Trends in the Reactivity of Pentacyclic Ether Derivatives on Silicon and Germanium Surfaces Revealed by Energy Decomposition Analysis for Extended Systems

Graphical Abstract

In this study, the S_N2 like ring opening reaction of pentacyclic ether derivatives with the heteroatoms O, S, Se, and Te on silicon and germanium (001) surfaces are investigated. The periodic trends for variation in group 14 elements of adsorbate and surface are analyzed using energy decomposition analysis for extended systems (pEDA) on the reaction path to enhance our understanding of surface chemistry and semiconductor functionalization.

Abstract

We analyze the adsorption and ring-opening reaction of pentacyclic chalcogen alkyls with chalcogen atoms ranging from oxygen to tellurium using computational analysis. Thus extends our previous investigation of THF on silicon towards germanium surface and towards the heavier chalcogen homologues. We found an increasing dative bond strength of the precursor state with the period of the chalcogen atom on both surfaces. Using energy decomposition analysis for extended systems (pEDA), differences in the trends between silicon and germanium were revealed. Following the dative bound state, subsequent ring-opening reactions were found to proceed via a nucleophilic back-side attack, similar to a molecular S_N2 reaction. Reaction energies and barrier heights show a maximum for the sulfur derivative. This trend was found to correlate with the position of the transition state in the reaction and agrees with the molecular reactivity. The uniquely low barrier of THF can be attributed to its ring strain. Our findings shed light on the fundamental aspects of surface chemistry and the benefits of using quantitative bonding analysis in this field. It also paves the way for future explorations into the functionalization of semiconductor surfaces using higher-period ether derivatives.

1 Introduction

Organic functionalization has emerged as a promising way of tailoring surface properties of semiconductors to fit a wide range of applications.^{1, 2} The approach leverages the ability of organic molecules to react with semiconductor surfaces, thereby altering the physical, chemical, and electronic characteristics in a controlled way. This allows for significant advancements in many research fields, including the development of biosensors,^3-5 the improvement of battery electrodes,⁶ the efficient manufacturing of microelectronics,⁷ and the development of organic light-emitting diodes.⁸ Silicon and germanium are the most important semiconductor materials here due to their widespread application and significant role in microelectronics manufacturing. Silicon has been the backbone of the semiconductor industry due to its abundance and well-established purification methods.^{9, 10} Its unparalleled role in the development of integrated circuits is well documented, making it a prime candidate for surface functionalization aimed at further enhancing its electronic and chemical properties and thereby broadening its range of applications. Similarly, while less ubiquitous than silicon, germanium plays a crucial role in optical applications and solar cells.¹¹ Both semiconductors show a diamond crystal structure^{12, 13} and buckled dimers formed during the reconstruction of their most relevant (001) surface.^{11, 14}

These buckled dimers lead to a rich surface reactivity especially towards organic molecules since electrophilic, nucleophilic and cycloaddition reactions are possible.^15-20 In an investigation of tetrahydrofuran (THF) on silicon, the ether ring is cleaved by the surface which unexpectedly happened in a regioselective fashion.^21-23 It was found that the reaction proceeds via a datively bonded intermediate (A). In a subsequent ring opening step, the X−C₁ bond is cleaved by a nucleophilic attack of a neighboring Si_up atom (Scheme 1).²⁴ This reaction step shows a sizeable energy barrier, indicating kinetic reaction control. The ring opening reaction of THF has been extensively analyzed on both silicon and germanium surfaces.^{24, 25} Later investigations of tetrahydrothiophene (THT) on germanium revealed significantly deviating reaction barriers and energies, indicating interesting trends.²⁶ Reports on the intrinsic barrier of heteroatom alkyls revealed interesting trends for chalcogen atoms.^{27, 28} Further it was found that the many properties of chalcogen alkyls vary with system parameters such as solvents.²⁹

Scheme 1

Two-step reaction of cyclic ether derivatives with heteroatoms X with a silicon surface. (A) Dative bonding of the ether onto partially positively charged Si_down atom. (B) Nucleophilic attack of partially negatively charged Si_up atom on the C₁ carbon atom. a) Schematic reaction mechanism with reaction energy (ΔE_R) and reaction barrier (ΔE^≠). The notation corresponds to the steps shown in b). A comparable reaction mechanism is found on germanium.

