MVIB: A system of programs for treating normal coordinates of chain molecules

0097-8485/90 63.00 + 0.00 Copyright Q 1990 Pergamon Press plc

Compurers them. Vol. 14, No. 1, pp. 59-67, 1990 Printed in Great Britain. All rights reserved

MVIB: A SYSTEM OF PROGRAMS FOR TREATING NORMAL COORDINATES OF CHAIN MOLECULES HIROATSU MATSUURA Department

of Chemistry,

Faculty

(Received

of Science, Hiroshima University, Hiroshima 730, Japan

16 February

1989; received for publicarion

Higashisenda-machi,

9 March

Naka-ku,

1989)

Abstract-A

system of programs for treating normal coordinates of chain molecules is presented. Input data are minimal, and consist mainly of the name of the molecule and its conformation. The system consists of a program written in FORTRAN-77 and a data base of force constants, structural parameters, etc. When executing the calculation for a particular molecule, the various required quantities are retrieved from the pertinent data base. This highly simplifiedinput format makes the system applicable, not only to specific research in vibrational spectroscopy, but also to casual calculations by nonspecialists. The relevance of the group coordinate

force field adopted in this system is also discussed.

INTRODUCTION In the analysis of i.r. and Raman spectra, a normal analysis is often used to extract as much available information as possible from the spectra. Several program packages for the normal coordinate analysis of polyatomic molecules have been developed (IUPAC, 1985; Painter et al., 1982; Schachtschneider, 1966; Shimanouchi, 1968) and have been widely utilized in studies of vibrational spectra of a variety of compounds (Shimanouchi, 1977). These standard programs are, in fact, quite useful, but preparing input data requires an intimate acquaintance with normal coordinate analysis. Also, a substantial problem often encountered is occurrence of errors in the input data, a problem that becomes increasingly serious for larger molecules since the amount of data necessary for computation increases rapidly as the number of atoms in the molecule increases. Under these circumstances a program more intelligent than the conventional ones is to be desired, one which would perform a normal coordinate analysis from minimal input of, say, only the name of the molecule. In line with this basic idea we have developed a system of programs for calculating normal vibrational wavenumbers, modes of vibrations and other related properties of chain molecules consisting of fundamental chemical groups. This system, called MVIB for molecular &rations, has been applied successfully to studies of molecular conformations of a variety of chain molecules (Matsuura & Tasumi, 1983, and references cited therein). The features of this system of programs will be presented in this paper.

coordinate

HITAC M-680H computer, consists of two components: one is the program written in FORTRAN-77 and the other is the data base. The latter consists of six data files of force constants, one of structural parameters, and one of atomic masses. A block diagram of the MVIB system is shown in Fig. 1. In this system the atomic groups, coordinates, force constants and atoms are all represented by computerrecognizable symbols. When executing the calculation of normal coordinates for a particular molecule, the information about force constants, structural parameters and atomic masses required for the molecule is retrieved from the pertinent data files. If no immediate information for the molecule is available in these files, particularly the force constants, the calculation can be performed by employing appropriate data that are transferred from analogous atomic groups or molecules; the information for this secondary choice is provided in one of the files. Users can also externally supply pertinent temporary data if the required data are not available in the files, or even if they are available. In the latter case, the external data take priority in the calculation over the internal data. The transfer and the external supply of part of, or all of, the necessary data make the calculations flexible. The program system can also treat the calculation of force constants by an iterative least-squares procedure and the values obtained for the force constants may be entered into the data file for future use.

METHOD Normal coordinate

OVERVIEW OF THE SYSTEM The MVTB program

treatment

The treatment of normal coordinates in the MVIB system is based on Wilson’s GF matrix method (Wilson er al., 1955). The potential energy of a

system, now running on a 59

60

HIROATSUMATSLIURA

molecule is given by: I’ = fSFS

St S2 s3 =f[S,S,S,...]

.

