Let me explain the whole paragraph to reach the last line.

Normally, when a bond is formed between the two atoms, there is an overlapping of the electron clouds of their AOs. Some region becomes common between the two and length of the bond bemes less than the sum of the covalent radii of the two combining atoms. In case of UO2 , a strange thing is happening. The bond length between U and O in UO2 ≈2.37 A^0. This is more than the sum of U and O radii[ 1.42+0.73=2.15A^0]. This is called lengthening of the bond and we have to explain it as follows:

Accoding to the explanation given in your paper- what is happening is that there comes the contribution from 6p( Although energically higher than 5f where the electrons of U^4 should rightfully be present) BECAUSE ACCORDING TO Special relativity and Mass-energy equivalence, THE ENERGY OF MICROSCOPIC PARTICLES LIKE ELECTRONS INCREASES WITH THE VELOCITY ACCORDING TO THE EINSTIEN’S FOLLOWING RELATION:

E=mc^2/(1-v^2/C^2)0.5-------[I]

Put denominator=γ

So E= γ mc^2. ------------------[II]

This means that the electron cloud encompasses the 6p while overlapping with 2px and 2py of O. In a way, rather than remaining in 5f of U^4 and 2px/2py of O, it enters the higher 6th shell(6p) of U^4 and thus the bond length between U^4 and O increases rather than this bond length should have been less than tha sum of radii of U^4 and O.

BUT STILL ONE POINT IS LEFT UNANSWERED AND THAT IS- WHY THIS HAPPENING HERE IN U?

PLS. KEEP IN MIND THAT BOTH THE ENERGY AND VELOCITY INCREASE {see relations given below} AS THE ELECTRON REACHES HIGHER SHELL SAY IN 6th . 7th ETC. BECAUSE THE HOLD OF THE NUCLEUS ON THE OUTERMOST 6th , 7th etc. SHELL ELECTRON DECREASES AND SO THE ELECTRON CAN MOVE WITH A HIGHER VELOCITY AND THUS CAN ATTAIN HIGHER ENERGY DUE TO THE ABOVE GIVEN RELATION[I].

En= - 1312/n^2 kJ/mole --[III]

V=nh/2 π mr --------------[IV]

Again, it should be borne in mind that this relativistic relation is not only applied here. Any one of my RG colleage must have noticed that in ESR, the theoretical value of “g” of a free electron as calculated by LANDE’s relation comes out to be EXACTLY 2.0 , but the books/ scientists report this value to be 2.0023; the quantity 0.0023 arrives from the relativistic effect.

Thank you dear Manohar Sehgal.