The question thus arises if the intriguing reactivity of ethers shows periodic trends with changing the chalcogen atom and if this trend is different for silicon and germanium. These systematic investigations on periodic trends are standard in molecular chemistry but are rarely done in surface chemistry³⁰ due to the challenges accompanied. We show that quantitative electronic structure analysis with an energy decomposition analysis method using periodic boundary conditions (pEDA) can be used to quantify these trends and provide insights comparable to molecular chemistry endeavors.

We thus analyzed the adsorption and ring-opening reaction of cyclic ether derivatives THF, tetrahydrothiophene (THT), tetrahydroselenophene (THSe), and tetrahydrotellurophene (THTe) on both silicon and germanium (001) surfaces using density functional theory (DFT) calculations.

Methods

Computational Details

Computational investigations were conducted using the Perdew-Burke-Ernzerhof exchange-correlation functional (PBE)³¹ with DFT−D4 dispersion correction^32-34 in periodic boundary conditions. The sampling of the Brillouin zone was executed through a Γ-centered (3×3×1) Monkhorst-Pack grid. The Vienna Ab Initio Simulation Package (VASP 6.4.2)^35-38 is used, incorporating the Projector Augmented-Wave (PAW) formalism.^{39, 40} Calculations for structures and energies were performed with a kinetic energy cutoff of 450 eV. Energies were converged to 10⁻⁶ eV and geometries to a force of 10⁻² eV Å⁻¹. The electronic and geometric convergence criteria for transition state structures were tightened to 10⁻⁷ eV and 10⁻³ eV Å⁻¹, respectively. The transition state structures were obtained using the dimer approach^41-44 based on initial structures determined using the climbing-image nudged elastic band method (CI-NEB).^45-47

To compare the location of the transition state between different heteroatoms, we define a reaction coordinate x as the relative X–C₁ distance d (Scheme 1) between the precursor structure d_pre and the ring-opening product d_prod.

$$ (1)

According to this definition of the reaction coordinate, the precursor of each reaction (Structure A in Scheme 1) is assigned a reaction coordinate of x=0, while the ring-opening product (Structure B in Scheme 1) is assigned x=1. The location of the transition state is denoted as x_TS=x (d_TS). Harmonic vibrational frequencies used for the characterization of stationary points on the PES were calculated using an electronic convergence criterion of 10⁻⁷ eV. Tracing reaction pathways was accomplished via intrinsic reaction coordinate (IRC) calculations, also confirming the nature of the transition states.⁴⁸ For the calculation of the ring strain of the carbon backbone E_RS, the energy difference between the fully relaxed butane chain E_chain and a calculation with constrained C₁ and C₄ carbon atoms is considered E_Ring.

$$ (2)

Using these ring strain energies E_RS, reaction energies ΔE can be adjusted for the effect of the ring strain by subtracting the difference in ring strain energy to calculate the strain-adjusted reaction energy ΔE_RS.

$$ (3)

The iterative Hirshfeld (Hirshfeld-I) method⁴⁹ was used to calculate atomic partial charges. Energy decomposition analysis for extended systems (pEDA)⁵⁰ and natural orbitals for chemical valence (NOCV) calculations were performed in AMS2023.101^{12, 13} using the TZ2P basis set⁵¹ with a large frozen core approximation, and a 3×3 k-grid. Scalar relativistic effects were considered via the ZORA approximation. The electronic density was converged to $$ while energies were converged to 3⋅10⁻⁴ eV.

The pEDA splits the bonding energy into a preparation energy ΔE_prep and an interaction energy ΔE_int term. Contributions to the preparation energy can be assigned to either the molecule ΔE_prep(mol) or the surface ΔE_prep(surf).

$$ (4)

$$ (5)

The interaction energy is further decomposed into the dispersion interaction from the DFT−D4 contribution ΔE_int(disp) and the electronic interaction ΔE_int(elec), consisting of electrostatic interaction ΔE_elstat, Pauli repulsion ΔE_Pauli, and orbital interaction ΔE_orb. More details on the method are found in the literature.⁵⁰

$$ (6)

$$ (7)

To decompose the activation barrier, respective activation energy decomposition terms are defined as the difference between these terms at the transition state and the precursor structure.