,

L

where s and S are the row and column vectors, respectively, consisting of appropriate coordinates S, , S,, S, , . _ . which describe motions of the molecule, and F is the potential energy matrix whose elements _L..L;z~fi3~ * ‘. are the force constants. We adopted in MVIB the group symmetry coordinates For the respective chemical groups constituting the molecule as Sis and the force constants associated with these coordinates asJjs. The force field expressed in terms of the group symmetry coordinates is called the group coordinate force field (GCFF) (Matsuura & Tasumi, 1983). On the other hand, the kinetic energy is given by: T=$G-Is,

(2)

where G is the inverse kinetic energy matrix which depends on the molecular geometry and the masses of atoms. The G matrix in terms of the group symmetry coordinates is incorporated with the F matrix to give the equations of motion in the Lagrange form: S+GFS=O.

(3)

By assuming periodic solutions of the form s = L cos(A”l 1 + a),

equation (3) becomes: GFL = Ld. The secular equation is therefore given by IGF-EELI=O,

(6)

where E is the unit matrix, and ;1 and L represent the eigenvalues and the corresponding eigenvectors, respectively, of the GF matrix. Since the GF matrix is not symmetric, we actually use a method of diagonalizing two symmetric matrices sequentially (Painter et al., 1982; Shimanouchi, 1968). In the MVIB system, the matrix diagonalization is made by either a Jacobi method or a Householder method by option. The wavenumber of the kth normal vibration is given by q( = a:‘2/2ac,

(7)

where c is the velocity of light. The mode of the normal vibration is conveniently represented by the potential energy distribution (PED) in percent: (PED),

(4)

Interactive

= 100 x Lfk_f&,

mode

Data files Data

(5)

files

Terminal mode Dump mode

Fig. 1. Block diagram of the MVIB system.

@)

61

MVIB which represents the fractional contribution of the itb symmetry coordinate to the potential energy of the kth normal mode, but neglects vibrational interactions between different coordinates, since

where (0) denotes the nonexistent adjacent group. The potential energy of a chain molecule is expressed in general by: ’ = C ?illW + C 51liW + C I

Group coordinate force fieZd (GCFF) Sotie features of GCFF relevant to the MVIB system will be presented below, since the description of the force field is an important point of this system. Organic molecules consist of various chemical groups such as -CHI,, -CH,-, -C(=O)and -NH, etc. and the molecule is represnted by a combination of these groups. Each of these atomic groups has certain local symmetry; for example, the -CH, group group has C2”, the has C& symmetry, the -CH,-NH2 group has C,, and so on. The coordinates based on the group symmetry are adequate as basis coordinates for describing the motion of a molecule composed of such atomic groups. In this coordinate system, the redundant coordinates involved in some of the atomic groups are easily eliminated in accordance with the group symmetry and the geometry. Accordingly, the group symmetry coordinates thus constructed are all independent of and mutually orthogonal to one another within the group. In this way, GCFF expressed in terms of these coordinates is mathematically well-defined, unlike the internal valence force field which has been used, along with GCFF, for normal coordinate analysis of chain molecules (Matsuura % Tasumi, 1983). The potential energy of a chain molecule a-b-cd, consisting of the atomic groups a, b, c and d, may be expressed on the basis of GCFF by:

+ V,, + v,+

V,, + v,+

V,,

(10)

where F’,, V, , V, and V, are the potential energies for the atomic groups a, b, c and d, respectively, V,, V,, and V, are the potential energies for the interactions between the nearest neighboring atomic groups, Q and b, b and c, and c and d, respectively, V,, and V, are those between the second-neighboring groups, a and c, and b and d, respectively, and so on. Since the force fields of the respective groups themselves are affected, in generai, by the adjacent groups through, for example, the chemical bonds connecting the groups. The atomic group is thus defined more specifically by designating its nearest neighboring groups: for example, the atomic group b given above is denoted by (a)b(c), indicating the atomic group b with the adjacent groups a and c shown in parentbeses. The potential energy of the molecule is then given by:

Jk

v(i)j(k)f(m) +

r . ‘.

(12)

P

The first term represents the intragroup potential and the second and higher terms represent the intergroup potential. The third and higher terms are much less significant than the first two terms and are safely omitted in usual cases from the potential function. The intragroup potential V,,,,,, and the intergroup potential Vtilik(,) are given in terms of the force constants:

+ Cf.

