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Optimized gaussian bond functions for CO
1 February L974
CHEMICAL PHYSICS LETTERS
Volume 24, number 3
OPTIMIZED
GAUSSIAN
BOND FUNCTIONS
FOR CO
T. VLADIMIROFF Propellams Divizion. Feltmm Research Laboratory, picatinny Arsenal. Dover, New Jersey 07801, USA Received 24 September 19 73 Revisedmanuscript received5 November 1973
Optimum bond function parameters of biS = 1.12 and czp = 0.70 placed at 0.44 of the bond distance from the the total ground-state energy is lower than that obtained by Neumann and Moskowitzusingtwo sets of 3d type polarization functions on each atomic center with exponents of 0.5 and 1.5. The one-electron properties, however, are slightly inferior to those calculated using the 3d functions. oxygen atom are reported for the CO molecule. Using these parameters,
Recentiy, we have explored [I ] the use of bond functions
(gaussian-type
functions
placed in the molecular bonding legion) in the case of the homonuclear molecules Nz and 02 - The heteronucfear molecule LiH has been considered by Russegger et al. [2]. In the present note we would like to explore the heteronuclear multiply bonded system, CO. The LCAO MO SCF calculations were performed using POLYATOM [3 1, a gaussian system of computer prog&s supplied by Professor Moskowitz. We employed the (9sSp) atomic basis of Huzinaga [4]_ The functions were contracted to [4s3pJ according to Dunnitig’s rvles [5]. The experimental equilibrium distance of’iQ ~2.132 au [6] was employed throughout thiswork. The z axis-was chosen to lie along the Xnt&nucletir axis. We optimized 1s; 2p,, and 2p,, offcenter orbit@ by varying both.their exponents and their common center simultane&sly. The minimum .~energy was found by passing a secdndidegree poly-. nomial inch&rig the cross ten& throughthe points &round the stispected minimum and then finding the mifiimum .for tjle_polynomialgnalytically. Our-re$ts .are stimtiarized in .table 1.4&g with the values ob: ‘. t&ed b$ Neumann and &foskow& [7 ] arid the high- : ly.accura&caI&@on& ofHgo‘,[8]. _ .’ .. . : -‘&e b&t energy we ob;tainkd:was-_l,i2,7648 $u :_ .which &F&ponds t&S&= I .j2;:sip k.O.70 at a posi-’ .,_ .. .. -$$;. ~~-,_.~~.:.-‘~~~:’ ‘. ~, --;.-_:::;1 j:];. 1 :. -q:. J,, .,.:.::~:-;:.;;:j$ .: __j.... .._.: ::y._ ._’ .. --....- ..-. ; . . ... . I,-. ‘.
‘;^
.-
tion R = 0.44 R. measured from the oxygen atom. Our energy is lower than the energy obtained by Neumann and Moskowitz [7J, but their one-eiectron properties are usually closer to the accurate properties computed by Huo 181. This is probably because the larger basis set has the required flexibility to obtain accurate properties while our basis set is too strongly slanted in favor of the energy. A glance at table 1 also reveals that the exact position for the additional center is not very important for a bond which is not too polar. The exponent for the more diffuse p orbital hardly changes as its center is moved. A position at the center’of the bond or displaced 5 to 10% towards the more electro-negative atom.should not be far from optimum. Our work [I] also suggests that the exponents of I,, = 1.1 .and czp = 0.7 should be a good fist approximation in multiply bonded systems involving first-row atoms. we, therefore, suggest that these values be used in the future either as a starting point in more elaborate: ojitimization schemes’or as an approx&nation tb the-optimized set for these tyies.of rnolect+s~~ -, .,T$ authoi tl$r&Di;]E~&. Sharkoff’ for.&ppor&g this rese&ch; MrS. &bdra_~~;.:de Boer for hi$pi@g with the @reparation df_t$e n&u+scri$; a$ MIS? for _ .. .-pra~idmg-cdrnputer fz+iliti& ?rofe&or,j&s ,_ .. . . __.. .: _z . ._,: ._c:-., : .. -. .,...._ ..-. ,. - ;._:. . . . <:.: _.
