Pol ish J. Chem., 83, 761 769 (2009) DFT Stud ies of H 3 N X (X = Li, Na, K, R, Cs and Fr) Sys tems * y R. Wieczorek, P. Durlak and Z. Latajka** Fac ulty of Chem is try, Uni ver sity of Wroc³aw, F. Joliot-Cu rie 14, 50-383 Wroc³aw, Po land **e-mail: latajka@wchuwr.chem.uni.wroc.pl (Re ceived No vem er 26th, 2008; ac cepted Jan u ary 6th, 2009) Com plexes of al kali at oms with am mo nium have een stud ied us ing the Den sity Func - tional The ory with nonlocal and quasi-rel a tiv is tic cor rec tions. The sta le com plexes were found for all al kali atom am mo nia com plexes. The cal cu lated in ter ac tion en er gies de crease as one pro gresses down the pe ri odic ta le and are in range from 18.9 kcal/mol for lith ium sys tem up to 6.5 kcal/mol for the frans com plex. Sim i lar ten dency is noted for the cal cu lated val ues of charge trans fer. The in flu ence of cal cu lated quasi-rel a tiv is tic (QR) cor rec tions on val ues of in ter ac tion en er gies is de ter mined. The QR cor rec tions have no ef fect on lith ium com plexes whereas re duce the ind ing en ergy from 0.1 kcal/mol for Na sys tem up to 0.9 kcal/mol for Fr com plex. The DFT cal cu lated IR har - monic fre quen cies are com pared with ex per i men tal val ues and dis cussed. The cal cu lated vi ra tional fre quen cies of am mo nia in com plexes ex hiit trends that for all sys tems they are par al lel to the strength of the ind ing en er gies. For the H 3 N Li com plex the vi ra - tional anal y sis was sup ported y an har mon ic cal cu la tions at the MP2 level. It has een shown that there is a dis crep ancy e tween the ex per i men tal as sign ment and MP2 har - monic and an har mon ic low fre quency intermolecular modes. Key words: density functional methods, MP2 method, molecular complexes, alkali atoms, ammonia, relativistic effects, virational frequencies, anharmonic virational spectra The al kali metal at oms with very unique elec tronic struc ture (sin gle va lence elec - tron) are the most re ac tive el e ments in the pe ri odic ta le. Re ac tions with clas sic Lewis ases are spon ta ne ous and very exo ther mic even at room tem per a tures. How - ever, on a monomolecular scale or in small clus ters as well as at cryo genic tem per a - tures are less re ac tive and formed mo lec u lar com plexes. The mo lec u lar sys tems con tain ing al kali at oms and dipolar mol e cules (e.g. am - mo nia [1 3,5 9], wa ter [4 7]) have een the su ject of sev eral ex per i men tal stud ies. Quan tum chem i cal in ves ti ga tions were mainly con cen trated on lith ium and so dium com plexes with am mo nia (for ex am ple see refs. [7,10 16]) whereas for the heavier al kali atom sys tems the o ret i cal cal cu la tions are yet not avail ale. On the other hand, the very sys tem atic stud ies us ing the in fra red spec tros copy in ma trix iso la tion have een car ried out for the full se ries of al kali atom com plexes with am mo nia [17,18]. * Dedicated to Professor Aleksander Koll on the occasion of his 70th irthday.