Ol~(kl_ ~'4s-O)/(k) P

_ s (lb(k)_9) (13)

PC@

where Sti)j(k)_-pis the group symmetry coordinate p belonging to the atomic group j with the adjacent groups i and k, and S~jtik~,l _, is the intergroup coordinate r associated with the atomic groups j and k with the adjacent groups i and I (for example, the C-C stretching or torsion coordinate of the (Cl)CH,-CH,(O) part). The constants f;,lxkJ_p and &W-W in V,,lAk,are diagonal and off-diagonal intragroup force constants, and f;i)jk(i) - p4, &kc,, _,, f.WM~)-.Dr and J&,~_ ,~ in V&,,, are intergroup force constants. Since the potential function of GCFF is composed of the tractable intragroup and intergroup potentials, these constituent potentials and therefore the force constants are readily transferable to structurally similar parts of different molecules. The explicit definitions of the group symmetry coordinates including their signs are particularly important, because these coordinates are linear combinations of the internal valence coordinates and the signs of the interaction force constants are directly correlated with the signs of the coordinates concerned. In the MVIB system, we adopt the definitions of the internal valence coordinates and the group symmetry coordinates recommended by the IUPAC Commission on Molecular Structure and Spectroscopy (IUPAC, 1978; Matsuura & Tasurni, 1983). Symboiism consrants

of atomic groups, coordinates and force

In the MVIB system, the atomic groups, the group symmetry coordinates and the associated force

62

HIROATSU MATSUURA

coordinates, with additional designation of the conformation when it is necessary. For the symbols of the intragroup force constants, the first three characI -CHFLJ -CH, ters denote the atomic groups, the second implying 2 -CH,K, L xH(CW3 -o-NHM,N the atomic group in question and the first and the 4 -SO -POthird implying the two adjacent atomic groups, the 5 -Cl ZH=CH, 6 fourth character is a blank, and the fifth character for -Br -NH> 6 7 -I R -OH the diagonal force constants or the fifth and sixth 8 s C(=S)characters for the off-diagonal force constants denote &O)_ T -CH(=O) : -NHU -SiH, the coordinate(s) in question. Thus, the diagonal and B V -SiH,-C(=CH,)_ off-diagonal force constants _&+ p and _&),cl;, _ w as -CHClW -SC C, D given in equation (13) are represented by ijkAp and X -C&N -CHBrE, F -CHI% -Co; GH QkApq, respctively, where A denotes a blank; actual Note: A represents a planar -NH- group,whileM and N represent examples are 123A5 for the diagonal CH, wagging B pyramidal-NH- group. C and D, E and F, G and H, I and force constant for the (CH,)CH,(O) group and’ J, K and L, and M and N, are antipodal to each other. 225A46 for the off-diagonal force constant for the Deuterated atomic groups are represented with suffixes such as ‘, ” and l; for example,2’ for -CD,- and 2” for -CHD-. CH2 rocking and the CH2 twisting within the C”Hz group of the (<=“H,)CbH,(C1) part. For the symbols of the intergroup force constants, constants are coded with alphanumeric characters the first four characters denote the atomic groups, the according to systematic symbolism for the purpose of second and the third implying the two atomic groups retrieving required quantities in normal coordinate in question and the first and the fourth implying their calculations. The symbols of the atomic groups are adjacent atomic groups, and the fifth character for given in Table 1. By using these symbols, a molecule the diagonal force constants or the fifth and sixth of CH,OCHzCH,Cl, for example, is represented by characters for the off-diagonal force constants denote 13225. The group symmetry coordinates belonging the coordinate(s) in question. The coordinates given to the respective atomic groups are also given by by the fifth and sixth characters belong, respectively, symbols. The symbols of the coordinates for -CH,, to the atomic groups given by the second and third -CH,-, -C(=Ojand -NH? groups are shown in characters. The seventh character, if any, denotes the Table 2. conformation of the internal-rotation axis given by The force constants are represented by combithe first to fourth characters. The force constants nations of the symbols of the atomic groups and the and &+,,)-, as given in equation (14) are hikW -w Table I. Symbols of the atomic groups used in the MVlB system Symbol

