deuterium instead of protium, and with ¹³C and ¹⁸O nuclei. The first entry on each line is the species label, exactly as it appears in the first column of the species block.

Not every atomic species needs to be listed in species_mass; any species omitted retains its default mass.

By default, the mass units are atomic mass units (amu) — this can be changed in the same way as other block keywords. Other possible units are grams (g) and kilograms (kg).

Selective Isotopic Substitution

Because species_mass acts on species labels rather than on elements, distinct labels must be introduced in the species block in order to substitute only some atoms of a given element. To deuterate a single hydroxyl hydrogen, for instance:

%block species
H    H   1   1   8.0
H_D  H   1   1   8.0
O    O   8   4   8.0
%endblock species

%block species_mass
H_D  2.014102
%endblock species_mass

Both hydrogen labels share the same element, atomic number and pseudopotential, and only the mass differs. Atoms are then assigned to one label or the other in the positions_abs block.

Default Masses

The ionic masses that ONETEP uses by default are tabulated here, which are generally natural abundance standard atomic weights.

Z	El.	Mass / amu	Z	El.	Mass / amu	Z	El.	Mass / amu
1	H	1.00794	38	Sr	87.62	75	Re	186.207
2	He	4.00260	39	Y	88.90585	76	Os	190.23
3	Li	6.941	40	Zr	91.224	77	Ir	192.217
4	Be	9.012187	41	Nb	92.90638	78	Pt	195.078
5	B	10.811	42	Mo	95.94	79	Au	196.96655
6	C	12.0107	43	Tc	98.0	80	Hg	200.59
7	N	14.00674	44	Ru	101.07	81	Tl	204.3833
8	O	15.9994	45	Rh	102.90550	82	Pb	207.2
9	F	18.99840	46	Pd	106.42	83	Bi	208.98038
10	Ne	20.1797	47	Ag	107.8682	84	Po	209.0
11	Na	22.98977	48	Cd	112.411	85	At	210.0
12	Mg	24.3050	49	In	114.818	86	Rn	222.0
13	Al	26.98154	50	Sn	118.710	87	Fr	223.0
14	Si	28.0855	51	Sb	121.760	88	Ra	226.0
15	P	30.97376	52	Te	127.60	89	Ac	227.0
16	S	32.066	53	I	126.90447	90	Th	232.0381
17	Cl	35.4527	54	Xe	131.29	91	Pa	231.03588
18	Ar	39.948	55	Cs	132.90545	92	U	238.0289
19	K	39.0983	56	Ba	137.327	93	Np	237.0
20	Ca	40.078	57	La	138.9055	94	Pu	244.0
21	Sc	44.95591	58	Ce	140.116	95	Am	243.0
22	Ti	47.867	59	Pr	140.90765	96	Cm	247.0
23	V	50.9415	60	Nd	144.24	97	Bk	247.0
24	Cr	51.9961	61	Pm	145.0	98	Cf	251.0
25	Mn	54.93805	62	Sm	150.36	99	Es	252.0
26	Fe	55.845	63	Eu	151.964	100	Fm	257.0
27	Co	58.93320	64	Gd	157.25	101	Md	258.0
28	Ni	58.6934	65	Tb	158.92534	102	No	259.0
29	Cu	63.546	66	Dy	162.50	103	Lr	262.0
30	Zn	65.39	67	Ho	164.93032	104	Rf	261.0
31	Ga	69.723	68	Er	167.26	105	Db	262.0
32	Ge	72.61	69	Tm	168.93421	106	Sg	263.0
33	As	74.92160	70	Yb	173.04	107	Bh	264.0
34	Se	78.96	71	Lu	174.967	108	Hs	265.0
35	Br	79.904	72	Hf	178.49	109	Mt	268.0
36	Kr	83.80	73	Ta	180.9479
37	Rb	85.4678	74	W	183.84

References

[Skylaris2005]

C.-K. Skylaris et al., J. Chem. Phys. 122, 084119 (2005).