762 R. Wieczorek, P. Durlak and Z. Latajka Re ceived ex per i men tal re sults sug gested de crease of ond ing en ergy with in creased atomic num er of al kali atom. In this pa per we pres ent very sys tem atic stud ies of the struc ture, energetics and vi ra tional prop er ties of am mo nia and al kali atom 1:1 com plexes us ing the Den sity Func tional The ory with nonlocal (gra di ent) cor rec tions as well as the quasi-rel a tiv is - tic ef fects. An other pur pose of this work is to pro vide an in for ma tion on the role of vi - ra tional anharmonicity for the H 3 N Li sys tem. COMPUTATIONAL DETAILS The full ge om e try op ti mi za tion for com plexes and the iso lated am mo nia mol e cule has een made y means of gra di ent method. Dur ing the ge om e try op ti mi za tion of the com plexes, a C 3V con straint has een as sumed with the al kali atom ap proach ing the ni tro gen of am mo nia along the C 3 axis. For H 3 N X com plexes (where X = Li, Na, K, R, Cs and Fr) was used the ADF den sity func tional pro gram [19] with the gra di ent cor rected BPW91 ex change-cor re la tion func tional and with the ADF s orig i nal tri ple-zeta Slat er Type Or ital (TZ-STO) a sis set plus a sin gle set of po lar iza tion func tion. The in ner shells were treated y the frozen core ap prox i ma tion. The quasi-rel a tiv is tic cor rec tions of frozen core were o tained us ing the Quasi-First-or der-sca lar Pauli for mal ism [20]. All cal cu la tions were car ried out at the un re stricted level. The spin con tam i na tion was neg li gi le. The an har mon ic vi ra tional spec tra for the H 3 N Li sys tem were cal cu lated at the MP2 level with the 6-311+G(2d,2p), 6-311++G(2d,2p) and aug-cc-pvtz a sis sets us ing a sec ond-or der perturative treat - ment ased on qua dratic, cu ic and semidiagonal quartic force con stants. The ap plied method was pro - posed y Barone [21,22] and is im ple mented in the GAUSSI AN 03 pack age [23]. The cal cu la tions were car ried out for the ge om e try reoptimized at the MP2 level with aove men tioned a sis sets. RESULTS AND DISCUSSION Struc ture and en ergy of in ter ac tion. The re sults of ge om e try op ti mi za tion for the iso lated am mo nia mol e cule and com plexes of am mo nia with al kali at oms (Li, Na, K, R, Cs, and Fr) at the TZ-STO a sis set and the quasi-rel a tiv is tic cor rec tions are re ported in Ta le 1. The intermolecular dis tance, R(N X), de fined e tween the ni - tro gen atom of am mo nia and the al kali atom, elon gates as one pro gresses down the pe ri odic ta le. Val ues of R(N X) are con sis tent with the larger size of the al kali atom and change from 2.07 Å for the lith ium sys tem up to 3.56 Å for the frans com - plex. More over, the val ues of intermolecular dis tance are sen si tive to the level of frozen core ap prox i ma tion. Lower level of freez ing gives shorter dis tances y aout 0.1 Å. For all stud ied sys tems the com plex for ma tion only mar gin ally de formed the in ter nal struc ture of am mo nia su unit. In the case of H 3 N Li sys tem the cal cu lated intermolecular dis tance is sim i lar to that re ported in the ear lier study of Salter and Ellis (2.040 Å) at the MP2/aug-cc-pVTZ level of cal cu la tions [16] as well as to the ap pro pri ate MP2 ge om e try op ti mi za tion cal cu la tions in this work.
DFT stud ies of H 3 N-X (X = Li, Na, K, R, Cs and Fr) sys tems 763 Ta le 1. Cal cu lated prop er ties of H 3 N X com plexes at the BPW91/TZ-STO level. Sys tem Level of freez ing R(N X) r(n H) (HNH) E ind [kcal/mol] E diss [kcal/mol] Charge transfer [Å] [Å] [deg.] rel. non-rel. rel. non-rel. [e] H 3 N 1.02 (1.01) a 105.7 (106.7) a H 3 N Li 1s 2.07 1.03 106.0 18.9 18.9 17.7 17.7 0.024 H 3 N Na 1s 2.51 1.03 105.9 13.9 12.5 13.0 11.7 0.019 1s 2p 2.61 1.03 105.8 10.9 11.0 10.1 10.1 H 3 N K 1s 2p 3.00 1.03 105.2 9.0 8.8 8.3 1s 3p 3.09 1.02 105.4 8.3 7.9 7.7 H 3 N R 1s 3d 3.18 1.02 105.4 7.8 8.4 7.2 1s 4p 3.32 1.02 105.5 7.2 7.5 6.6 0.008 0.009 H 3 N Cs 1s 4d 3.46 1.03 105.3 7.1 7.7 