The NOCV method is used to decompose the orbital interaction energy term further.⁵⁰ This results in charge transfer channels with pairwise eigenvalues±ν which can be visualized using deformation densities Δρ.

$$ (8)

$$ (9)

For NOCV calculations, the Brillouin zone was sampled at the Γ-point only. The silicon and germanium surface models were adapted from our previous work.^{24, 25} They consist of a frozen double-layer model of a 4×4×6 supercell representing the c(4x2) surface reconstruction saturated with hydrogen atoms and separated by a vacuum layer 19.0 Å and 21.7 Å for silicon and germanium surfaces, respectively. All 3D-structures and densities have been visualized with Blender using the “import ASE” addon.⁵²

2 Results and Discussion

2.1 Precursor Structures

Previous research on ring-opening reactions on THF showed that the reaction proceeds via a precursor state.^{23, 25, 26} This structure is formed by a dative bond between the partially negatively charged heteroatom of the ether derivative and the partially positively charged Si_down/Ge_down atom on the surface (Scheme 1, A). To investigate trends in the dative bonding, precursor structures ranging from THF–THTe were analyzed using pEDA on silicon (Table 1) and germanium (Table 2) (001)c(4x2) surfaces.

Table 1. Comparison of pEDA data for precursor structures of ether derivatives on silicon (001).^[a]

Adsorbate	THF		THT		THSe		THTe
▵Eint	−152		−177		−183		−198
▵Eint(disp)^[b]	−42	(28 %)	−51	(29 %)	−54	(29 %)	−60	(30 %)
▵Eint(elec)^[b]	−110	(72 %)	−127	(71 %)	−129	(71 %)	−138	(70 %)
▵EPauli	602		565		540		557
▵Eelstat^[c]	−383	(54 %)	−341	(49 %)	−331	(49 %)	−341	(49 %)
▵Eorb^[c]	−329	(46 %)	−350	(51 %)	−338	(51 %)	−354	(51 %)
▵Eprep	28		24		23		24
▵Eprep(mol)	9		3		2		2
▵Eprep(surf)	20		21		20		22
▵Ebond^[d]	−123	(−121)	−153	(−149)	−161	(−155)	−196	(−169)
ρmol^[e]	0.22		0.35		0.40		0.49
αmol^[f]	77		46		43		40
dSi-X^[g]	1.92		2.35		2.48		2.65

• [a] All values in kJ/mol, calculated at PBE−D4/TZ2P level. Fragmentation: Molecule and surface in singlet states. [b] Relative contributions of dispersion and electronic effects to ▵E_int in parenthesis. [c] Relative contributions to the attractive pEDA terms ▵E_elstat+▵E_orb in parenthesis. [d] Values calculated using the PAW formalism at PBE−D4/450 eV level in parenthesis. [e] Sum of partial charges for atoms of the ether derivatives, calculated using the iterative Hirshfeld method. [f] Angle between the molecular plane (C₁−X−C₄−plane, Figure 2) and the surface. [g] Distance between the Si_down and the heteroatom X in Å.

Table 2. Comparison of pEDA data for precursor structures of ether derivatives on germanium (001).^[a]

Adsorbate	THF		THT		THSe		THTe
▵Eint	−103		−138		−148		−164
▵Eint(disp)^[b]	−44	(43 %)	−50	(36 %)	−54	(36 %)	−59	(36 %)
▵Eint(elec)^[b]	−59	(57 %)	−88	(64 %)	−94	(64 %)	−105	(64 %)
▵EPauli	283		414		423		473
▵Eelstat^[c]	−192	(56 %)	−261	(52 %)	−271	(52 %)	−304	(53 %)
▵Eorb^[c]	−150	(44 %)	−241	(48 %)	−246	(48 %)	−274	(47 %)
▵Eprep	9		14		15		13
▵Eprep(mol)	4		1		1		1
▵Eprep(surf)	5		13		13		13
▵Ebond^[d]	−99	(−92)	−124	(−124)	−133	(−133)	−163	(−148)
ρmol^[e]	0.11		0.30		0.35		0.44
αmol^[f]	69		52		49		46
dBond^[g]	2.20		2.49		2.60		2.74

• [a] All values in kJ/mol, calculated at PBE−D4/TZ2P level. Fragmentation: Molecule and surface in singlet states [b] Relative contributions of dispersion and electronic effects to ▵E_int in parenthesis. [c] Relative contributions to the attractive pEDA terms ▵E_elstat+▵E_orb in parenthesis. [d] Values calculated using the PAW formalism at PBE−D4/450 eV level in parenthesis. [e] Sum of partial charges for atoms of the ether derivatives, calculated using the iterative Hirshfeld method. [f] Angle between the molecular plane (C₁−X−C₄−plane, Figure 2) and the surface. [g] Distance between the Ge_down and the heteroatom X in Å.