F0tlZWla

Symbol

FCWtTtUla

Table 2. Symbols of the group symmetry coordinates for -CH,, -CH,-, C(=Ob groups Group symmetry coordinate

Symbol

=H, (G) I

2 3 4 5 6

7 8

and -NH,

Symmetry species

CH, symmetrical stretching CH, symmetrical deformation CH, asymmetrical stretching CH, asymmetrical deformation CH, rocking CH, asymmetrical stretching CH, asymmetrical deformation CHI rocking

X-CH,-X (C,,), X-CH,-Y (C,) : 3 4 5 6 D x-C(=o)_X 1

: B -NHz (Cd 1

2 3 4 5

CH, symmetrical stretching CH, scissoring CH, antisymmetrical stretching CH, rocking CHP wagging CHZ twisting XCX or XCY deformation (C,,), X-c(=Q-y (C,) c--O stretchimz CL=0 in-plane bending c--O out-of-plane bending XCX or XCY bending NH, NH; NH, NH, NH,

svmmetrical stretchine scissoring antisymmctrical stretching twisting wagging

c*

C,” 0, 6, b, Ql

u’ a’ a” a’ a’ a’ a” a” a’

Note: the coordinates (3, 4, 5) and (6, 7, 8) for the -CH, group constitute pairs of the doubly degenerate coordinates.

63

MVIB

represented by ijklpq or ijkipqs and ijkCr, respectively, s denoting the conformation of the i-j-k-l part. Actual examples are 012325 for the off-diagonal force constant for the CH, symmetrical deformation and the CH, wagging of the CH,CH2(0) part, 222346G for dhe off-diagonal force constant for the C*H, twisting of the the CcH2 and rocking (C”H&)C*H,C’H,(O) part in the gauche conformation, ~and 22329 for the diagonal force constant for the C&O stretching of the (C”H,)C*H,O(C’H,) part. This symbol representation method of the force constants and other constants enables the MVIB system to treat a variety of molecules collectively. Symbolism of structural

parameters

and atomic masses

The MVIB system also uses appropriate symbols for the structural parameters and the atomic masses. In accordance with the symbols of the atomic groups (Table I), the length of the C-O bond for the CH,-O part, for example, is represented by L13 (or equivalent L31) and the valence angle C-C-G for the CH,-CH,-0 part is represented by Al23 (or equivalent A321). In addition, the length of the C-H bond is given by LO1 and the valence angles H-C-C and H-C--O, for example, are given by Al02 and A103, respectively. The masses of atoms are represented by the symbols of elements with the mass numbers for the specified isotopic species; for example, Cl2 for the mass of ‘*C and CL35 for the mass of WI. On the other hand, the mean relative atomic masses (isotope abundance weighted) are represented by the symbols of elements only; C for the mass of carbon and CL for the mass of chlorine. DESCRIPTION

OF THE SYSTEM

The MVIB program system wrforms normal coordinate calculations for any chain molecule consisting of possible combinations of the atomic groups listed in Table 1. The current version is capable of treating molecules of 120 atoms or less. The input data are minimal, and consist mainly of the molecular name with conformation and the specification of optional output. The molecular name is entered, for (in symbol form) or example, as 13225-TG CH30CH2CHZCL TRANS-GAUCHE (in formula form) for CH,OCH,CH&l in the trans-gauche conformation. In the MVIB system, two modes are available for data input. In the interactive input mode, users respond to the system messages. If the input data entered are wrong or insufficient, the system gives pertinent error/warning messages and suggests appropriate input. This facilitates the use of MVIB by nonspecialists in vibrational spectroscopy. In the batch input mode, on the other hand, users prepare in advance of execution a batch of relevant input data records, each consisting of label part and data part. The label part consists of four characters representing the prompting system messages, to