6.5 7.1 0.009 H 3 N Fr 1s 5d 3.56 1.02 105.4 6.5 7.4 5.9 6.8 0.001 a Gas-phase ex per i men tal val ues from ref. 24. Lack of SCF con ver gence dur ing fre quency cal cu la tions. The cal cu lated ind ing (E ind ) and dis so ci a tion en er gies (E diss ) are pre sented in Tale 1. The ind ing en er gies of com plexes were cal cu lated as the dif fer ence of the to tal en er gies of the com plex and the iso lated mono mers. For com par i son with stan - dard re ac tion enthalpies ( H 0 ) the cal cu lated ind ing en er gies have to e cor rected y the difference in zero point vi ra tional en er gies ( ZPE) e tween the com plex and the su units. The dis so ci a tion en er gies pre sented in Ta le 1 were the sum of cal cu - lated ind ing en er gies and ap pro pri ate ZPE. Just as in the case of the intermolecular dis tance, the ind ing and dis so ci a tion en er gies are re lated to the na ture of al kali atom. There is a clear trend in the com puted data to wards smaller val ues as one prog resses from Li to Fr atom. The stron gest com plex with am mo nia is formed y the lith ium atom with the ind ing en ergy of 18.9 kcal/mol whereas the sta il ity with Fr is three times smaller and equal to 6.5 kcal/mol. It is worth point ing out that the neu tral com - plexes are al most two times weaker than anal o gous sys tems with the al kali metal cat - ions, whereas the intermolecular dis tances for oth groups of com plexes are prac ti cally un changed [14 16]. Com par i son of ind ing en er gies clearly shows the in creas ing role of rel a tiv is tic ef fects for heavier al kali atom com plexes. In clu sion of the quasi-rel a tiv is tic cor rec - tions has no ef fect on lith ium com plex whereas re duces the ind ing en ergy from 0.1 kcal/mol for Na com plex up to 0.9 kcal/mol for Fr sys tem. The last row of Ta le 1 con tains the val ues of charge trans fer as a net charge trans - ferred from one su unit to the sec ond and were cal cu lated on the a sis of Mulliken s charges. Sign mi nus means that the elec tron den sity is trans ferred from the metal atom to the am mo nia su unit. Re ceived re sults show that only for the lith ium sys tem there is the trans fer of charge of 0.024 e from am mo nia mol e cule to al kali atom. It is con trary to the chem i cal in tu ition and means that the lith ium atom acts as a weak Lewis acid giv ing the (H 3 N) + - Li elec tronic re ar range ment. Re ceived the o ret i cal
764 R. Wieczorek, P. Durlak and Z. Latajka re sult is in agree ment with con clu sions from ex per i men tal ESR stud ies of the H 3 N Li sys tem in ar gon ma tri ces [25] as well as with the value of 0.029 e re ceived from the MP2/6-311+G(2d,2p) cal cu la tions. For re main ing com plexes the charge trans fer is in op po site di rec tion, i.e. from the al kali atom to am mo nia mol e cule giv ing the (H 3 N) - - X + charge re ar range ment. The o ret i cal re sults are con sis tent with sug ges - tions pu lished y Süzer and An drews [17] al though they in di cate that a re ver sal charge trans fer will ap pear for the heavier al kali com plexes e gin ning from the H 3 N K sys tem. Scan ning down the col umn of Ta le 1 with val ues of charge trans fer we see that for the com plexes with K, R, and Cs the same amount of charge trans fer is re ceived and it is smaller than for the Li and Na sys tems. For the frans com plex the charge trans fer is al most neg li gi le. Rel a tively large amount of charge trans fer for the H 3 N Li sys tem is also par tially re spon si le for su stan tial en hance ment of di pole mo ment (3.33 D) due to a com plex for ma tion. Vi ra tional fre quen cies and in ten si ties. Ta le 2 list the fre quen cies and in ten - si ties cal cu lated with the quasi-rel a tiv is tic cor rec tions for the iso lated NH 3 mono mer and al kali metal am mo nia com plexes. The data re ported were o tained us ing the har monic ap prox i ma tion at the DFT/TZ-STO level and no at tempt has een made to scale the cal cu lated fre quen cies. 1 and 2 