Analysis of the dative bond in the precursor state revealed a strengthening of the bond with the period of the chalcogen atom. On silicon, the bond energy gets stronger by 48 kJ/mol going from THF (ΔE_bond=−121 kJ/mol) to its tellurium-based derivative (ΔE_bond=−169 kJ/mol). Similarly, a strengthening of 71 kJ/mol was found on germanium. Furthermore, the bond strength towards silicon is consistently stronger than toward germanium. With increasing period, the difference in bond energy ΔE_bond between the two surfaces decreases from 28 kJ/mol for THF to 21 kJ/mol for THTe (Figure 1), which follows the trend of decreasing differences in bond dissociation energies of Si/Ge – chalcogen bonds.⁵³

Figure 1

Adsorption energy for precursor structures of THF derivatives with heteroatom X=O, S, Se, Te on both silicon and germanium surfaces.

As expected for datively bonded species, the preparation energy ΔE_prep – which quantifies the distortion of the molecule and surface towards the bonding configuration – contributes only marginally to the overall bonding energy which is dominated by the interaction energy ΔE_int. For all investigated systems, the electronic interaction energy ΔE_int(elec) is stronger than the dispersion energy ΔE_int(disp), which allows for classification as a chemisorbed state.⁵⁴ Both terms’ ratios remain relatively constant on a given surface with slight deviations for THF on germanium (lesser interaction energy). The contribution of electronic interaction ΔE_int(elec) to the overall interaction energy ΔE_int was found to be higher on silicon, at 71 %, compared to the 62 % found on germanium. With identical dispersion energies on both surfaces, this indicates that the increased adsorption energy on silicon results solely from a more substantial electronic interaction energy on silicon. This agrees with the generally higher bond dissociation energy of chalcogen elements on silicon.⁵³

To understand the increase in interaction energy ΔE_int with the period of X, it is further decomposed into Pauli repulsion ΔE_Pauli, electrostatic interaction ΔE_elstat, and orbital interaction energy ΔE_orb. Figures 2 (Si) and 6 (Ge) show the trends in these terms along with the interaction energy ΔE_int, preparation energy ΔE_prep and bonding energy ΔE_bond relative to the values found for THF. On silicon, we find a general decrease in Pauli repulsion due to the increasing bond length between the molecule and the surface. Interestingly, the electrostatic contribution becomes less stabilizing even though the partial charge of the molecule increases from 0.22 e to 0.49 e. The contribution of the orbital interaction to the overall bonding energy increases slightly. Values for the tellurium-based derivative were found to show a slight decrease in electrostatic interaction energy ΔE_elstat and an increase in Pauli repulsion ΔE_Pauli. This is likely due to a larger basis set super position error for this calculation, indicated by the difference between PAW and STO bond energies (Table S2).

Figure 2

Silicon: Trends in selected pEDA terms‘ for THF derivatives with heteroatoms X=O, S, Se, Te in the precursor state w.r.t. the THF structure. Si_down−X distance d and Si_down−X−C₁ angle α shown below.

Further decomposition of the orbital interaction term with help of the NOCV analysis revealed one dominating deformation density which is shown in Figure 3 (Si) and Figure 4 (Ge). The deformation density shows the charge transfer from the heteroatom of the ether to the Si_down atom, which increases with the period in magnitude (eigenvalue ν) and energy contribution (ΔE). While the deformation densities for S, Se, and Te derivatives match the shape of the highest occupied molecular orbital (HOMO) of the ether molecule (out-of-plane π-orbital), the deformation density for THF shows a significant contribution of the HOMO-1 (in-plane π-orbital). A possible reason for this trend is the increasing localization of the out-of-plane π-orbital on the heteroatom, as shown in Figure 5. This leads to a stronger tilting of the heavier homologues with respect to THF which can be understood – in a valence-bond type interpretation of the Kohn-Sham orbital picture – as donation from the in-plane lone pair for THF, while the out-of-plane lone pair is active for X=S, Se, Te (see Figure 7).