which the associated data are applicable as in the interactive mode. The important data labels are given in Appendix. The system gives output of not only wavenumbers and assignments of normal vibrations but also, by users’ option, other relevant information about the force constants, structural parameters, molecular geometry, masses of atoms, Cartesian coordinates, internal valence coordinates, group symmetry coordinates, potential energy distributions (in full form), matrices of U, B, G, Lt, Z, F, L, L-‘, L,, J and P (for these matrices, see Shimanouchi, 1968, 1970), and other related quantities such as amplitudes of vibrations, moments of inertia, rotational constants and Coriolis coupling constants. Output of the MVIB system is designed to be in two ways. One is suitable for output of only essential results usually shown on a terminal display or printer (terminal mode). The other is suitable for output of a mass of calculated results (dump mode); the output may be written in a computer file or dumped from a line printer. The MVIB system incorporates eight data files (see Fig. 1). These data are utilized in turn in the calculation of normal coordinates. for a variety of molecules. Description of the respective files is given below. FORCE FEQVL

file-Force constants. file-Equivalence relations of force constants. FRANK file-Ranks of force constant accuracy. FAVLB file-Atomic groups, for which the associated force constants are available in the FORCE and/or FEQVL file. FEQVZ file-Secondary equivalence relations of force constants, which are assumed if lie immediate information for a molecule in question is available in the FORCE or FEQVL file. ZMATX file-Locations of nonzero elements of Z matrices for individual atomic groups. STRUC file--Structural parameters. MASSA file-Masses of atoms. The program part of the MVIB system is written in FORTRAN-77. It consists of a main program, which performs central normal coordinate calculations, and a preprocessing program, which prepares input data for the main program from users’ primary minimal input (Fig. I). The main program was originally taken from a package of programs GCCC, BGLZ, LSMB and LXZ developed by Shimanouchi ahd his group (Shimanouchi, 1968) and was then adapted to our purpose so that it recognizes the symbols of various constants employed in the MVIB system. The input/output format was also revised to be suitable for our system.

HIROATSUMAXWURA

64

A distinctive feature of MVIB is the introduction of the preprocessing program incorporated in the system. This program reads primary input data that the user specifies, and generates full organized data, which are to be transferred to the main program for normal coordinate calculations. These organized intermediate data are similar to the input data for the conventional normal coordinate programs. This means that the preprocessing program works as a generator of such input data as that which have been conventionally prepared manually by users themselves. The preprocessing program examines if the molecular name and conformation entered are appropriate. For example, 221 S-G or CH2CH2CH3CL GAUCHE and 1225-TG or CH3CH2CH2CL TRANS-GAUCHE are rejected accordingly. The program also examines if the force constants necessary for a molecule in question are available in the FORCE and/or FEQVL file. If part of, or all of, the relevant force constants required are missing, specification of the secondary choice is made automatically in accordance with the information in the FEQVZ file. Approximate accuracy of the force constants to be used in the calculation is indicated with four ranks (good, fair, poor and provisional) for the respective atomic groups. This information, although it is a rough estimate, is useful for users to judge the accuracy of the calculated results. EXAMPLES

CHrCHrCHrCl with the frutrs conformation. Some error messages shown are intentionally generated. In this calculation, the essential results of wavenumbers and assignments (ordinary output) and the supplementary results of Cartesian coordinates and masses of atoms (optional output) are printed. The assignments of the normal vibrations are indicated with their PED in percent. The symbols of the coordinates are the same as those of the corresponding diagonal force constants. The phase relations among the coordinates are indicated by the signs. The full PED results can optionally be obtained. The same calculation is made by using the following data set in the batch input mode: NAME # CH3CH2CH2CL DATA ATOM

In the batch mode, appropriate standard values are assumed in default of explicit specification. For example, the default value for CALC is V, that for LEVL is 1, and that for DATA is N (no optional output). The following is the batch input data for the calculation of force constants: CALC F NAME 1321-T OBSW ,,,,, 1485,1472,1462,1456,1392,1365, ---- 1208,1120,1094,1015,853,468,298. ____ ,,,1456,1445,1269,1169,1150,815, ---- 252,200,126 NAME 13(2)2.1-TT OBSW ,,,,,, 1486,1475,1469,1465,1439,1389,

OF CALCULATIONS

Figure 2 shows a printout of the interactive input/ output dialog and the calculated results for GO00 AFTERNOON WELCOME TO MVIB CVERSION=OZ-02 AT 16:54:C8 ON OCT/06/1988 CTHU> TYPE IN MESSAGE MODE (D: OETAILEO GUIOING

CO. S OR MESSAGES.