cor re spond to A 1 sym met ric stretch and end, re spec tively, while the suc ceed ing two vi ra tions de scrie de gen er ate E modes of am mo nia. 5 and 6 are the intermolecular modes and cor re spond, re spec tively, to the intermolecular N X ond stretch and the dou le de gen er ated rock ing of am mo nia su unit. As nor mally ex pected, the fre quen cies cal cu lated at the har monic ap prox i - ma tion are some what higher than ex per i men tal data, due chiefly to the ne glect of anharmonicity. As o served in ex per i men tal low-tem per a ture ma tri ces [17,18] and the o ret i cal stud ies pre sented in Ta le 2, in ter ac tion with al kali atom in duces the change in the vi - ra tional spec tra of am mo nia su unit. Due to the com plex for ma tion the 1, 3 and 4 mode are red shifted whereas the 2 end ing mode is lue shifted. The larg est per tur - a tion of am mo nia mode due to a com plex for ma tion is noted for the sym met ri cal NH stretch ing mode ( 1 ). Also for this mode su stan tial in crease of in ten sity is o served. Cal cu lated fre quency shifts for stud ied se ries of com plexes are in rel a tively good ac cord with avail ale ex per i men tal data from the low-tem per a ture ma trix iso la tion ex per i ment [17,18] and fol low the same ten dency like the ind ing en ergy. The larg est shifts are noted for the lith ium com plex and are smaller as one prog ress down the pe ri - odic ta le. The agree ment e tween cal cu lated and avail ale ex per i men tal data is mod er ate in a quan ti ta tive sense, ut the cal cu la tions do ap pear to re pro duce the im - por tant ex per i men tal trends. Ow ing to the dif fi culty in de tec tion of ands in the far in fra red re gion which cor - re spond to the intermolecular modes, quan tum chem i cal cal cu la tions can play a par - tic u larly im por tant role in pre dic tion and in ter pre ta tion of this part of spectrum. The fre quen cies and in ten si ties cal cu lated for the intermolecular stretch, 5, and the rock - ing of am mo nia, 6, are dis played in the last two col umns of Ta le 2. In all cases, the high est fre quency vi ra tion is pre dicted to e the rock ing of am mo nia su unit in a
DFT stud ies of H 3 N-X (X = Li, Na, K, R, Cs and Fr) sys tems 765 T ale 2. D FT calculated and experimental frequencies (, c m 1 ) and intensities (I, km/mol). System Level of freezing ( stretch I5 6 (rock. ) 3 c I3 1 I1 4 c I4 2 I2 5 ) c I6 H3N c alc. 3 50 3 4 3 38 3 4 1 63 3 3 4 1 04 1 13 4 expt. H3 N L i a 3 447 4 3 34 6 2 1 63 9 2 0 9 7 4 10 0 c alc. 1 s 3 41 5 1 5 6 3 29 5 5 6 3 1 61 0 1 2 1 15 6 6 8 3 4 2 1 6 2 3 9 9 5 expt. a 3 37 9 3 3 27 7 3 0 1 13 3 10 0 expt. 3 38 0 3 27 8 1 60 5 1 13 4 3 2 0 38 1 H3 N N a c alc. 1 s 3 45 1 6 8 3 32 4 3 0 2 1 61 5 8 0 1 10 9 1 0 9 2 7 1 4 2 2 0 2 0 expt. a 3 29 4 4 0 1 07 9 10 0 H3 N K H3 N R H3 N C s H3 N F r c alc. 1 s 2 p 3 45 4 8 0 3 33 0 3 2 7 1 62 8 4 0 1 10 6 1 3 0 2 2 7 6 6 1 2 6 1 expt. a 3 29 2 6 0 1 06 4 10 0 c alc. 1 s 2 p 3 45 6 6 0 3 33 4 3 6 6 1 62 8 6 0 1 09 5 1 2 7 2 0 9 7 0 1 0 5 2 c alc. 1 s 4 d 3 45 9 8 4 3 33 5 5 0 3 1 63 0 3 0 1 08 7 1 4 6 2 0 1 1 4 0 8 3 5 expt. a 3 28 7 7 0 1 04 9 10 0 c alc. 1 s 5 d 3 45 5 1 8 4 3 33 5 6 5 3 1 62 9 2 8 1 08 7 1 8 5 2 1 0 1 7 6 9 0 8 F rom the Ar matrices, ref. 17. The integrated intensities normalized to the strongest and of ammonia and complex ( 2 and). F rom the Ar matrices, ref. 18. Doule degenerated. a c
766 R. Wieczorek, P. Durlak and Z. Latajka T ale 3. Harmonic and anharmonic virational frequencies calculated at the MP2 leve l a. S ystem 6-311+G(2d,2p ) 6-311+G(2d,2p ) a ug-cc-pvt Z Expt. H3N h arm. a nharm. h arm. a nharm. h arm. anharm. 3 d 3 67 3 ( 8 ) 3 50 1 3 67 3 ( 8 ) 3 50 2 3 65 0 ( 8 ) 3 48 4 344 7 1 3 53 3 ( 3 ) 3 38 2 3 53 2 ( 2 ) 3 38 1 3 50 3 ( 3 ) 3 36 0 334 6 4 d 1 69 1 ( 17 ) 1 64 0 1 69 2 ( 17 ) 1 64 0 1 66 9 ( 14 ) 1 62 1 163 9 2 1 05 6 ( 172 ) 9 6 7 1 06 0 ( 170 ) 9 7 0 1 03 7 ( 139 ) 9 5 9 97 4 H3 N L i c 3 d 3 61 1 ( 64 ) 3 42 5 3 61 0 ( 64 ) 3 42 4 3 59 1 ( 63 ) 3 41 1 3 37 9 338 0 1 3 47 6 ( 237 ) 3 30 9 3 47 4 ( 253 ) 3 30 6 3 44 8 ( 278 ) 3 29 0 3 27 7 327 8 4 d 1 67 5 ( 15 ) 1 63 7 1 67 5 ( 15 ) 1 63 6 1 65 6 ( 14 ) 1 61 8 160 5 2 1 20 7 ( 196 ) 1 14 6 1 20 7 ( 191 ) 1 14 6 1 18 3 ( 178 ) 1 12 7 1 13 3 113 4 5 4 2 4 ( 11 ) 4 0 0 4 2 4 ( 11 ) 4 0 0 4 2 4 ( 13 ) 4 0 0 32 0 6 3 8 0 ( 206 ) 3 7 1 3 7 9 ( 204 ) 3 7 0 3 7 1 ( 203 ) 3 6 3 38 1 1 Frequencies in cm, intensities From Ar matrices, ref. 17. From Ar matrices, ref. 18. Doule degenerated. in km/mol (given in parentheses). a c d