Figure 3

Silicon: Precursor structure on silicon: 1^st deformation densities of a) THF, b) THT, c) THSe, and d) THTe. Eigenvalue ν and contribution to the orbital energy ΔE/kJ mol⁻¹ shown. Iso value=0.03 e⁻/ų.

Figure 4

Germanium: Precursor structure on silicon: 1^st deformation densities of a) THF, b) THT, c) THSe, and d) THTe. Eigenvalue ν and contribution to the orbital energy ΔE/kJ mol⁻¹ shown. Iso value=0.03 e⁻/ų.

Figure 5

Representation of the out-of-plane π-orbital (HOMO) and the in-plane π-orbital (HOMO-1) of a) THF, b) THT, c) THSe, and d) THTe. Iso value=0.05 e⁻/ų.

On germanium (Figure 6), some of these trends are inverted. While the electronic interaction energy remains decreasing with the period, the decrease can now be attributed to stronger electrostatic and orbital interactions. Also, the Pauli repulsion was found to increase with the period, which is likely due to the more diffuse electron density of higher period heteroatoms. The difference in trends between the two surfaces can likely be found in the Ge−X bond distance which is between 0.10 Å (THTe) and 0.32 Å (THF) longer compared to the respective silicon bonds.

Figure 6

Germanium: Trends in selected pEDA terms for ether derivatives with heteroatoms X in the precursor state w.r.t. the THF structure. Ge_down−X distance d and Ge_down−X−C₁ angle α shown below.

The stronger dispersion interactions for higher period heteroatoms can be attributed to two effects. First, the dispersion interaction is expected to increase due to the increased polarizability of higher period heteroatoms, which is considered in the pairwise dipole-dipole coefficients of the D4 dispersion correction used for the calculation.³² Second, the decreasing contribution of the in-plane π-orbital to the dative bond results in a lower angle between the molecule and the surface (Figure 7), decreasing from 76° for THF on silicon to 42° for THTe. On germanium (Figure 8), a similar decrease from 69° to 46° is observed. This causes increased dispersion interaction between the carbon backbone and the surface atoms. Both effects occur for silicon and germanium surfaces, explaining the similar dispersion energies on both surfaces.

Figure 7

Silicon: Precursor structure on silicon a) THF, b) THT, c) THSe, and d) THTe with Si_down−X bond length, the angle between the surface, and the C₄−X−C₁ plane noted.

Figure 8

Germanium: Precursor structure on silicon a) THF, b) THT, c) THSe, and d) THTe with Ge_down−X bond length, the angle between the surface, and the C₄−X−C₁ plane noted.

2.2 Ring-Opening Reaction

From the outlined precursor state, the molecules can react in a ring-opening reaction. The reaction is similar in mechanism as a molecular S_N2-like reaction with a nucleophilic attack of a surface Si_up/Ge_up atom on the C₁ carbon in the α-position of the ether center.²⁴ Concurrently, the X−C₁ bond is cleaved. While there are several product structures available when considering both the (2×2) and the c(4×2) surface reconstructions, this work will focus on the most stable across-trench (AT), inter-dimer (ID) and on-top (OT) structures, shown in Figure 9.

Figure 9

Ring–opening products of THSe on silicon in the across-trench (AT), inter-dimer (ID) and (OT) reaction paths. Si_down−X, Si_down−Si_up distance and X−Si_down−Si_up angle are listed.

Reaction energies are shown in Figure 10. The OT ring opening reaction was found to be thermodynamically favored for all ether derivatives on both surfaces. AT features the least thermodynamic stability for all structures. While the energy of ID can be found between the ones of the AT and OT modes, its energy is close to AT on silicon while thermodynamically more favorable on the germanium surfaces.

Figure 10

a) Silicon, b) germanium: Reaction energy of cyclic ether derivatives with heteroatom X=O, S, Se, and Te in AT, ID, and OT relative to their respective precursor structures.

One reason for the observed trend can be attributed to the structural differences between the silicon and germanium surface: The longer dimer bonds on germanium decrease the Ge_up−Ge_down−X angle for OT and, thereby, destabilize it.