TRANS

UPOATE=OCT/Ol/88)

<--OATA SIMPLIFIED

LABEL CMESG> MESSAGES; L:

(1.

2.

3

STANDARD

(2)

OF

MOLECULAR

L> S:

DATA

LABELS)

-s #

s

TYPE

ENTERED IN

CALCULATION

MODE

(V

OR

F>

-V #

v

TYPE

ENTEREO

IN

DATA

PROCESSING

LEVEL

OR

0:

VALUE

=

NOT

FOR

‘I>

-1 #

1

ENTERED

TYPE IN MOLECULAR NAME -)2225-Y MOLECULAR COOE=2225-Y r*rERROR**+

FIRST

+++ERROR*++

UNDEFINED

CHARACTER

CHARACTER



OF

CONFORMATION

TYPE IN MOLECULAR NAME -1225-T MOLECULAR CODE=lZ25-T TYPE -AtON

IN

***ERROR**+

OPTIONAL

OUTPUT

UNDEFINED

DATA

KEYWORD

(ATON

CODE

>

IS

TERMINAL

GROUP

MVIB TYPE IN *ATOM # ATOM

CORRECT

KEYWORD

ENTERED

SYMMETRY OUT-OF-PLANE

PLANE

CONTAINING VIBRATIONS

BACKBONE ATOMS WILL BE SEPARATED

** RANK
OF FORCE CONSTANT ACCURACY B:FAIR C:POOR X:PROVISIONAL): 122
TYPE

MOLECULAR

IN

65

FOR

HAS

THIS

BEEN

MOLECULE.

1225
IN-PLANE

ASSUMED:

INDICATED

AND

IN

PARENTHESES

ZZSO

NAME

-N #8# NO

REVIEW OF MOLECULAR MOLECULE-CONFORMATION 1225-T

1

NAMES

ENTERED

OUTPUT

***********c**************** CARTESIAN MOLECULE: CH3CHZCHZCL ATOM 1 2 3 4 5 6 7 8 9 10 11

NO. cc
COORDINATES 1225-T TRANS

AND

MASSES

OF

OF

****************************

MVIB

ATOMS

FORM

X -2.559881 -3.297302 -2.725568 -2.725568 -1 .129912 -0.984594 -0.984594 -0.062833 -0.145601 -0.145601 1 .584288

? ZJ 1 J > I 1 I 1 1

###

Y 0.071498 -0.744719 0.692233 0.692233 -0.497457 -1.169386 -1.169386 0.611535 1 .223278 1.223278 -0.084121

MASS 12.011000 1 .007825 1 .007825 1 .007825 12.011000 1 .007825 1 .007825 12.011000 1 .007825 1.60’1825 35.453000

2 0.000000

o*oooooo 0.892881 -0.892881 0.000000 0.858717 -0.856717 0.000000 -0.910450 0.910450 -0.000000

MOLECULE: 1225-T CH3CHZCHZCL TRANS FORM _--_____----___---__-----------------_____________________________________ OBSD CALCD ASSIGNMENT 2956 225 1 <98+> 2880 012 1 <95+) 2869 122 1 <94+> I 478 122 2 <56+> 1452 012 4 <55+> 1430 225 2 <86+> 1379 012 2<105*> 1342 122 5 (59+) 1269 225 5 (67+> 1101 012 5 (27+> 1030 0122s (79-j 898 012 5 <39+1 728 22505 <80-) 364 122 D <35+) 238 225 0 <71+) _______________---__________~---~~~~~__-_---__--~~~~~~~------------------3005 225 3 (99-l 2962 012 6 C99+) 2905 122 3 <99+> 1463 012 7 C81+> 1295 122 6 C56-2 1228 225 6 (CO+> 1077 225 6 <32+) 864 225 4 <45*1 743 122 4 C60,) 227 0122T C96+) 129 1225T <88+> _____________________~~~-__~~~~~~~~~~~~~~~~~~~~~~----~~------------------###

END

OF

Fig. 2. Printout

MVIE

X1

012 122

4 2

<28+> (37->

225 122 12255 12255 1225s 225 22503 122

5 5

D

(30-> (24+) C27-) C20+> C39+) <19+1 <49-)

012 225 012 225 012 225

8 6 8 4 8 4

Cl4+> C23+> <17-) <21-> C41+> <26->

0

1225s

(15+>

122

5

<14+>

122 225

D D

Cll+) Cl7*)

122 012 122 012

4 8 6 8

ClC+) Cl6+> C23+) C13+>

122

0

c

122 122

6 4

c11+> c14-)

91)

##It

of the interactive

mode

of the MVIB arrows.

system.