DFT stud ies of H 3 N-X (X = Li, Na, K, R, Cs and Fr) sys tems 767 com plex. Our cal cu lated value 399 cm 1 for the H 3 N Li com plex agrees well with the ex per i men tal value of 381 cm 1 [18]. The intermolecular stretch is lo cated at the lower wavenumers. Also in this case the cal cu lated value of 342 cm 1 for the H 3 N Li com plex agrees nicely with the ex per i men tal and lo cated at 320 cm 1 [18]. The fre quen cies of the intermolecular modes are roughly pro por tional to the ind ing en er gies in stud ied sys tems in that the more strongly ound com plexes tend to have larger intermolecular fre quen cies. We also note that the intermolecular stretch ing 5 mode is consideraly more in tense than the 6. In Ta le 3 are pre sented har monic and an har mon ic vi ra tional fre quen cies of the iso lated NH 3 mol e cule and the H 3 N Li com plex cal cu lated at the MP2 level with three dif fer ent a sis sets: 6-311+G(2d,2p), 6-311++G(2d,2p) and aug-cc-pvtz. Anal y sis of pre sented data in di cates that cal cu lated re sults at the an har mon ic level are in much etter agree ment than the har monic one. Es pe cially large anharmonicity ef fect is noted for the NH stretch ing modes of am mo nia ( 1 and 3 ). Sur pris ingly, the anharmonicity has very small in flu ence on the intermolecular modes ( 5 and 6 ). Choice of the a sis set, at least for rel a tively large a sis sets used in this pa per, has al - most no in flu ence on cal cu lated fre quen cies. For the in ter nal modes of am mo nia in a com plex sim i lar fre quency shift is o served like for the re sults o tained at the DFT level. The main dif fer ence is for the low-fre quency intermolecular modes. Con trary to the pre vi ously de scried DFT re sults and ex per i men tal as sign ment pro posed y Loutellier and co work ers [18], the MP2 cal cu lated har monic and an har mon ic intermolecular stretch ing mode is at higher wavenumers (400 cm 1 ) than the rock - ing mode of am mo nia (e.g. 363 cm 1 at the MP2/aug-cc-pVTZ level). Sim i lar fre - quency or der at the har monic level re cently was o tained y Salter and Ellis on asis of the MP2/aug-cc-pVTZ cal cu la tions [16]. Noted dis crep ancy needs an ex pla na tion and will e the su ject of fu ture work [26]. CONCLUSIONS The cal cu la tions re ported herein rep re sent a sys tem atic and uni form den sity func tional study of the am mo nia al kali atom, from Li to Fr, com plexes. Use of the same qual ity a sis set and the same the o ret i cal pro ce dure for all sys tems al lows di rect com par i son in the se ries of com plexes un der con sid er ation. All stud ied al kali at oms form sta le 1:1 com plexes with am mo nia. Com plex with lith ium is the most strongly ound, E ind = 18.9 kcal/mol, and strength of ind ing di - min ishes with in creased atomic num er of al kali atom. Rel a tiv is tic ef fects, as o - tained us ing the Quasi-First-Or der-sca lar Pauli for mal ism, play an im por tant role for heavy al kali atom com plexes. A small amount of charge trans fer noted in the se ries of com plexes in di cates on the di pole in duced di pole as the dom i nant mech a nism of in - ter ac tion. The cal cu lated vi ra tional fre quen cies of am mo nia su unit in a com plex ex hiit trends that for all sys tem par al lel the strength of in ter ac tion. The fre quen cies of the intermolecular modes are also roughly pro por tional to the ind ing en er gies. Calcu-
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