One notable difference between the two surfaces is the localization of the negative partial charge: We found that Ge_up shows a significantly lower negative charge compared to the Si_up atom (Figure 11). The negative charge is instead found at the subsurface germanium atom between the surface dimers. This difference might contribute to the generally lower adsorption energies for ring–opening products on germanium as well as the relative energy of ID, which is on average 14.8 kJ/mol lower on germanium relative to AT compared to products on silicon.

Figure 11

Partial charges of surface atoms in the silicon (001) and germanium (001) surfaces.

Looking at the trends with increasing period of the heteroatom X on silicon, we found that the THF based structures deviate significantly from structures with higher period heteroatoms. Between the sulfur and the tellurium-based derivatives the reaction energies ΔE_R remain largely constant at ΔE_R=−76 kJ/mol, −92 kJ/mol, and −120 kJ/mol for AT, ID, and OT, respectively. The ring opening reaction of THF was found to be between 74 kJ/mol (ID) and 66 kJ/mol (OT) more exothermic compared to THT. This agrees with experimental molecular trends for ethers and thioethers.⁵⁵

Next, we discuss how to correct the trend for the different ring strain since this is a sizeable energy contribution which distorts the trend in electronic effects (259 kJ/mol are reported for a five-membered alkane ring).⁵⁶ The ring strain of the molecules investigated is shown in Figure 12 using the comparison with butane as outlined in the method section.

Figure 12

Ring strain of the carbon backbone in the investigated cyclic ether derivatives with heteroatoms X=O, S, Se, Te.

The ring strain decreases down the period. THF shows the highest ring strain at 92 kJ/mol, with a sharp decrease towards the sulfur derivative at 22 kJ/mol. This now allows us to adjust the energies for the difference in ring strain between the reactant molecules and the ring-opening products leading to the ring strain adjusted reaction energy ΔE_RS (Figure 13). This curve now shows a consisting decrease with the period of the chalcogen atom, indicating a consistently increasing electronic interaction after applying the correction term for the ring strain.

Figure 13

a) Silicon, b) germanium: Ring strain adjusted reaction energy of cyclic ether derivatives with heteroatom X=O, S, Se, and Te in AT, ID, and OT relative to their respective precursor structures.

For germanium, we find a similar trend with the reaction energy of the THF structures to be between 29 kJ/mol (AT) and 25 kJ/mol (OT) lower than that of THT (Figure 11b). As on silicon, the decreased reaction energy for THF can partly be attributed to ring strain, which contributes −83 kJ/mol to the reaction energy of THF in the AT path but only −13 kJ/mol for THT. Accounting for these differences, the ring strain adjusted reaction energies ΔE_RS are calculated and plotted in Figure 13. In contrast to silicon, the molecular trend of increased reaction energies for sulfur alkyls persists even when compensating for the ring strain.

In line with previously reported results of THF on silicon and THT on germanium, we found all investigated systems to be exceptions of the Bell–Evans–Polanyi principle as the thermodynamically disfavored across-trench product is kinetically favored.⁵⁷ In the following section, we will discuss the transition state of the system of THSe on silicon as an example with equivalent data and figures for the remaining seven systems listed in the supporting information.

The AT energy barrier ΔE^≠ of the ring–opening reaction of THSe on silicon was found to be significantly smaller at ΔE^≠=53 kJ/mol compared to the barriers found for the ID and OT reaction paths at 142 kJ/mol and 132 kJ/mol, respectively. This difference is a result of the transition state geometries (Figure 14): Since the ring-opening reaction requires a nucleophilic backside attack on the C₁ carbon atom, a trigonal bipyramidal structure at the C₁ carbon with a resulting X−C₁−Si_up angle of 180° represents the ideal transition state geometry.⁵⁸ In the transition state of AT (AT^≠), an X−C₁−Si_up angle of 155° is achieved, while the angles for ID^≠ and OT^≠ are significantly more acute at 83° and 76°, respectively. For OT^≠, this can be attributed to the short distances between the silicon atoms of only 2.42 Å. In comparison, the distance of the participating silicon atoms for ID^≠ is larger at 3.92 Å compared to AT^≠ at 3.57 Å. The difference in geometry is thus likely due to steric interaction with the subsurface atoms.

Figure 14

Geometries of AT^≠, ID^≠ and OT^≠ of THSe on germanium shown along noted direction. Bond distances for the X−C₁ and C₁−Si_up bonds as well as X−C₁−Si_up angle labeled.