The user’s input data

are

indicated

with

HIROATSUMATSUURA

66

---- 1381,1309,1204,1131,1096,1040,958, ---- 902,443.418,205 ,,,,, 1460,1454,1284, ---- 1249,1174,11SO,902,7S6,223(O.S), ---- 223(0.5),,; NAME SAME-TG OBSW ,,,,,,,,,,1486(0),1475(0),1469(0), ---- 1465(0),1460(0),1454(0),1439(0), ---- 1389(0),1376,1343,1284(0),1249(0), ---- 1204,1163,1141,1116,1096(0),1050, ---- 933,911,876,7S6(O),SO5,3S8,312,, ---- 19s,,; ITER NCYCLE = 3 FCON 223 4,223 5,223 6,0132S With this data set, the force constants 223A4, 22385, 223A6 and 0132s are adjusted through three cycles of iterative least-squares calculations by utilizing the observed i.r. and Raman wavenumbers for CH30CH,CH, (trans form) and CH,O(CH,)&H, (~rans-trans and trans-gauche forms). DISCUSSION The MVIB system has been utilized, at an early stage, for a systematic investigation of vibrational spectra and rotational isomerism of chain molecules including alkanes, alkyl ethers, alkyl sulfides and halogenoalkanes (Matsuura & Tasumi, 1983, and references cited therein). Compiled tables of the calculated results for a total of 203 conformers of these molecules have been published as standard reference data (Shimanouchi et al., 1978; Shimanouchi et al., 1980). Systematic vibrational studies of alkylsilanes, alkyl selenides, alkyl ketones and alkyl esters have also been made using the MVIB system (Matsuura & Tasumi, 1983, and references cited therein). Based on these studies a reliable data base of force constants has been accumulated for fundamental organic chain molecules (Matsuura & Tasumi, 1983; Shimanouchi et al., 1978; Shimanouchi ef al., 1980). This system of programs has also been successfully applied in a recent study of chain conformations of poly(oxyethylene) (-OCH,CH,-), , in which more than 200 conformers of CH,(OCH,CH,),OCH, (n = 2, 3 and 6) were examined systematically (Matsuura & Fukuhara, 1986). In addition

to applications

to specific

research

as

mentioned above, the MVIB system may also be used conveniently for estimating vibrational wavenumbers and modes of molecules whose spectra are experimentaIly unavailable or for assigning observed vibrational spectra of novel molecules. The highly simplified input format is perhaps the most remarkable feature of this system. Moreover, the automatic data preparation by the preprocessing program guarantees that input data for the main program are free from errors.

This

convenience

is particularly

relevant

to

large molecules of, say, 20 atoms or more, for which the data necessary would be voluminous and the data check accordingly time-consuming. The advantage of

the MVIB system mentioned above over the conventional programs is that it becomes possible for nonspecialists in vibrational spectroscopy and even casual users to calculate vibrational properties of molecules without knowledge of normal coordinate analysis. In the MVIB system, the force field employed is exclusively GCFF. The intragroup force constants are explicitly defined for individual atomic groups and the intergroup force constants for interacting atomic groups. Once the force constants associated with the respective atomic groups are determined, they are directly applicable to the corresponding atomic groups in other molecules. The symbol representation of the force constants is particularly useful for the data management in this system. Thus, for a molecule of 19321 (or CH,COOCH,CH,), for example, the system retrieves from the data files the intragroup force constants 019A-, 193A-, 932A-, 321A- and 21OA-, and the intergroup force constants 0193-, 1932-, 9321- and 321&, where - implies coordinate(s). The adoption of GCFF in this system is found to be effectual. The atomic groups that the MVIB system deals with are now limited to those given in Table 1. Introduction of further groups is desired in order for the system to be more comprehensive. MVIB is still under continuous development and more sophisticated algorithms are being considered. The program is available from the author upon request, and a revised version is now in preparation for Quantum Chemistry Program Exchange, Depart-

ment of Chemistry, Indiana ton, IN 47405, U.S.A.