Volume 24, number 3
1 February 1974
CHEMICAL PHYSICS LETTERS -Table I Summary and comparison of computed properties for the CO moiecuiea) primitive basis (lOsSp2d)b)
(4s3pid10c)
(QsSp; lslp) Contwcted
[Ss3p2d]
basis
14s3p; lslp] 0.44 1.12 0.70
0.5 1.18 d) 0.69 d)
0.3
0.4
1.09 d) o=Iod)
1.01 d)
0.70 d)
I5.0.5 -112.7622 2.002270 -20.66136 -11.3605 1 -1.52128 -0.80308 -0.5.5430 -0.63776 0.245 -2.089 1.036 3.129 -31.457
-112.7860 2.001278 -20.66123 -11.35927 -1.51920 -0.80235 -0.55304 -0.63771
-112.7648
-112.7640 2.001222 z--2O.66922 -11.36466 -1.52636 -0.79974 -055 369 -0.64060 0.381 -2.48 1.24 5.98 -31.624
-31.462
2.00i310 -20.66968 -I 1.36454 -1.52543 -0.80127 -055299 -0.64048 0.346 -2.47 1.23 6.04 -31.621
-17.884 -0.153 0.361 0.208 326.40
-17.858 0.146 -D.f38 0.0077 326.54
-17.825 0.236 -0.59 I -0.355 326.48
-17819 0.208
271.10
271.20
270.80
354.05
3S4.21
354.3 1
444.53
444.90
410.52 461.54 -1.135 0.565 -0.697 0.3485 117.321 287.218
0.274
-2.14 1.07
-l.12.7646 2.001345 -20.67015 -11.36465 -1 s2520 -0.80220 -055256 -0.64047 0.323 -2.46 1.23 6.09 -31.620 -17.832 0361 -0535 -0.274 326.47
-17.850 0.338
270.83 354.30
270.79
270.82
354.3 1
354.27
444.69
444.70
444.68
444.64
411.16
420.23
420.17
410.29
410.49
461.75 -1.18 0.590 -0.679
461.92 -1.115 ofi57 -0.644 0.322 120.752 295.672
461.97 -1.109 a.554 -0.678 0.339 120-77 1 295.669
461.87 -2.118 0559 -0.617 0.309 120.742 295.667
461.72 -1.122 0.561 -0.549 0.274 120-722
0.3395
a) AU.quantities in atomic units tantess specified ctlterwise. seerefs. [7, IO]_ b) Taken from rd [?I. ._c) Taken from ref. {8]. d) Optimiied at the specified el Dipole mdment. 0 Quadi&& moment computed gl Octopote moment ccmp&ed at th¢er of &ass. at, the center of mass. i) Force, 1 au =0.82352? X j? Electronic contribution to the diamagnetic shieldiag.~
-0.702 -0.494
326.48
-0.459 -0.121 326.45
295.694
For definitions of the properties see, For example, ref. 19 J. in addition .. value of RlRo. .. at the center of mass. h} Elect&& con@i$ution to thk d&&de ru&ptib& C%Wtptitud lo? dyne. @,Density_at tke nucleus. ‘. .. k) EIectric.field gradient.
‘. ‘. ,.
‘.
.
-112.7620 2.001377 -20.67194 -1 I.36557 -1.52586 -0.80416 -0.55172 -0.64077 0.277 -2.44 1.22 6.18 -31.627
suppged computer . prbgr&ns; Thanks tire &o due to ---‘. .. . .. . -. :
..-mp’t. -.: ..-
: rl-.. y .:. :
_,.
.‘:;
:
:
..,., -:.
.. .,.../ .; ,_.’ -2., ...-
.Volume 24, number 3
CHEhWAL
Reference8 [Ll T. VLa$mLroff, J. Pbys. Chem. 77 (1973) 1983. 121 P. Ruscgger. H. Lischka and P. Schuster. Chem. Phys. Letters 12 (1971) 392. [3 J LG. Csizmadia, M.C. Harrison, J-W. Moskowitz and B.T. SutcLiie, Theoret. Chim. Actu 6 (1966) 191. [4] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293.
E’HYSiCS LETTERS
I Febrnary 1974
[S] T.H. Dunning Jr., 3. Chem. Phys. 53 (1970) 2823. [6j D.H. Rank, A.H. Guenther, G-D. Saksena, J.N. Shearer and T-A. Wiggins, J. Opt. Sot. Am. 47 (1957) 686. 171 D-B. Neumann and J-W. Moskowitz, J. Chem. Phys. 50 (1969) 2216. [81 1%‘. Hue, J_ Chem. Phys. 43 (t965) 624. f9] XI. Krauss. Natl. Bur. Std. Tech. Note No. 438 (1967). [lo] D.B. Neumanu and J.W..Moskowitz, 3. Chem. Phys. 49 (1968) 2056.