By decomposing the energy barrier with pEDA (Figure 15), the role of the transition state geometry in the increased energy barrier for ID^≠ and OT^≠ can be shown: For all transition states, dispersion interaction contributes only marginally to the energy barrier (−7 to 8 kJ/mol). The electronic interaction energy ΔE_int(elec) contributes significantly more to the barrier, but its contribution is almost constant across all reaction paths with ΔE_int(elec)=−38 kJ/mol, −56 kJ/mol, and −55 kJ/mol, respectively. The main difference stems from the THSe molecule's preparation energy ΔE_prep(mol), which is >80 kJ/mol lower for AT^≠. The preparation energy describes the energy required for the deformation of the relaxed geometry of the molecule to its fragment geometry. Thus, this energy correlates with the breakage of the Se−C₁ bond, which is elongated by 0.29 and 0.25 Å for ID^≠ and OT^≠ respectively compared to AT^≠.

Figure 15

pEDA of the activation energy for the ring-opening reactions of THSe on silicon at the transition state AT^≠, ID^≠, and OT^≠.

Broadening our view towards the trends of other ether derivatives, we found only a small dependence of the energy barriers on the chalcogen atom in the ether derivative. For THF (Figure 16a), ID^≠ and OT^≠ are more favorable with barrier heights of 100 kJ/mol and 117 kJ/mol, respectively compared to their sulfur derived counterparts at 150 kJ/mol and 145 kJ/mol. The barrier of the across-trench path increases by 24 kJ/mol going from THF to THT.

Figure 16

Energy barriers between the ring opening products and their respective precursor structures for the cyclic ether derivatives THF, THT, THSe, and THTe on a) a silicon surface and b) a germanium surface.

Comparable to the reaction products, the favoring of THF can be attributed to the decrease in ring strain, which contributes −60 kJ/mol to the AT^≠ barrier for THF but only −18 kJ/mol for THT.

From THT onward, a slight decrease in barrier heights is observed. On germanium (Figure 16b), the activation energies follow a similar trend with a maximum barrier height for the sulfur-based derivative. Comparable to the reaction energies, this trend can be interpreted using the ring strain energies: For THF, the ring strain contribution for AT^≠ on silicon was determined at −60 kJ/mol, while the contribution for the sulfur derivative significantly lower at only −18 kJ/mol.

This trend in activation energies for the AT ring-opening reaction was found to correlate with the location of the transition state on the reaction path x_TS: When comparing the location of the transition state x_TS (Figure 17) on silicon, we find the transition state for THF 11 % earlier than its respective sulfur-based reaction, which shows its transition state latest. For the selenium-based structure the transition state occurs slightly earlier in the reaction, correlating with the slightly reduced activation barrier, while the tellurium-based derivative shows a later transition state that does not agree with the reaction barrier. On germanium comparable trends can be found: The transition state for the THF ring-opening occurs 8 % earlier than for THT, which shows the latest transition state at x_TS=0.39. From THT onwards, transition states occur earlier, matching the trend of the reaction barriers. In general, the transition states occur earlier on silicon, because of the generally shorter distance between the silicon atoms (5.35 Å vs 5.60 Å on germanium).

Figure 17

Location of AT^≠ in the ring-opening reaction of THF derivatives with heteroatoms X=O, S, Se, and Te.

Looking further at the geometries (Figure 18) of the AT^≠ transition states, we found the X−C₁−Si_up angle, required for the backside attack, to stay relatively constant for different chalcogen atoms. On silicon, it ranges from 154° (THTe)–157° (THF) and 156° (THTe)–159° (THF) on germanium. This is achieved by an increasing tilt of the molecule towards the surface which compensates for the longer Si/Ge−X and X−C bonds. Another effect of the longer and weaker bonds with the heteroatom are the generally shorter bond distances of the C₁−Si_up and C₁−Ge_up bonds on both surfaces.

Figure 18

Geometries of AT^≠ for the cyclic ether derivatives THF, THT, THSe, and THTe (from left to right) on silicon (top) and germanium (bottom) surfaces. Bond length of the X−C₁ and C₁−Si_up bonds as well as X−C₁−Si_up angle shown respectively.