University,

Blooming-

Acknowledgements-I wish to dedicate this naver to the late Professor Takehiko Shimanouchi, who suggested an original idea of the MVIB system in 1973. I thank Dr Shirley S. Hui, Miss Norika Nagaoka and Mr Tetsuya Sato far their assistance in coding the program. My thanks also extend to many people who have provided many valuable suggestions throughout the development of this system.

REFERENCES IUPAC (1978) Definition and symbolism of molecular force

constants. Pure Appl. Chem. SO, 1707. IUPAC (1985) Test data for normal coordinate calculations. Pure Appl. Chem. 57, 121. Matsuura H. & Fukuhara K. (1986) J. Polymer Sci., Part B, Pofymer. Phys. t4. L383. Matsuura H. & Tasumi M. (1983) In Vibrational Specrru and Srructure (Edited by Durig J. R.), Vol. 12. Chap. 2, pp. 69-143. Eisevier, Amsterdim. Painter P. C., Coleman M. M. & Koenig J. L. (1982) The Theory of Vibrational Spectroscopy and Its Application fo Polymeric Materials. Wiley, New York. Schachtschneider J. H. (1966) Technical Rept No. 5745, Shell Development Co. Shimanouchi T. (1968) Computer Programs for Normal Coordinate Treatmenf of Polyaromic Molecules. University of Tokyo. Shimanouchi T. (1970) In Physics! Chemti!ry, An Advanced Treatise (Edited by Eyring H., Henderson D. & Jost W.),

MVIB Vol. IV, Chap. 6, pp. 233-306. Academic Press, New York. Shimadouchi T. 119771 I%rurion Soectroscopv and Its Chemical App1ichtion.k University o?’ Tokyo.- _ Shimadouchi T., Matsuura H., Ogawa Y. & Harada I. (1978) .J. Phys. Chem. Ref: Data?, 1323. Shimatjouchi T., Matsuura H., Ogawa Y. & Harada I. (l98@, . , J. Phvs. Chew. Ref. Dora 9. 1149. Wilson E. B. Jr, Decius J. C.“& Cross k. C. (1955) Molecular Vibrarions, The Theory of Infrared and Ramm Vibrational Specfru. McGraw-Hill, New York.

APPENDIX The data labels which are applied in the batch input mode are described below. MESG-Messaee mode. D = detailed, S = simplified, L = data labels. CALC-Calculation mode. V = vibrational analysis, F = force constant determination. LEVL-Data processing level 0, 1, 2, 3. Transfers/ changes/additions of force constants, structural parameters etc. are possible in accordance with the level. NAME-Molecular name and conformation e.g. # CH30CH2CH2CL TRANS13225-TG, GAUCHE.

67 TANG-Torsion angles of molecular skeleton. If not specified, f60” is assumed for gauche* and 180” for zrults. APRO-Approximate calculation by assumed/ transferred force constants to be made or not, in case that no immediate force constants are available in the files. REPL-Replacing force constants. FDAT-Force constant data to be added/changed e.g. 22609 2.590, 323A5 = 223A5. STRC-Structural parameters to be added/changed e.g. L12 1.54, Al41 98.9. MASS-Atomic masses to be changed. DATA-Ootional outuut data (suuulementarv results) e.g. FORCE; ATOM, ‘G; *Z, PED, -ALL, N; SAME. PAX =Y, PLN= N, HOUS =Y, DUMP-Y. ITER-Information of iterative calculation to determine force constants e.g. NCYCLE = 3, SKIP=Y. P=N. FCON-Force constants to be determined e.g. 225A4, 222446G. OBSW-Observed wavenumbers (with their weights) e.g. 1492.5, 992(0.2).

Note: ITER, FCON and OBSW are applicable only in the case of CALC = F (force constant determination). For full details of the input data, see the Manual.