CHEMICAL PHYSICS LETTERS
Volume 24, number 3
OPTIMIZED
GAUSSIAN
BOND FUNCTIONS
FOR CO
T. VLADIMIROFF Propellams Divizion. Feltmm Research Laboratory, picatinny Arsenal. Dover, New Jersey 07801, USA Received 24 September 19 73 Revisedmanuscript received5 November 1973
Optimum bond function parameters of biS = 1.12 and czp = 0.70 placed at 0.44 of the bond distance from the the total ground-state energy is lower than that obtained by Neumann and Moskowitzusingtwo sets of 3d type polarization functions on each atomic center with exponents of 0.5 and 1.5. The one-electron properties, however, are slightly inferior to those calculated using the 3d functions. oxygen atom are reported for the CO molecule. Using these parameters,
Recentiy, we have explored [I ] the use of bond functions
(gaussian-type
functions
placed in the molecular bonding legion) in the case of the homonuclear molecules Nz and 02 - The heteronucfear molecule LiH has been considered by Russegger et al. [2]. In the present note we would like to explore the heteronuclear multiply bonded system, CO. The LCAO MO SCF calculations were performed using POLYATOM [3 1, a gaussian system of computer prog&s supplied by Professor Moskowitz. We employed the (9sSp) atomic basis of Huzinaga [4]_ The functions were contracted to [4s3pJ according to Dunnitig’s rvles [5]. The experimental equilibrium distance of’iQ ~2.132 au [6] was employed throughout thiswork. The z axis-was chosen to lie along the Xnt&nucletir axis. We optimized 1s; 2p,, and 2p,, offcenter orbit@ by varying both.their exponents and their common center simultane&sly. The minimum .~energy was found by passing a secdndidegree poly-. nomial inch&rig the cross ten& throughthe points &round the stispected minimum and then finding the mifiimum .for tjle_polynomialgnalytically. Our-re$ts .are stimtiarized in .table 1.4&g with the values ob: ‘. t&ed b$ Neumann and &foskow& [7 ] arid the high- : ly.accura&caI&@on& ofHgo‘,[8]. _ .’ .. . : -‘&e b&t energy we ob;tainkd:was-_l,i2,7648 $u :_ .which &F&ponds t&S&= I .j2;:sip k.O.70 at a posi-’ .,_ .. .. -$$;. ~~-,_.~~.:.-‘~~~:’ ‘. ~, --;.-_:::;1 j:];. 1 :. -q:. J,, .,.:.::~:-;:.;;:j$ .: __j.... .._.: ::y._ ._’ .. --....- ..-. ; . . ... . I,-. ‘.
‘;^
.-
tion R = 0.44 R. measured from the oxygen atom. Our energy is lower than the energy obtained by Neumann and Moskowitz [7J, but their one-eiectron properties are usually closer to the accurate properties computed by Huo 181. This is probably because the larger basis set has the required flexibility to obtain accurate properties while our basis set is too strongly slanted in favor of the energy. A glance at table 1 also reveals that the exact position for the additional center is not very important for a bond which is not too polar. The exponent for the more diffuse p orbital hardly changes as its center is moved. A position at the center’of the bond or displaced 5 to 10% towards the more electro-negative atom.should not be far from optimum. Our work [I] also suggests that the exponents of I,, = 1.1 .and czp = 0.7 should be a good fist approximation in multiply bonded systems involving first-row atoms. we, therefore, suggest that these values be used in the future either as a starting point in more elaborate: ojitimization schemes’or as an approx&nation tb the-optimized set for these tyies.of rnolect+s~~ -, .,T$ authoi tl$r&Di;]E~&. Sharkoff’ for.&ppor&g this rese&ch; MrS. &bdra_~~;.:de Boer for hi$pi@g with the @reparation df_t$e n&u+scri$; a$ MIS? for _ .. .-pra~idmg-cdrnputer fz+iliti& ?rofe&or,j&s ,_ .. . . __.. .: _z . ._,: ._c:-., : .. -. .,...._ ..-. ,. - ;._:. . . . <:.: _.