The lower bond energies with higher period chalcogens becomes apparent in the activation energy decomposition (Figure 19) as well: Since we could show that the preparation energy of the molecule is dominated by the energy required for the X−C bond breaking, it is only reasonable that the activation preparation energy ΔΔE^≠_prep decreases with the period as this bond is weakened. While the tilt of the molecule increases, the activation dispersion energy ΔΔE^≠_disp is not affected, since there is no significant change in tilt from the respective precursor states. Instead, an increase in activation interaction energy ΔΔE^≠_int is observed because of increasing electronic interaction. The activation interaction energy ΔΔE^≠_int was found to decrease with the period of X, even though the length of the newly formed C₁−Si_up/Ge_up bond shortens. Likewise, the electrostatic interaction shows an increasing trend. The Pauli repulsion, on the other hand, was found to strongly decrease with the period of the chalcogen, which is due to the larger distances of the molecule and the surface and the resulting lower steric repulsion.

Figure 19

Trends in selected activation energy pEDA terms heteroatoms X=O, S, Se, and Te for AT^≠ relative to THF for a) silicon and b) germanium. X−C₁ distance d and the nucleophilic attack angle (X−C₁−Si_up) α shown below. Raw values listed in Tables S2 and S5 in the supporting information.

The orbital interaction energy can be further decomposed using the NOCV method. This results in two significant NOCVs which can be classified according to their deformation density: The first NOCV corresponds to the charge transfer between the molecule and the surface, which was already observed in the precursor state, the second NOCV (Figure 20) corresponds to the S_N2 like back-side attack. Both contributions have been found for THF on Si initially.²⁴ We can match the NOCV analysis to a Kohn-Sham orbital picture as shown in Figure 21: The deformation density represents the donation of electron density from the highest occupied crystal orbital (HOCO) of the fragment to the lowest unoccupied molecular orbital (LUMO) of the selenoether fragment (see Figure S2a–h for the other systems). While the orbital interaction energy ΔΔE^≠_orb and the energy contribution of this NOCV was found to decrease with the period, the transferred charge (proportional to the pairwise NOCV eigenvalue±ν) increases. This increase can be attributed to the more diffuse electron density at the chalcogen atom, enabling more electron transfer towards it. On germanium the same trends in the eigenvalue and NOCV energy can be observed. However, an additional polarization contribution to the NOCV can be identified in the deformation densities.

Figure 20

Deformation density for the transition state of the across-trench ring–opening reaction of the cyclic ether derivatives THF, THT, THSe, and THTe on silicon and germanium surfaces. Plotted using an iso value of 0.001 e⁻/ų. [a] Contribution to the total orbital energy.

Figure 21

LUMO of the THSe fragment (orange/cyan) and HOCO of the silicon surface (blue/yellow) fragment that participate in between which charge is transferred in the NOCVs shown in Figure 19. Representation using iso=0.05 e⁻/ų.

3 Conclusions

Our computational study provides insights into cyclic ether derivatives’ adsorption and ring-opening reactions on silicon and germanium surfaces. We found that the adsorption energy of the precursor structures decreases with the period of the chalcogen atom. On all investigated systems, the on-top ring-opening reaction was thermodynamically favored across all systems, whereas the across-trench pathway was kinetically preferred due to lower preparation energies. Notably, tetrahydrofuran displayed lower reaction barriers and more exothermic reaction energies on both surfaces, underscoring its unique reactivity compared to the heavier homologues. The reaction barriers peak with tetrahydrothiophene, correlating with the transition state's location on the reaction path. The results show that simple periodic trends in the series of chalcogen elements lead to complex surface reactivity similar to molecular investigations. This work transferred the understanding of trends in molecular main-group chemistry into the territory of surface chemistry. Insights provided in this work form the basis for further research in the functionalization of semiconductor surfaces using higher-period ether derivatives and the application of bonding analysis methods to understand surface chemistry.

Acknowledgments

We thank Dr. Pascal Vermeeren (VU Amsterdam) for discussions. Computational resources were provided by URZ Leipzig, ZIH Dresden, HLR Stuttgart and CSC-LOEWE Frankfurt. Open Access funding enabled and organized by Projekt DEAL.

Conflict of Interests

The authors declare no conflict of interest.

Open Research

Data Availability Statement

All data underlying the results shown are uploaded to open access repository: 10.17172/NOMAD/2024.05.21-2.