Volume 24, number 3
1 February 1974
CHEMICAL PHYSICS LETTERS -Table I Summary and comparison of computed properties for the CO moiecuiea) primitive basis (lOsSp2d)b)
(4s3pid10c)
(QsSp; lslp) Contwcted
[Ss3p2d]
basis
14s3p; lslp] 0.44 1.12 0.70
0.5 1.18 d) 0.69 d)
0.3
0.4
1.09 d) o=Iod)
1.01 d)
0.70 d)
I5.0.5 -112.7622 2.002270 -20.66136 -11.3605 1 -1.52128 -0.80308 -0.5.5430 -0.63776 0.245 -2.089 1.036 3.129 -31.457
-112.7860 2.001278 -20.66123 -11.35927 -1.51920 -0.80235 -0.55304 -0.63771
-112.7648
-112.7640 2.001222 z--2O.66922 -11.36466 -1.52636 -0.79974 -055 369 -0.64060 0.381 -2.48 1.24 5.98 -31.624
-31.462
2.00i310 -20.66968 -I 1.36454 -1.52543 -0.80127 -055299 -0.64048 0.346 -2.47 1.23 6.04 -31.621
-17.884 -0.153 0.361 0.208 326.40
-17.858 0.146 -D.f38 0.0077 326.54
-17.825 0.236 -0.59 I -0.355 326.48
-17819 0.208
271.10
271.20
270.80
354.05
3S4.21
354.3 1
444.53
444.90
410.52 461.54 -1.135 0.565 -0.697 0.3485 117.321 287.218
0.274
-2.14 1.07
-l.12.7646 2.001345 -20.67015 -11.36465 -1 s2520 -0.80220 -055256 -0.64047 0.323 -2.46 1.23 6.09 -31.620 -17.832 0361 -0535 -0.274 326.47
-17.850 0.338
270.83 354.30
270.79
270.82
354.3 1
354.27
444.69
444.70
444.68
444.64
411.16
420.23
420.17
410.29
410.49
461.75 -1.18 0.590 -0.679
461.92 -1.115 ofi57 -0.644 0.322 120.752 295.672
461.97 -1.109 a.554 -0.678 0.339 120-77 1 295.669
461.87 -2.118 0559 -0.617 0.309 120.742 295.667
461.72 -1.122 0.561 -0.549 0.274 120-722
0.3395
a) AU.quantities in atomic units tantess specified ctlterwise. seerefs. [7, IO]_ b) Taken from rd [?I. ._c) Taken from ref. {8]. d) Optimiied at the specified el Dipole mdment. 0 Quadi&& moment computed gl Octopote moment ccmp&ed at th¢er of &ass. at, the center of mass. i) Force, 1 au =0.82352? X j? Electronic contribution to the diamagnetic shieldiag.~
-0.702 -0.494
326.48
-0.459 -0.121 326.45
295.694
For definitions of the properties see, For example, ref. 19 J. in addition .. value of RlRo. .. at the center of mass. h} Elect&& con@i$ution to thk d&&de ru&ptib& C%Wtptitud lo? dyne. @,Density_at tke nucleus. ‘. .. k) EIectric.field gradient.
‘. ‘. ,.
‘.
.
-112.7620 2.001377 -20.67194 -1 I.36557 -1.52586 -0.80416 -0.55172 -0.64077 0.277 -2.44 1.22 6.18 -31.627
suppged computer . prbgr&ns; Thanks tire &o due to ---‘. .. . .. . -. :
..-mp’t. -.: ..-
: rl-.. y .:. :
_,.
.‘:;
:
:
..,., -:.
.. .,.../ .; ,_.’ -2., ...-
.Volume 24, number 3
CHEhWAL
Reference8 [Ll T. VLa$mLroff, J. Pbys. Chem. 77 (1973) 1983. 121 P. Ruscgger. H. Lischka and P. Schuster. Chem. Phys. Letters 12 (1971) 392. [3 J LG. Csizmadia, M.C. Harrison, J-W. Moskowitz and B.T. SutcLiie, Theoret. Chim. Actu 6 (1966) 191. [4] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293.
E’HYSiCS LETTERS
I Febrnary 1974
[S] T.H. Dunning Jr., 3. Chem. Phys. 53 (1970) 2823. [6j D.H. Rank, A.H. Guenther, G-D. Saksena, J.N. Shearer and T-A. Wiggins, J. Opt. Sot. Am. 47 (1957) 686. 171 D-B. Neumann and J-W. Moskowitz, J. Chem. Phys. 50 (1969) 2216. [81 1%‘. Hue, J_ Chem. Phys. 43 (t965) 624. f9] XI. Krauss. Natl. Bur. Std. Tech. Note No. 438 (1967). [lo] D.B. Neumanu and J.W..Moskowitz, 3. Chem. Phys. 49 (1968) 2056.